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An analysis of the prominent translation and storage effects is considered in the presence of a wavy flow of generalized Newtonian fluid, namely Cross fluid. A class of practical applications is related to the significance of a reservoir in terms of water and other liquid materials which helps to bind the stream's natural flows. In particular, the fluid reservoir is also experiencing some natural and forced convection, which can be practically represented via the mixed convection phenomenon. However, the current assumptions for the entire study indicate the physical effects of gravity, activation energy, viscous dissipation, wavy surface amplitude, Joule heating, and vertical external magnetic field. All the results are disposed of in the form of wavy flow speed, thermal as well as concentration plots. Furthermore, the drag forces along vertical and horizontal directions, rate of heat, and mass flows are illustrated to show the surface force effect on the flow. The amplitude enhances the drag force and an opposite trend is noticed in the visualization of the rate of heat transfer. The higher Lorentz forces and Weissenberg number reduced the flow velocity of the liquid. The rate of mass transfer is escalated through larger values of Schmidt number and reduced for higher values of activation energy. The larger variation in the Richardson number escalates the flow speed of the materials. A well-matched comparison with the previous results is provided to show the validity of the method.

The industrial significance of stability analysis for dual solutions and heat transfer sets the stage for this research. Focusing on Maxwell ternary nanofluid flow, the study aims to enhance thermal conductivity and stability by delving into viscous dissipation and velocity slip effects on a stretching/shrinking sheet. Employing a mathematical model, refined with nondimensional transformations and MATLAB’s BVP4C solver, the research identifies dual solutions and examines the influence of key parameters on fluid dynamics and heat transfer. Results showcase a progressive improvement in convective heat transfer and skin friction from mono nanofluid (NF) to binary hybrid nanofluid (HNF), culminating with ternary hybrid nanofluid (THNF). These improvements are significantly associated with the suction/injection parameter (S), whereas the slip (σ) and elastic (K) parameters enhance thermal transfer but negatively affect skin friction efficiency at elevated levels. The robustness of the upper branch solutions underscores the reliability of these findings. Remarkably, at λ=−1.25 with a nanoparticle volume fraction of 0.04, ternary nanofluids achieve a 2.9% thermal efficiency leap over HNF, which itself surpasses NF by 0.46%. These findings hold potential for significant advancements in sectors such as electronics, manufacturing, energy, biomedical, environmental engineering, aerospace, and automotive, aiming at elevating thermal efficiency.

The aim of this work is to investigate the entropy generation and thermal characteristics of couple stress blood nanofluid on the peristaltic flow of gold nanoparticles being conveyed through an asymmetric channel through a porous medium. The distinctive characteristics of the nanoparticles such as their inspiring thermal conductivity make them a vital aspect of contemporary heat exchangers and nanotechnology. To create contrast-enhanced tracers intended for dynamic X-ray imaging of blood flows, gold nanoparticles have been incorporated into human red blood cells. The possibility for dynamic imaging with X-rays of blood flows provided by red blood cells in combination with gold nanoparticles has the potential to be advantageous for clinical applications. The main investigation focuses on the current situation of peristaltic motion with gyrotactic microorganisms in which the effects of Brownian motin, thermophoresis, thermal radiations, convective boundary conditions, wall slip, magnetic field, viscous dissipation and Joule heating are present. Lubrication approximations are implicit for interpreting the controlled partial differential equations. Numerical results were obtained using an effective Runge–Kutta method was developed using MATLAB software. This technique is commonly used to solve these problems since it is affordable, effective, and accurate to fourth order. Graphical interpretations are also used to calculate the effects of different physical parameters on temperature, concentration, velocity, dynamics of gyrotactic microorganisms, entropy generation, and Bejan number. Additionally, heat and mass characteristics of blood pumping were studied. According to certain results, entropy generation rises with the couple stress parameter. Furthermore, tables and bar charts are included to illustrate how certain data categories compare to earlier model-related research The findings indicated that gold nanoparticles are effective for drug transport as well as delivery systems due to their ability to control velocity using the thermophoresis and Brownian motion parameters. Gold nanoparticles additionally improve temperature dispersion, allowing it to damage cancer cells. In addition, the validity of findings is assured by reaching an agreement with earlier investigations. Flow, heat, and mass distributions are represented by streamlines, concentrations, and microorganisms. A graphical representation of the average Nusslet number and Sherwood number is also included. It is anticipated to provide a novel concept for improving the performance of controlling energy loss and improving the fluid’s thermal performance are both critical in varied engineering applications.

Recently, researchers are facing great challenges to form the homogeneous solutions of various liquids at biomedical and industrial levels. Such homogeneous solutions can be controlled through stratification phenomenon directly which is ignored by the researchers in the existing literature specifically quadratic stratification and melting heat mechanism which is valid only for higher temperature processes. Thus, to form the homogeneous and stable liquid solutions for various industrial processes, we investigate the melting heat phenomenon in quadratic stratified Jeffery Nano fluid flow deformed due to linearly stretching sheet along with stagnation point. Inclined constant magnetic field is implemented on the fluid through an arbitrary angel. Characteristics of heat and transportations are disclosed through viscous dissipation, Brownian motion and thermphoresis. Temperature and concentration of the surrounding fluids are assumed higher than the stretching surface. The resultant governing equations are reduced to ordinary differential equations through proper transformations. Convergent analytical series solutions are computed via homotopic approach. Impact of various emerging parameters on temperature, velocity and concentration fields are illustrated and discussed comprehensively. Sherwood and Nusselt numbers and drag force are scrutinized mathematically, physically and graphically. It is analyzed from the study that (i) dominant melting reduces the temperature field (ii) higher thermal and solutal stratification decay the temperature and concentration fields respectively (iii) higher thermophoresis enhances the temperature field. Further, it is concluded that stable and homogeneous solutions may be made by increasing melting and reducing stratification phenomena. This study will help us to provide actual amount of heat for heating processes in industries and biomedicine which is the basic requirement for excellent quality of products.

Maxwell-fluid represents the flow of polymers used in the food processing industry and the cooling of copper plates. Much research has focused on maxwell-fluid flows across stretched surfaces. This article takes a different approach by examining the impacts of the magnetic and electric force on such surfaces. We aim to understand the behaviour of non-Newtonian Maxwell hydromagnetic boundary layer flow when exposed to magnetic and electric fields. The novelty of this investigation is to construct a two-equation non-similar model. It aims to examine the momentum, thermal and mass transport of Maxwell fluid with suspended conducting nanoparticles, which incorporates viscous dissipation, chemical reaction, an external magnetic and electric field, Brownian motion and thermophoresis. Moreover, the rheological behaviours of the nanofluids are significant in defining them for convective heat transfer. The partial differential equations describe the problem, and after applying suitable transformations, it is finally transformed into a set of non-similar, nonlinear and coupled non-dimensional ordinary differential equations. To get results, the bvp4c method built within MATLAB is utilized. An analysis of pertinent parameters affecting non-Newtonian fluids and the nanophase of fluids is shown in this study. Findings show that as the strength of the inclination angle decreases, the velocity profile becomes more pronounced. The temperature field improves as the heat generation parameter rises. The dimensionless concentration tends to decrease with Brownian motion. Its potential applications include medical sciences, microelectronics, biomedicine and various industrial processes.

Ternary nanomaterials are now recognized as useful not only for thermal efficiency importance but also to enhance physical characteristics of liquids. Insertion of three nanoparticles in base liquid is characterized as ternary hybrid nanomaterial. Such materials have better magnet properties, electrical conducting and mechanical resistance. Here we discuss three-dimensional magnetized stretched flow of ternary nanofluid through porous space is addressed. Porous space is scrutinized by Darcy-Forchheimer relation. Convective condition is imposed. Nanoparticles here include copper, polyphenol coated and aluminum oxide and water as conventional liquid. Energy equation consists of radiation, magnetohydrodynamics, dissipation and heat generation. Resulting dimensionless system is computed by Newton built in-shooting technique. Outcomes of velocity, temperature, skin friction and Nusselt number for emerging parameters of interest are organized. Comparison of results for ternary nanofluid (CoFe2O3+Cu+Al2O3/H2O), hybrid (CoFe2O3+Cu/H2O) and nanofluid (CoFe2O3/H2O) is examined. It is found that temperature and velocity against Hartman number have reverse trends. Temperature and Nusselt number for radiation have increasing features. Similar characteristics for temperature through heat generation and Eckert number is noticed. Larger thermal Biot number corresponds to rise the Nusselt number and temperature. An increase in temperature through Forchheimer number is witnessed while reverse trend holds for velocity.

A mixed convective driven wavy motion of the pseudo-plastic materials is very significant in different practical fields, like the production of paints and ketchup, etc. Blood flow through wavy vessels is another very practical aspect of this study. Energy conversion processes and effective resource use are one of the burning and hot topics when studying heat flow rate through materials. Main theme of this work is to optimize the heat energy conversion by introducing irreversible viscous dissipation and thermally radiative factors. In particular cases, the heat flow rate needs to be enhanced for low energy consumption. This is why, in such cases, the wavy surface flows are preferred by plane surfaces. The proposed problem is presented with highly non-linear mathematical equations. Some assumptions and variables address the mathematical equations in easily solvable forms. The findings are shown regarding the material's velocity, concentration, temperature, resistive forces, and heat-mass flow rates. A remarkable reduction in liquid velocity and enhancement in concentration and temperature is observed with the variation in amplitude of the wavy surface. The irreversible process is maximized due to the higher involvement of temperature ratio and thermal radiation factors, respectively. The ratio of infinite and zero shear rate viscosities reduced the concentration of the liquid. For method validation, a best-matched comparison is provided with literature.

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

This article emphasis on the impacts of Soret and viscous dissipation on Magneto Casson fluid flow past a non-linear inclined sheet in a porous Forchheimer medium with thermal radiation. In this mathematical model, the impacts of chemical reaction, heat source/sink, velocity and thermal slips are also examined. The velocity, temperature, and concentration of the inclined surface are presumed to exhibit nonlinear fluctuations with respect to distance. The partial differential equations controlling the investigation are transformed into non-dimensional ordinary differential equations that include a set of physical factors. By implementing the Keller Box approach, the resultant equations are numerically solved. As the Soret parameter rises, the concentration profile increases the coefficient of skin friction values falls and Nusselt number values rise with the Soret parameter. The temperature rises for the increasing values of Ec. Numerical data is also used to analyze the outlines in the changing rates of thermal and mass transport as well as the drag force factor. The results of the current investigation indicate that the rising magnetic and suction components have reduced fluid motion while enhancing thermal profiles. Furthermore, the suction component adversely affects both temperature and concentration gradients. In this perspective, these factors have a substantial influence on numerous engineering applications, including the nuclei of nuclear reactors, the production of polymers, metal layers, paper sheets, and the biochemistry industry. To advance and enhance the computational analysisfor this work, the computational findings are corroborated by comparing specific instances of the current research with those from previous studies, yielding strong concordance.

This research presents a statistical investigation of heat transmission in the time-reliant flow of blood-based hybrid nanofluid-containing microorganisms via a squeezing permeable channel utilizing a couple-stress non-Newtonian fluid model. Nanoparticles of SWCNT (single-wall carbon nanotubes) and MWCNT (multi-wall carbon nanotubes) are incorporated in the base liquid due to their low toxicity, special physio-chemical characteristics, and suitable surface modifications. In addition, chemical reactions, heat sources and sinks, radiation, viscous dissipation, and an external magnetic field impact the flow. The current numerical study stands out because it optimizes heat transmission rate using a face-centered central composite design framework with RSM (Response Surface Methodology) and analyses its sensitivity toward effective parameters. Examining the system's efficiency by evaluating the entropy produced in the flow process is another noteworthy part of this research. The complex system of interrelated non-linear partial differential equations is converted into a set of ordinary differential equations using suitable transformations. Later, solved via a semi-analytical technique, HAM (homotopy analysis method). According to the outcomes of the comparison, the hybrid nanofluid (blood/SWCNT-MWCNT) outperforms the nanofluid (blood/SWCNT) in terms of thermal performance. The rates of thermal energy transmission are very sensitive to the Eckert number and somewhat least affected by thermal radiation. Nanofluids and hybrid nanofluids have their heat transmission rates improved by including nanoparticles, heightened radiation, and magnetic effects. The system produces more entropy when the magnetic parameter and Eckert number are higher; however, it can be minimized by controlling the radiation effect. The results have important consequences for engineering industries, especially in the development and improvement of biomedical equipment and drug delivery systems, where accurate management heat transfer is crucial.

This research focuses on exploring the flow and temperature distribution of forced convection in a channel of horizontally placed parallel plate under the existence of a bidisperse porous medium (BDPM) emphasizing the consequences of viscous dissipation. The temperature-dependent thermal conductivity and viscosity are considered while maintaining the momentum slip and constant wall temperature at the channel walls. Analysis of the dynamics of fluid flow and the temperature distributions in both the fluid and solid phases is conducted by following the two-velocity and two-temperature models in this work. The model governing equations are non-dimensionalized following the relevant dimensionless parameters and the study calculates the temperature and velocity profiles for each phase using the Homotopy Analysis Method (HAM). The obtained temperature and velocity are discussed and explained with the help of graphs. Certain fluids exhibit varying behaviors at different temperatures. Therefore, it is crucial to consider the temperature-dependent physical properties of the fluid for specific applications. This highlights the importance of implementing temperature-dependent physical properties in the analysis. Throughout the investigation, it is discovered that the viscosity parameter has a greater influence on velocity as compared to temperature, the same for thermal conductivity on temperature. The impact of physical parameters including skin friction, volume flow rate, and Nusselt number on both plates are also examined in this study. The findings are discussed, and tables displaying numerical values for various physical characteristics are provided for both the liquid and solid phases. The results obtained were also compared with existing literature, revealing a strong alignment between them.

Electroosmosis regulated model of peristalsis with nanoparticles is significant for heat transfer efficiency regarding optimization of thermal energy process. Such investigation is useful for processes in nano-drug delivery systems, pharmacology, renewable energy, energy saving, drying, biochip fabrication, Sensing and imagining, hyperthermia, cryosurgery, oil mobility improvement, filtration and purification, drilling, cell separation and microelectro-mechanical Systems (MEMS). Therefore, mixed convective peristaltic flow of nanomaterial filling porous medium is addressed. Asymmetric flow configuration is taken. Nanomaterial comprising silver and water is considered. Thermal radiation and dissipation are invoked. Peristaltic pumping is studied under the process of electroosmosis. Electroosmosis process is modeled by Nernst-Planck and Poisson equations. Debye-Huckel assumption is used for electric potential distribution along electron double layer. Velocity slip and convective boundary constraints are considered in this analysis. Dimensionless equations are presented employing lubrication approach. Related problems have been computed numerically. Behaviors of temperature, velocity, pressure gradient and streamlines are examined graphically. Heat transfer coefficient is also studied. Result shows that temperature decreases by volume fraction of nanoparticle. Pressure gradient decays for larger porosity. Temperature reduces for larger radiation. Rate of heat transfer enhances by Grashof number whereas it reduces by volume fraction of nanoparticles.

The field of hybrid nanofluid transport through porous media holds immense promise for optimizing thermal processing and various thermodynamic applications. This study investigates the flow dynamics of a hybrid nanofluid, comprising water and a synergistic combination of single-walled and multi-walled carbon nanotubes (SWCNT-MWCNT), as it traverses a vertically stretched porous surface. The mathematical modeling of this flow scenario considers the influential factors of magnetohydrodynamics (MHD), viscous dissipation, heat sources, and ohmic heating. The Darcy–Forchheimer–Brinkman model is employed to capture the transport of fluid through the porous medium. Through the application of Local Non-Similarity (LNS) technique, the governing equations are converted into a dimensionless system and solved numerically using the robust bvp4c function in MATLAB. Interestingly, higher values of heat source parameter leads to a rising trend in the temperature profile, highlighting the intricate interplay between the thermal and fluid dynamic aspects of the system. This work provides valuable insights into the tailored design of hybrid nanofluids and porous media configurations to harness their enhanced thermal transport capabilities, with potential applications in diverse fields such as energy storage systems, heat exchangers, and thermal management devices. The findings contribute to the broader understanding of hybrid nanofluid transport in porous media and pave the way for the development of innovative thermal management solutions in a wide range of industrial and technological domains.

The viscous dissipation of Maxwell nanofluid movement on a stretching sheet is examined in the present article. Constructed the modelling equalities with assumptions and emerging parameters such as Magnetic parameters, thermophoresis, Brownian motion, and Biot number etc. Convert those equation to simple third-order ODEs by applying stream functions, MATHEMATICA software used to solve ODE by applying the RK method approach with shooting technique. Presented our outcomes graphically by incorporating the parameters. The elasticity of the Maxwell fluid is directly proportional to temperature, resulting in a reduction in its velocity. The factors that affect fluid flow include viscous dissipation, Lewis number, Brownian motion, and the reversibility of temperature and velocity. Increasing the parameters of Brownian motion leads to significant movement of the nanofluid particles, which in turn increases their kinetic energy and enhances heat generation in the boundary layer. The Lorentz force, which hinders the movement of fluid, leads to a decrease in velocity profiles. This is determined by the magnetic parameter. The heat transfer rate, the velocity decay rate, and the occurrence of viscous dissipation are all occurring in close proximity to the sheet. Also, the model tabular validation presented and current results align well with previously published studies. Cancer treatment and the cooling process in industries, polymer processing, biotechnology and medicine, food industry, cosmetics, oil and gas, textiles, aerospace and automotive, and construction are just a few of the technical and biological uses for it. Industries may enhance material performance, process efficiency, and product quality in a variety of applications by using Maxwell fluid models.

The article presents a comprehensive study that thoroughly assesses the effects of Carreau fluid flow over a curved stretch surface. The study meticulously considers various factors, including nonlinear thermal radiation, convective boundary conditions, viscous dissipation, thermophoresis, Brownian motion, and nonlinear mixed convection. By using similarity variables, the problem's governing equations are transformed from nonlinear partial differential equations to nonlinear ordinary differential equations, and then the shooting method is applied to obtain the results. The study also rigorously examines the effect of modifying flow factors on velocity, temperature, and concentration in shear-thickening situations through graphical assessment. Furthermore, according to the corresponding values, a table is provided with data on skin friction, Nusselt, and Sherwood numbers. This study offers new perspectives on the complex mechanisms of Carreau fluids flowing over curved surfaces, with potential applications in materials engineering and fluid mechanics.

Forced convection in Newtonian and non-Newtonian fluids flowing through pipes maintained at uniform heat flux or uniform wall temperature are important for understanding heat transfer characteristics in design and thermal management of heat exchangers. Convective heat transfer in both Newtonian and non-Newtonian fluids flowing through pipes and parallel plates, subjected to uniform wall heat flux condition, were extensively studied by researchers. But for uniform wall temperature, studies on non-Newtonian fluids in pipes are rarely considered. Forced convective heating and cooling of a third-grade fluid, flowing in a pipe subjected to uniform (constant) wall temperature is considered. Effect of viscous dissipation is included in the energy equation. Separate energy conservation equations for heating and cooling are formulated and their dimensionless forms are obtained. Numerical solutions by shooting technique are obtained for the governing equations. The same equations are also solved by the least square method and semi-analytical solutions are yielded. Least square method is a widely used semi-analytical tool used for solving non-linear differential equations. Results of the numerical solution and semi-analytical solutions are compared and are observed to be in close agreement. This validates the numerical solution. Few important observations are presented. For heating, when the non-Newtonian parameter increases from 0 – 0.1, the peak temperature drops from 1.15 – 0.55 which occurs at the centre. In case of cooling, when non-Newtonian parameter increases from 0 – 0.1, the difference in central line temperature and wall temperature increases to 0.17 from 0.09. For change in the non-Newtonian parameter from 0.2 – 0.3, both for heating and cooling the peak temperature change is not drastic. Heat transfer coefficient, in case of heating, differs by nearly 3.5 when the non-Newtonian parameter increases from 0 – 0.1.

The study of Bingham–Papanastasiou fluids is conducted in lid-driven cavity with consideration of viscous dissipation. The upper and left wall of the cavity is cold while other walls are insulated. Numerical simulations are conducted to study the isotherms, temperature profile, local and average Nusselt number. The main focus of work is to analyse the behaviour of heat transfer within trapezoidal cavity. The governing system of nonlinear dimensionless partial differential equations is analysed by using PDE solver of finite element method in COMSOL. The analysis is carried out for different parameters like Reynolds number, Bingham parameter, stress growth parameter, Eckert number and Prandtl number. It is observed that impact of Bingham parameter on temperature variation is negligible while the impact of stress parameter leads to the reduction in temperature within cavity. The novelty of this work is that no work is done for the case of trapezoidal cavity where Bingham–Papanastasiou fluid behaviour is observed under the consideration of viscous dissipation and mixed convection.

The global requirement for sustainable energy supply to enhance industrial productivity and reduce production costs has focused researchers’ attention to renewable energy in recent years. Solar energy mitigates the dangers connected with the use of fossil fuels in electricity generation. This work is set to evaluate the heat transmission capacities of Williamson hybrid nanofluid flow across a flat plate with viscous dissipation and heat source. The mathematical model explaining the flow interaction of Williamson hybrid nanofluid, combining viscous dissipation, heat source, and temperature-variation thermal conductivity and viscosity, is created using conservation laws. The specified system of non-linear coupled partial differential equations undergoes non-similarity transformation. The resulting non-dimensional model is solved using the bivariate spectral weighted residual method. The accuracy of the method is proven by comparing obtained results with those in the literature, and a good agreement is observed. Graphs are utilized to explain the thermophysical properties that are being considered. The results show that the fluid temperature rises when there is a source of heating and viscous dissipation. The velocity and the fluid parameter (We) have an inverse connection, whereas the temperature of the fluid has the opposite impact. Moreover, when nanoparticles are present, the thermal boundary layer rises along with the nanoparticles, thickening the velocity boundary layer and decreasing fluid velocity. Findings also show that for the Vd∈[0.1,0.5], the skin drag force and Nusselt number retard by 0.64%,14.06% for the shrinking sheet and 0.21%,6.57% for the stretching sheet respectively. In the same vein, an 100% surge in the porosity parameter escalate the skin friction coefficient by 19.13% and 26.91% and the Nusselt number by 4.92% and 2.06% respectively for both the contracting and elastic sheet. The findings in the research will provide more insight in the design and improvement of solar panel plate efficiency.

The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

This study aims to investigate the Joule effect, thermal radiation, and Coriolis effects in unsteady magnetohydrodynamics (MHD) micropolar flow over a 3-D unstable sheet. A magnetic field is typically applied to the surface; additionally, it is assumed that the fluid is conducting electricity. Other micro-rotations are also considered. The physical issue is resolved with the help of the fundamental equations, and the issue's complexity is reduced with the use of similarity variables. In the present approach, the homotopy analysis method (HAM) is employed. The heat, skin's friction factor, temperature, micro movements, and velocity associated with the emerging parameters and transfer rates are considered. The boundary layer thickness is increased as the parameter of vorticity increases. When the magnitude of the magnetic field increases, the skin friction coefficient decreases. The state variables are approximated up to six decimal places numerically. The numerical values of −f″(0) and −θ′(0) are computed to higher decimal places and compared with the available literature to validate the results. The outcomes obtained are compared with the available literature; the results here are corroborated, and the performance of the HAM is demonstrated.

This study examines the molecules motion influences and thermal attributes in power-law non-Newtonian dissipative fluids' magnetohydrodynamic behavior, Joule heating, electromigration, and Cattaneo-Christov effects. Effects of Hall on both flow velocity and temperature, as well as the heat transport are considered. The investigation looks at heat transference that occurs when there is a slippage consequence, how the temperature influences the viscosity of the fluid, and how the potential parameters influence the exponential non-Newtonian flow of fluid via an extensible sheet. Runge-Kutta-Fehlberg's approach, which is based on the shooting procedure, was used to develop computational solutions for nonlinear ordinary differential equations. When exposed to a deformation that is generated by expansion, pressure, or agitation, a dilatant fluid is characterized by a phenomenon in which its viscosity rises and may harden. This phenomenon is referred to as the dilatation phenomenon. High shearing rates provide the impression that it is stable. When expanded, subjected to pressure, or agitated, dilatant fluids become more viscous and transform into solids. Both the non-equilibrium that occurs within the fluid and the reduction of the irreversibility processes that occur within it are caused by the acquired charges that are a result of Hall effect of fluid molecules.

Owing to rapid progress in field of nanotechnology, various mathematical model has been proposed regarding the flow of nanofluids. Based on boosted thermal properties, multidisciplinary applications of such materials has been claimed in various engineering and industrial processes. In current work, a theoretical analysis is performed for bioconvective flow of Carreau fluid with applications of magnetic dipole. The significance of magnetic dipole are presented with interaction of ferrofluid. The applications of viscous dissipation have also been entertained. The flow is subject to applications of stretched surface. Similarity variables are used for making transformation to obtain set of nonlinear ODEs from set of PDEs. The numerical computation is also made by using of well-known numerical method termed as bvp4c. Influences of various non dimensional fluid parameters like Brownian motion, viscous dissipation, Curie temperature, Weissenberg number, motile difference parameter and bioconvection Paclet number are examined and expressed graphically. It is perceived that ferrofluid's concentration declines when Brownian diffusive variable is augmented while opposite characteristics are reported for Schmidt number. Current results conveying applications in the biofuels, better heat transport medium, fertilizers, catalysts, electronics, paints, semiconductors, speakers, drug delivery, fertilizers etc.

Heating profiles and reaction rates, which are crucial in the mixed convection Falkner–Skan flow of nanofluids down a wedge, are strongly influenced by the binary chemical reaction and activation energy. Slower chemical reactions caused by higher activation energy affect concentration layers and heat transmission mechanisms. Heat generation, absorption, flow, and thermal properties are all changed by binary processes. In a variety of technical and industrial applications, their combined effects are crucial in either increasing or decreasing the efficiency of heat and mass transport. The governing equations have been appropriately converted into a set of ordinary differential equations in order to handle these dynamics. The bvp4c scheme in MATLAB software has been used to solve the resulting equations. Skin friction, local Nusselt number, and velocity, temperature, and nanoparticle concentration profiles are discussed and illustrated graphically in the paper. The findings show that increasing the wedge angle parameter increases the nanofluid's velocity, whereas the Darcy number shows the opposite trend.

The current approach aims to investigate the behavior of Williamson fluid model convoyed with thermal radiation, viscous dissipation and activation energy between sinusoidal walls. The electro-osmotic phenomenon is modeled through Poisson-Boltzmann equation. Electro-osmotic fluid has many applications such as, electro-osmotic fluid pumps, liquid medicine delivery, micro-fabricated fluid devices and lab-on-a-chip devices, etc. The model is produced by using a very relatively small Reynolds number and the long-wavelength approximation. Dimensionless transformations are used to reduce the system into dimensional form. DSolve command in MATHIMATICA and perturbation approach is used to simplify the governing equations. After applying the perturbation technique, graphs are used to illustrate the physical effects of temperature, velocity, concentration, pressure gradient, and streamline distribution.

In modern days, proper waste fluid disposal is important in different industries and ecological systems. The present article aims to prevent and resolve pollution in the fluids supply. Implementing advanced treatment processes, such as filtration, sedimentation, and chemical treatment, can help in reducing the concentration of pollutants in waste discharge, and we can use Bingham fluids in industries to manage the flow of waste materials, ensuring that pollutants are contained and treated effectively before discharge. The article investigates the impact of pollutant discharge concentration on the movement of non-Newtonian Bingham hybrid nanofluids across permeable expanding surfaces, taking into account the influence of electromagnetic field, Joule heating, and chemical reaction effects. There is a lack of study on electromagnetic and Joule heating effects on chemically reactive hybrid nanofluids with energy and mass transfer, authors utilized the research gap. Heat source/sink effects were added to the temperature equation, to understand the irreversibility of processes functionality authors studied the entropy generation analysis, partial differential equations are calculated into ordinary differential solutions by similarity variables after that, they are calculated by using the shooting method. Outcomes reveal that increasing the magnetic field decreases the velocity, increasing the external source difference factor and external pollutant term increases the concentration of the fluid movement, upsurging the thermal radiation parameter upsurges the temperature and entropy generation, increasing the porosity parameter decreases the velocity of the fluid flow, increasing the Bingham parameter decreases the velocity of the fluid flow which are used in processes involving slurries, pastes, and other materials that require controlled flow under specific stress conditions.

Entropy generation optimization has significant applications in biomedical engineering, including angioplasty therapy, more rapid focused medication delivery and streamlining of medical instruments functionality. This study seeks to explore entropy generation optimization in stagnant blood flow region with tetra-hybrid nanofluid through a curved stretching surface embedded by blood tissues. Aiming to enhance heat transfer rate, SiO2+TiO2+Fe2O3+Au nanoparticles are considered with a combination of radiation effects, viscous dissipation and joule heating. Numerical solutions are obtained by Runge-Kutta-Fehlberg 5th order method with shooting strategy. Validation of code is done by comparing the current result of distinct curvature parameter values for drag force to existing studies and attaining high concordance. Numerical results in surface drag force and thermal transmission rate for unsteadiness parameter and curvature parameter are investigated. Improvement of curvature parameter enriches the blood flow's velocity and reduces the pressure distribution. Tetra-hybrid nanofluid volume fraction and platelet shape factor for nanoparticles have efficient heat transfer rate. Curvature parameter enhances the heat transfer rate by 141.4 % and minimizes the resistance of blood flow as 42.49 %. Entropy generation optimization worked well for tetra-hybrid nanofluid compared to pure blood flow, enhanced by 47.7 %. Overall results have major utilization in biomedical engineering field and medical devices optimization.

A promising material for improving heat transfer is titanium dioxide (TiO2), which has great chemical and physical stability. In numerous types of heat exchangers, including circular tubes, double tubes, and shell and tubes, TiO2 nanoparticles dispersed in ordinary fluids were widely used. The present work is to investigate the behavior of titanium dioxide TiO2- copper oxide CuO/H2O hybrid type of nanofluid flow for enhancing thermal transfer by a horizontal rotating cylinder surface under solar radiation, viscous dissipation and Lorentz forces. Here, the combinations of TiO2-CuO/H2O as hybrid nanofluids and TiO2/H2O as nanofluid are implemented. The slip and convective conditions are imposed at the surface of the rotating cylinder. The computational MATLAB software’s bvp4c solver is used to numerically integrate the resulting dimensionless equations. According to the results, higher Reynolds number values upsurge the system’s inertial force, which counteracts the force accelerating the liquid and reduces velocities as well as heat transfer. The thermal profile benefits from the nonlinear radiation and decays for growing estimations of nanoparticle volume fraction. The rate of heat transfer is higher for TiO2-CuO/H2O hybrid nanofluid as compared to TiO2/H2O nanofluid.

The rotating disk system is widely used in several important applications, including turbomachinery design, mixing and stirring processes, centrifugal blood pumps development, optimizing electronic component, cooling efficiency, and various others. Moreover, regression models offer comprehensive and reliable prediction for important parameters in flows developed by revolving disks. This article presents similarity solutions for coupled heat and mass transfer with viscous dissipation in an inelastic non-Newtonian fluid flow across a permeable revolving disk. The inclusion of diffusion terms due to Dufour and Soret effects establishes coupling between energy and concentration equations. Temperature and concentrations at disk surface are supposed to vary quadratically along the radial direction. The impacts of MHD, heat source/sink dynamics and Joule heating effects on thermal boundary layer are also scrutinized. MATLAB's bvp5c tool, based on collocation scheme, generates numerical results. Homotopy analysis method, a widely accepted analytical solution procedure, is then applied to produce the series solution. Selection of the optimal auxiliary parameter values featured in the series solution is also included. The impact of Reiner-Rivlin fluid assumption on the torque required by the disk is assessed. Furthermore, linear and quadratic regression models are developed for the skin friction factors, Nusselt number and Sherwood number.

Recent advancement in nanotechnology brings the idea of hybrid nanomaterials which offer distinguish applications in thermal reservoirs, cooling systems, energy applications, chemical engineering, vehicle engines etc. The understating of shape features for hybrid nanomaterials is quite essential as such consequences highly influenced various thermal properties like viscosity, thermal conductivity, optical properties, stability etc. The objective of current work is to examine heat transfer analysis due to thin film unsteady flow of hybrid nanofluid. The properties of hybrid nanofluid are justified for entertaining the copper (Cu), aluminium oxide (Al2O3) nanoparticles with water (H2O) base fluid. Additionally, applications of viscous dissipation, heat source and nonlinear radiated effects are attributed to current flow problem. The thermal properties of nanoparticles are examined in presence of five shape features consisting of blades, platelets, cylinders, bricks and spheres. Numerical simulations of problem are performed via Runge-Kutta-Fehlberg method. Comparative heat transfer is performed for mono nanofluid (Cu/H2O) and hybrid nanofluid (Cu−Al2O3)//H2O. It has been observed that heat transfer enhancement is more stable for cylindrical particles as compared to spherical nanoparticles. The skin friction enhances due to Hartmann number for both mono nanofluid (MNF) and hybrid nanofluid (HNF). Current results claim applications in coating thin films, lubrication systems, improving the thermal efficiency in thermal and industrial systems, heat exchangers, cooling systems etc.

Ternary hybrid nanofluids offer significant advantages in heat transfer due to their enhanced thermal conductivity compared to traditional fluids. Investigating their flow behavior over expanding surfaces can contribute to the development of more efficient heat exchangers and cooling systems in the electronics, energy production, and transportation industries. This paper presents a detailed analysis of the flow and thermal transfer characteristics of a ternary hybrid nanofluid (SiO2–Cu–Al2O3/H2O) over a radially stretching surface, utilizing both numerical techniques (Keller Box method) and statistical techniques. Furthermore, the model includes factors like convective heat transport, radiation, internal fluid friction, and suction. Similarity transformations transform the governing equations for fluid flow and heat transfer into a system of nonlinear ordinary differential equations. Then the equations are solved numerically using the Keller Box method with the aid of MATLAB software. Additionally, we have employed statistical techniques such as correlation analysis, probable error estimation, and multivariate regression to validate and ensure the accuracy of the numerical outcomes. Parameter ranges for Biot number, radiation, unsteadiness, Eckert number, and energy generation parameter are 0.1 ≤ Mp ≤ 0.7, 0.1 ≤ Ks ≤ 1.5, 0.2 ≤ Ps ≤ 0.8, 0.1 ≤ EN ≤ 0.4, 0.5 ≤ RN ≤ 2, 1≤ BT ≤ 2.5, 0.1 ≤ Hsc ≤ 0.7 and found to significantly impact heat transfer behavior within these bounds. This study utilizes 3D surface plots to visualize the influence of key parameters on engineering quantities. R squared values show that the data strongly match the regression model. The findings demonstrate excellent concordance between the predicted values and the actual Nusselt number and skin friction measurements. Biot number has a very strong correlation with heat transfer, with minimal chance of error. And the same is evidenced by the correlation matrix and multiple regression analysis. Eckert number also exhibits a negative correlation with the Nusselt number. This translates to a situation where increasing Eckert number directly leads to a decrease in the rate of heat transfer, with no margin for error. Energy generation parameter demonstrates a negative correlation with heat transfer. However, there's a slight possibility of error, with an estimated error percentage of around 0.0017.

Here flow for radiative hybrid-nanomaterial (MgO+MoS2) satisfying Darcy-Forchheimer relation is addressed. Ethylene glycol C2H6O2 is utilized as a base fluid. Magnesium oxide (MgO) and Molybdenum disulfide (MoS2) are considered as distinct nanoparticles. Thermal expression is examined through heat generation and viscous dissipation. Analysis for Cattaneo-Christov theory is carried out. Condition for melting heat is deliberated. Entropy generation is examined. Variable thermal conductivity of hybrid nanomaterial is taken. Suitable transformations are implemented to obtain nonlinear dimensionless systems. Optimal homotopy analysis method (OHAM) is implemented for computations. Temperature, velocity and entropy generation are scrutinized physically. Nusselt number and skin friction are discussed. Conclusion synthesis salient points. Present work is relevant in metallurgical engineering and polymer processing. The findings conclude that Forchheimer number correspond to decline in velocity. Entropy rate and thermal field have similar trend for heat generation variable. A decrease in velocity against melting variable is noted. Temperature increases for variable thermal conductivity and thermal relaxation parameters. Entropy optimization improved for Brinkman number. Skin friction decays for porosity parameter and Forchheimer number. Skin friction improves for melting variable and Forchheimer number. Entropy augments against higher thermal relaxation time. Higher melting variable lead to an enhancement for Nusselt number. There is an improvement for radiation through Nusselt number and temperature.

This study aims to thoroughly investigate the flow behaviour of a Reiner–Philippoff nanofluid over a nonlinearly stretching sheet, with a particular focus on the effects of viscous dissipation. The research delves into the complex interactions within the nanofluid, assessing how viscous dissipation influences heat and mass transfer rates. To model the nanofluid flow, the Darcy–Forchheimer model was employed alongside slip velocity effects. Thermal radiation was incorporated to control heat transfer, while activation energy was considered for mass transfer regulation. The Buongiorno hypothesis was used to account for thermophoresis and Brownian motion in the governing equations. Following appropriate transformations, the nonlinear ordinary differential equations were formulated and solved using the shooting method. Key parameters such as skin friction, Nusselt number, and Sherwood number were analysed in tabular form, while graphical representations highlighted the impact of variables like concentration, velocity, and temperature. The study found that considering slip velocity in combination with the Darcy–Forchheimer model significantly enhances mass transfer. A comparison with existing data demonstrated the consistency of the results. This research holds relevance for applications in acid rain, pollution migration, groundwater treatment, and related environmental processes. It has been noted that raising the porosity parameter and the Forchheimer number causes the temperature and concentration levels to drop while boosting the fluid’s velocity.

This paper examines how nanoparticle aggregation and a consistent magnetic field influence the peristaltic movement of a dissipative nanofluid, which is caused by the sinusoidal deformation of the boundary. The viscosity of TiO2/H2O nanofluids is accurately determined by the Krieger-Dougherty model with nanoparticle aggregation, while thermal conductivity (TC) is estimated through the Bruggeman model. The set of governing equations are modeled in a fixed frame by utilizing the conservation laws of energy, mass and momentum. Galilean transformation is utilized to transform the system of equations into a wave frame, which is then converted into a dimensionless form. The assumption of a small Reynolds number and long wavelength serve to further simplify the set of equations, which are subsequently addressed through the implementation of the differential quadrature method (DQM), a highly effective numerical technique. Quantities of interest, namely velocity, pressure gradient, temperature, trapping phenomena, heat transfer, and volumetric entropy generation are analyzed across a range of physical parameters, including the solid volume fraction (Φ=0.01−0.04), Eckert number (Ec=0.0−0.1), Hartman number (Mh=0.2−2.2), Grashof number (Gr=1.0−3.0) and temperature ratio parameter (θd=0.5−2.5). A comparative analysis is conducted between the scenario involving aggregation and the one without aggregation. It is observed that nanoparticle aggregation significantly alters these quantities.

Hybrid nanofluids are crucial for enhancing thermal management, efficiency, and longevity in industrial applications such as heat exchangers, automotive cooling, and advanced manufacturing. The current study primarily investigates the impact of viscous and Joule dissipation on copper-alumina hybrid nanofluid flow over a stretching surface, with a particular focus on magnetic field effects resulting in a strong Lorentz force along the vertical direction. The governing equations are non-dimensionalized using similarity transformations, resulting in coupled, highly nonlinear ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically using the Shooting technique and a fourth-order Runge-Kutta scheme in MATLAB. The results are plotted graphically. The outcomes mainly indicate that at the surface, momentum intensifies with increased stretching but declines significantly under a stronger magnetic field, while reduced permeability slows down flow momentum, resulting in higher temperature elevations. The outcomes revealed that copper-alumina hybrid nanofluids with lower permeability could improve the performance of miniature industrial devices.

This study explores the effects of multiple shape factors on nanofluids within Marangoni mixed convection flows through porous media. Nanofluids, containing nanoparticles in a base fluid, show unique thermal properties, making them valuable in cooling systems, energy storage, and medical devices. Marangoni mixed convection, driven by surface tension gradients, adds complexity to fluid dynamics and heat transfer in porous media. Analytical and numerical analyses examine how various particle geometries, nanoparticle volume fractions, and porous medium configurations influence transport phenomena. Entropy analysis calculates thermodynamic irreversibilities. Findings reveal relationships between shape factors, heat transfer rates, velocity profiles, temperature distribution, and entropy generation rates, offering insights for optimizing nanofluid-based systems. The study also investigates magnetic forces, heat source/sink effects, and viscous dissipation on thermal energy transfer in Graphene oxide/water and Molybdenum disulfide/water nanofluids. Using similarity transformations, Partial Differential Equations are converted into Ordinary Differential Equations, solved with HAM and NDSolver by using the Wolfram tools. Results graphically depict velocity, temperature, entropy, and skin friction values, providing practical insights for engineering applications.

In this analytical study, the fluid motion within a microchannel is induced by the oscillation of one surface parallel to the other stationary surface, termed the extended Stokes’ problem. The novelty and research gap are acquiring the thermal effect of such motion due to the viscous dissipation or fluid friction, subject to symmetric isothermal boundary conditions. The study may shed light on the role of viscous dissipation in temperature rise in the synovial fluid of an artificial hip joint, or in the fluid layer of a mechanical bearing. The full exact analytical temperature field, until now, has been unsolved, as it involves unsteady flow with manipulation of a complicated velocity field. The assumptions in the model are one-dimensional, incompressible, laminar, Newtonian flow with constant properties in a microchannel. Through the methodology of partial differential equation analysis, the temperature field is obtained in terms of Brinkman number, Prandtl number and a dimensionless angular frequency, and results are verified with a reported numerical solution, for specified range of the variables. Results complement recent approximate solutions which are valid only for the limited condition of the dimensionless angular frequency being less than or equal to unity, whereby suggesting a new Stokes number.

Aim: This paper presents a numerical simulation of the mixed convective boundary layer (BL) motion of a bio-rheological liquid over an inclined plate under viscous dissipation and Joule heating effects. This is significant because of the various applications of electro-osmotic force, inclined plates, and viscoelastic fluids in the biochemical engineering and industrial domains. Furthermore, the BL flow is controlled by electromagnetic force (EMF). In this study, a non-Newtonian liquid model, called the Jeffrey fluid model, was employed. Method: The rheological equations of the current study are nonlinear partial differential equations (PDEs). By applying a set of similarity transformations, these PDEs become coupled ordinary differential equations (ODEs), which are then solved numerically using the NDSolve method under realistic boundary constraints. Outcomes: Numerical solutions for the velocity profile (f′(ξ)), temperature distribution (Θ(ξ)), skin friction (shearing stress), and Nusselt number (heat transfer rate) were obtained subject to convective boundary constraints. These numerical outcomes are dependent on 12 embedded parameters: Hartmann number (Ha), viscoelastic time relaxation parameter (γ), inclination of the inclined plate with a horizontal line (ω), mixed convection parameter (Ω), electro-osmotic parameter (k), electro-osmotic velocity parameter (Uhs), Prandtl number Pr, Brinkman number (Br), suction/blowing parameter (s), velocity slip parameter (ϱ), Joule heating parameter (Γ), and thermal slip parameter (δ). The authors discussed how these embedded variables affect rheological features through graphs and tables. The numerical solutions of viscous liquids are also discussed, and these outcomes are compared with the numerical solutions of a viscoelastic liquid. The enhancements of the Θ(ξ) and f′(ξ) are largely dependent on the Joule heating parameter, Brinkman number, and Hartmann number. As the Prandtl number increases, diminishing behavior is observed in the Θ(ξ) and f′(ξ). Increasing the magnetic and viscoelastic parameters increases the magnitudes of the skin friction coefficient and local Nusselt number. The validation of the numerical procedure is discussed by recovering the outcomes of research works from the available literature. Significances and applications: This mathematical study has diverse applications in the electromagnetic multiphase processes, magnetic power generators, chemical engineering phenomena, polymer industry systems, and the thermal enhancement of mechanical and industrial processes.

The current thermal slip and Magnetohydrodynamic analysis plays prominent importance in heat insulation materials, polishing of artificial heart valves, heat exchangers, magnetic resonance imaging and nanoburning processes. The main objective of the existing article is to deliberate the impact of thermal slip, thermal radiation and viscous dissipation on magnetized cone embedded in a porous medium under reduced gravitational pressure. Convective heating characteristics are used to increase the rate of heating throughout the porous cone. For viscous flow along a heated and magnetized cone, the conclusions are drawn. The simulated nonlinear partial differential equations are transformed into a dimensionless state by means of suitable non-dimensional variables. The technique of finite differences is implemented to solve the given model with Gaussian elimination approach. The FORTRAN language is used to make uniform algorithm for asymptotic results according to the boundary conditions. The influence of controlling parameters, such as thermal radiation parameter Rd, Prandtl number Pr, porosity parameter Ω, viscous dissipation parameter Ec, δ thermal slip parameter, Rg reduced gravity parameter and mixed convection parameter λ is applied. Graphical representations were created to show the consequences of various parameters on velocity, temperature and magnetic field profiles along with fluctuating skin friction, fluctuating heat and oscillatory current density. It is found that velocity and temperature profile enhances as radiation parameter enhances. It is noted that the amplitude and oscillations in heat transfer and electromagnetic waves enhances as magnetic Prandtl factor increases.

As a result of the tremendous development in all aspects of life, the increase in population day after day, and the scarcity of freshwater resources sufficient to meet the needs of living organisms on the surface of the earth, all these reasons called for an attempt to treat wastewater supported by solar energy to raise the temperature and facilitate the operation of wastewater treatment systems. Health in areas rich in solar resources. This approach reduces reliance on traditional energy sources in the wastewater treatment process. This theoretical study aims to create a mathematical model for the problem of water turbidity due to impurities (wastewater). Non-Newtonian fluid flow equations are established in the case of using renewable energy in various forms of nano-photocatalysts, as well as magnetic force which has a clear effect on the process of removing impurities from the aqueous fluid. Chebyshev's method was used to obtain numerical solutions to the problem, which were represented by a set of drawings and tables, that highlighted the effective role of both the magnetic field and sunlight in eliminating impurities. Increasing the Lorentz force and thermal radiation increases the strength of hydrogen bonding of the aqueous liquid mixed with particles of tri-hybrid nanomaterials larger than the aqueous liquid, which in turn works to raise the thickness of the thermal layer in the blade shape higher than the rest of the shapes. This study gives future insights for further research endeavors.

Present problem concerns may be found in a wide variety of various industries and can takes a shape of round toroid's, cones, cylinders, domes (Axisymmetric shape), and other shapes as well. When it comes to actual applications, they are represented by aerosol cans, submarine pressure hulls, cooling towers, offshore drilling rigs, radomes, nuclear reactors, and other similar objects. The aim of this research is to improve the performance of MHD flow using Darcy-Forchheimer, viscous dissipation, porous and a heat source. The viscous convective permeable flow flowing over a bullet-shaped item is examined. Using similarity transforms, the structure of nonlinear differential equations are converted into dimensionless ODEs. Employing bvp4c shooting technique to decrypt the findings. Influences of physical entities on velocity and temperature were sketched and briefly described. Physical behaviors of skin friction and heat transfer rates are explored. The fluid velocity drops for Eckert number Ec as ε 1.0, The fluid velocity improves with Darcy-Forchhemier parameter Fr when stretching ratio ε 1.0. The enhancement of fluid temperature is observed with enhanced Ec. A enhance in the Darcy-Forchhemier parameter Fr associated with improvement in skin-friction. In the absence of viscous dissipation, hall current, porous and Dacy-Forchhemier influences, the outcomes are in splendid covenant with those of previous studies.

This research introduces novel theoretical assumptions through the use of a non-Newtonian Sutterby model with variable properties, demonstrating significant advancements in thermal conductivity and diffusivity, which enhance heat and mass transfer in fluids, particularly under magnetic field exposure. The study is notable for its comprehensive examination of the effects of thermal radiation and viscous dissipation within a porous medium. Additionally, it explores the role of suction velocity to provide a deeper understanding of transport phenomena. Following the Darcy hypothesis, the fluid flow is modeled as resulting from the linear stretching of an elastic sheet in a saturated porous medium. The core physical model, comprising equations of mass, motion, concentration, and energy, is transformed into ordinary differential equations using appropriate similarity transformations. Employing the shooting technique, the numerical solution to the problem is obtained. The research uncovers and quantitatively analyzes intriguing physical parameters influencing velocity, concentration, and temperature fields. These parameters are further investigated both numerically and graphically, providing valuable insights into their effects. Quantitative outcomes include enhanced thermal and concentration fields by magnetic field parameter, the porous parameter and the viscosity parameter and improved the rate of mass transfer by both suction and thermophoretic parameters, highlighting the model’s efficacy in optimizing fluid dynamics especially under magnetic fields. The obtained outcomes were juxtaposed with previous studies, revealing a significant level of agreement.

This manuscript reveals the mathematical analysis of dual simulations in tangent hyperbolic rheology with heat transfer and mass diffusion mechanisms on the needle (expanding and shrinking). Further, Darcy's Forchhiermer law is employed with the occurrence of the magnetic field. The models of hybrid nanofluid utilized are Xue- and YO-hybrid nano-fluid models. Such models apply to optical fibers, solar systems, surgical implants, electronics and biological applications. Transfer of thermal energy and diffusion related to mass species occurs employing a non-Fourier approach. The transformed system of non-linear Odes is numerically tackled with the finite element method. Furthermore, because fluid and needle movement have opposite directions, the current model has dual solutions. It visualizes that such a complicated model is not solved numerically by FEM. The applications of Xue- and YO-hybrid nano-fluid model with non-Fourier's law on a needle are implemented for the first time. It concludes that adding YO-hybrid nanofluid with base fluid increases the entropy profile, temperature profile and Bejan profile rather than the Xue hybrid nanofluid model. Fields of concentration, velocity and heat energy for the case of upper solutions are higher than concentration, velocity and heat energy profiles for lower solutions.

The study of heat transfer in fluid flows across permeable media is critical in many engineering applications, including energy systems, cooling technologies, and chemical processes. This study aims to explore the impact of joule heating and heat transfer flow of an MHD dissipative ternary fluid through a channel embedded in a Darcy-Forchheimer permeable medium. Additionally, the utilization of ternary hybrid nanofluids, composed of a base fluid and three nanoparticles Al2O3, MoS2, and Cu has emerged as a promising avenue for augmenting thermal conductivity and heat transfer rates. The governing equations are transformed into a set of coupled ordinary differential equations by employing similarity variables and simplified by bvp4c and artificial neural network (ANN) model approaches. Results reveal that significant enhancement in the velocity field at the lower channel wall and reductions at the upper wall, while fluid temperature decreases with increasing Prandtl number. Further, the heat transfer rate increases with an increase in the Prandtl number and magnetic field whereas the skin friction decays with an increase in the magnetic field. Meanwhile, the comparison was carried out for the temperature field by using bvp4c & ANN and the results are strongly correlated.

The remarkable thermophysical characteristics of hybrid nanofluids have considerable potential for the enhancement of heat transport. In recent years, there has been a significant surge in research on hybrid nanofluids, with findings indicating that these fluids are favorable for transferring heat in engineering contexts. Therefore, a theoretical investigation is conducted by adopting the Tiwari and Das model, for viscous dissipative flow and thermal transport characteristics of hybrid nanoparticles in an exponentially permeable porous shrinking surface. The convective thermal transport features are studied with the influence of Ohmic heating and thermal generation/absorption effects. To solve the governing flow problem of hybrid nanofluid, a standard conversion and numerical approach are used. The numerical findings indicated the existence of dual solutions within a certain range of shrinking and mixed convective parameters. The results reveal that high suction strength higher the skin friction coefficient and heat transfer rate. It also reveals that in opposing flow regions, the addition of nanoparticles resulted in a lower heat transport rate and a higher skin friction coefficient. Furthermore, as thermal radiation increases, the rate of heat transfer increases, but the upward Eckert number exhibits the opposite behavior. In addition, the velocity profile displays opposite behavior for upper and lower behavior when the mixed convection parameter increases. Besides, the thermal distribution grew when the radiation, Eckert number, and Biot number were raised.

The recent study concentrates on magnetohydrodynamics (MHD). Williamson fluid drifts over an exponentially extending sheet. The porous medium is also crucial to improving thermal efficiency. The flow pattern model considers the inspirations of Joule heating, heat generation, viscous dissipation, and thermal radiation. This study also comprises the activation energy, bio-convectional, and gyrotactic microorganism phenomena. Furthermore, the Brownian and thermophoresis effects of nanoparticles are taken into consideration. Using proper similarity transformation, PDEs of the impetus, temperature, concentricity, motility microbe density, and boundary constraints upgrade into a non-linearly ordinary differential equations (ODEs) mode. Using MATLAB, transformed non-dimensional ODEs are dealt with using shooting procedures and results of significant physical strictures using a built-in bvp4c solver. Finally, it is elaborated and briefly explored numerically and visually can find interesting physical strictures versus the velocity gradient, temperature gradient, solutal gradient of species, and microbes' gradient. Incorporating microorganisms and nanoparticles into Williamson fluids can create novel materials with tailored properties for diverse applications. However, it's crucial to consider stability, biocompatibility, and environmental impact when designing these advanced fluid systems.

Peristaltic flow of Sisko fluid with temperature-dependent viscosity and viscous dissipation is considered in this paper. The constitutive equations for viscous and non-Newtonian power-law fluids are generalized to Sisko fluid. The governing equations take the form of two coupled nonlinear partial differential equations. The analytic solution is calculated using long wavelength and small Reynolds number approximations. The Sisko fluid, being the blend of viscous and non-Newtonian fluids, includes all the rheological properties of non-Newtonian fluid and viscous fluid. The effects of variable viscosity parameter translate into two independent parameters giving rise to two cases. The one corresponding to low shear rate and the other corresponding to infinite shear rate. This is a new approach to look up the effects of fluid properties characterizing Sisko fluid. The paper is essentially a theoretical work with applications in science and technology including biotechnology. In the absence of any empirical data; the results for the viscous and power-law fluids with variable viscosity are deduced from the generalized solution of Sisko fluid presented in this study.

The concept of nonlinear thermal convection is taking place for the process of cooling/heating in some thermal industries like solar collectors, combustion, and reactor safety. The significance of linear and nonlinear thermal convection is implemented in the present mathematical modeling to handle nonlinear density-temperature caused by viscous dissipation and flow through a porous medium. Further, the inclined magnetic field is implemented to analyze the flow characteristic at various inclination angles which will be helpful in glass manufacturing, geophysics, crude oil purification, and paper production. Furthermore, entropy generation analysis is made for the stagnation point flow of viscous fluid over a shrinking Riga sheet. Using boundary layer assumptions, the present model made up of fluid motion and energy equations is formed and converted to a system of nonlinear differential equations. Numerical results are collected using the MATLAB bvp4c solver and these results were utilized to study important parameters on the entropy generation and heat transport of fluid flow. The presence of nonlinear thermal convection will intensify the impact of major parameters and the least entropy generated for the inclination angle of the magnetic field. Also, entropy enhanced significantly with the Eckert number and modified Hartmann number. In addition, the surface drag is enhanced by 12%-18 % and the thermal transmission rate is diminished by 4%-7% in the case of nonlinear thermal convection compared to the linear case. The findings of this study are more important to optimize heat transfer and irreversibility in the applications of the automotive industry, ceramics, paints, food packaging, fabrics, pharmaceuticals, and cancer treatment.

Non-Newtonian fluids flow generated by “cilia” are critical in medicine and bio-medical engineering. Such investigations are created by the back-and-forth movement of a microscopic hair-like structure connected to the walls, which causes a metachronal wave to form and drive biological fluids. Motivated by a wide range of biological applications, this study aims to explain the incompressible flow of Ellis fluid caused by the propagation of an infinite metachronal wave train traveling along channel walls owing to constantly beating cilia. The problem is simplified by low Reynolds number and long wavelength assumption. The mathematical model is solved with the aid of symbolic computational software Mathematica 13 version. The consequences of emerging parameters are then shown in graphical form and discussed comprehensively. From the study, it is worth mentioning that velocity declines with increasing material constants. Temperature distribution is also improved in the core sector of the channel and reduced at the walls. It is predicted that this approach will make an essential contribution to the progress and enhancement of various types of drug delivery systems in the biomedical industry and biomechanics.

In current years, storage of energy is a challenging task for the scientists and researchers. So, they are interested to develop some extra ordinary techniques of energy storage. Thus, our main theme here is to focus on the latent heat energy (melting heat) which is more economical and sustainable. Transportation of melting heat in quadratic stratified Jeffrey fluid flow in the vicinity of stagnation point is scrutinized. The flow is deformed by linear stretchable sheet. Characteristics of heat transportation are scrutinized through viscous dissipation and heat generation or absorption. Constant magnetic field is implemented to electrically conducting fluid in vertical direction. The arising governing equations are converted in the non-dimensional state through suitable transformations. Homotopic technique is utilized for simulation of solutions. Graphical behavior of velocity and temperature fields is investigated corresponding to relevant parameters. As a conclusion, higher amount of energy can be achieved as melting phenomenon enhances, and also results in low temperature. Further, dominant stratification decays the temperature field. Current study will play key role in industrial liquids like polymer solutions to make high quality fiberglass, paints, silicone heat valves etc. This study will also deliberate efficiently for the storage of energy through phase change procedure i.e., melting phenomenon.

In this study, authors explore how magnetic fields and the buoyancy force resulting from temperature differences work together. The study is focusing at how an Eyring-Powell nanofluid behaves in a ciliated channel when both natural convection and magnetic effects are at play. A technique called the symplectic metachoronal wave has been used to analyze this analysis. A physical assumption of small Reynolds number is considered to simplify the equations describing the flow rate of the Eyring-Powell nanofluid, making it easier to understand. To get a closed form solution, we have incorporated Adomian decomposition method (ADM). It has been observed that the flow is sped up by 10% with increase in the Eyring-Powell fluid parameter M. The quantity of heat transfer increases with increasing values of the Hartmann, Eyring-Powell fluid parameters, and Brinkmann numbers. This study has implications for bio-inspired engineering, medical applications, and the design of microfluidic devices.