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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.

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 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.

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.

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.

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 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.

The significant importance of present research is to remove the extreme temperature along the magnetic driven horizontal circular cylinder. The induced electromagnetic field is applied around the surface of cylinder. The main novelty of current research is to control thermal and magnetic boundary layer in the presence of viscous dissipation and induced electromagnetic field. The dimensional mathematical form is developed with defined boundary conditions. The dimensional equations are transformed into dimensionless equations to generate physical factors. The primitive form is used to reduce dimensionless equations into convenient form for smooth algorithm. The finite difference method with Gaussian elimination technique is applied for numerical results in FORTRAN language tool. The velocity, temperature and electromagnetic field are sketched graphically with asymptotic sequence. The oscillatory shear stress, oscillating heat rate and periodical current density is plotted graphically and numerically. It is found that fluid velocity improves significantly as buoyancy force increases around each position. It is noticed that the increasing oscillations in heat transfer are sketched for maximum choice of Prandtl number. It is found that the maximum oscillations in current density are obtained for each Eckert parameter. It is noticed that the significant distribution in temperature profile is obtained in the presence of viscous dissipation and magnetic field.

The Riga plate is an electromagnetic actuator made out of permanent magnets and alternating electrodes on a flat surface. In the boundary layer flow across the Riga Plate, viscous dissipation is surveyed in this paper. The suitable boundary conditions have been assigned to the governing model for mass and heat convection phenomenon. A governing equation can be converted into non-dimensional form using similarity transformations. To create numerical solutions to physical phenomena, the finite difference approach can be utilized. Extensive graphical illustrations are provided for the effects of the buoyancy coefficient parameter, modified Hartmann number, parameter related to electrode and magnet width, Prandtl number, slip parameter, thermophoretic parameter, thermal radiation parameter, Schmidt number, chemical reaction rate parameter, suction parameter, Brownian motion parameter, volume fraction, Biot number, and Eckert parameter on velocity, temperature, and concentration distributions. By varying the Eckert number, the viscous dissipation effects can be obtained. Suction and slip parameters increase the velocity while decrease the temperature in both nanofluid cases. The high temperature and velocity of equally distributed nanofluids rise as the volume fraction increases. Thermal radiation promotes heat transport. The concentration of nanoparticles in the region around the plate increases as the chemical reaction parameter increases. The research findings are useful for thermal engineers and practitioners involved in the design and optimization of systems where boundary layer fluxes and heat transfer are important factors. Understanding the effects of viscous dissipation can lead to more reliable heat transfer estimates and more effective thermal management in real-world structures.

The objective of present analysis is to control excessive thermal behavior in microelectronic devices using heat sink and magnetic field. Improving technological innovation demands proper temperature evacuation in microelectronic components. A feasible method for cooling microelectronics is to use nanofluid, a novel heat-transport liquid. To achieve significant cooling, microelectronic devices must be small with specific operating liquids than regular liquids. The present work investigates the fluid motion and heat transmission properties of nanofluids as advanced cooling fluids for microelectronic coolant systems. A numerical technique is used to investigate the cooling mechanism using stretching surface. Computational fluid dynamics and 2D liquid movement simulation are employed to determine the mathematical model. The governing model is transformed with Keller box method and Newton Raphson technique through MATLAB program. The base liquid is water using laminar motion. The influence of nanoparticles volume fraction, heat sink, variable density and viscous dissipation in the base liquid on heat transmission efficiency of coolant devices is investigated. It is noticed that the fluid temperature decreases as heat sink increases. It is found that the excessive heat is reduced by using magnetic layer and heat sink. The present numerical mechanism is significant for the cooling of microelectronic devices.

The motivation behind the current contribution is to establish a framework that examines the influence of sunlight on a novel Sutterby nano-liquid with magnetic field impact. The fluid flows through a photovoltaic (PV) plate. A model for tri-hybrid nanofluid has been developed and utilized to explore the effects of tri-hybrid nanoparticles on the flow, particularly focusing on heat transport and its gradient. The technique employed involves converting the partial differential equations (PDEs) derived from the initial prototype into ordinary differential equations (ODEs) through similarity transformation. Numerical results are obtained using the bvp4c method, which belongs to the Runge-Kutta family of ODE solvers. The notable finding from the results indicates that the incorporation of novel tri-hybrid nanoparticles into the conventional liquid leads to a faster enhancement of heat transfer rate and temperature profile compared to existing conventional hybrid and nanofluids in the literature. It is noticed that when nanomaterials are introduced into the liquid, their temperature rises in both shear thinning and shear thickening scenarios. A higher volume percentage of tri-hybrid nanoparticles, coupled with increased thermal radiation and heat joule, amplify the heat absorbed by PV plate.

The study of magnetohydrodynamics (MHD) incompressible flow of a fluid having hybrid nanoparticles making the colloidal combination with base fluid is presented in this research. Comparative analysis is carried out for the nanofluids Al2O3/Kerosene and ZnO/Kerosene oil with the hybrid nanofluid Al2O3–ZnO/Kerosene oil. The subject flows are influenced with thermal radiation and viscous dissipation. A numerical technique Keller box is employed to examine the envision mathematical model. For computational procedure MATLAB software will be used. Tabulated and graphical outcomes of different effects are presented for the appraisal of velocity and temperature distributions. It is comprehend that the thermal radiation and viscous dissipation parameters possess up surging trends for the hybrid and nanofluid temperature profile but opposite trend has been observed for different volume fractions of nanoparticles.

Here two-dimensional electrically conducting bioconvection flow involving Maxwell liquid is explored. Darcy-Forchheimer relation is taken for porous space. Thermal expression comprises nonlinear radiation, heat generation and dissipation. Influences of Arrhenius activation energy and gyrotactic microorganism are discussed. Novel characteristics of diffusion thermo and thermo-diffusion are discussed. Suitable variables are implemented in obtaining required differential system. ND-solve technique is implemented for computations Flow, microorganism field, thermal distribution and concentration are graphically examined. Tabulated values give rise to interest for physical quantities. A decrease in flow is noticed for magnetic variable and Deborah number while reverse behavior holds through mixed convection. An improvement in temperature occurs for higher magnetic field. Dufour number corresponds to upsurge heat transport rate and temperature distribution. Larger radiation results in temperature enhancement. A rise in concentration is observed for Soret number whereas reverse effect seen for Schmidt number. Reduction in microorganism field is noted versus higher Peclet number.

This study is of significant importance as it focuses on exploring the intricate dynamics of viscous dissipation over a layered stretching surface in the context of MHD free and forced convective flow influenced by Powell-Eyring fluid. The primary aim of this research is to analyze the impact of heat emission and immersion phenomena on the flow, and to achieve this, conformable transformations of similarity have been pragmatic to adapt the governing equations from a set of non-linear PDE's into ODE's. The research methodology employed in this study involves numerical analysis using a 4th order Runge-Kutta formulation, implemented through MATLAB. The study precisely examines the stimulus of different flow constraints on velocity and temperature profiles. The outcomes of this investigation are presented through graphical representations, providing a comprehensive view of the flow characteristics. Furthermore, this study goes beyond the basic analysis by presenting important engineering metrics, the Nusselt number and skin-friction coefficient, explicitly across dissimilar variables. In conclusion, the findings of this research reveal as the Eyring-Powell fluid velocity profile rises, the temperature profile decreases, while the temperature profile rises with rising radiation.

The current study represents a sensitivity analysis of the flow of gold nanoparticles in blood over a rotating disk with the combined impacts of viscous dissipation, nonlinear thermal radiation, joule heating, and slippage using response surface methodology. We use response surface methodology to investigate the relationships between the model's parameters (the input parameters), and the response variables. Response Surface Methodology is a useful method for finding the best values for the input parameters that improve the output. It can also help researchers create a list of experiments to predict the output. We often use response surface methodology with sensitivity analysis to see how the output depends on the input parameters and to suggest the optimal values of them. After incorporating the effects of MHD, viscous dissipation, nonlinear thermal radiation, and joule heating, the boundary layer flow equations are solved using NDSolve command of Mathematica. The influences of dimensionless parameters on all flow profiles and physical quantities are presented and discussed. The arithmetic has been considered for a specific range of values for the apparent parameters in order to calculate and analyze the physical quantities of interest for various relevant parameters, for instance 2≤M≤5, 0≤β≤2, 0.6≤A≤1.5, 0.1≤Br≤0.65, 0.5≤δ≤2, 0≤φ≤0.15, 15≤Pr≤21, 0.1≤Rd≤1.5. For sensitivity analysis, we consider skin friction coefficient and local Nusselt number for three independent input parameter namely, the radial stretching rate, the magnetic field parameter, and the thermal slip parameter. After using the statistical measures such as residual quantile – quantile plots, hypothesis testing, and adjusted R2, we concluded that our models for the skin friction coefficient and local Nusselt number are best fitted.

There are numerous applications related to engineering and industrial manufacturing and processing in which the boundary-driven hydromagnetic flow of non-Newtonian fluids play a vital role. Examples includes glass fiber, electronic devices, paper production, medical equipment, filaments, polymer sheets and medicine. Researchers investigated the heat transportation in fluid flows with linear stratification. However, linear stratification fails when there exists large temperature difference between different bodies. Owing to such facts, here our aim is to explore the features of convective heat model in Casson fluid flow with inclined magnetic field with exponential stratification deformed by linearly stretchable inclined sheet. Characteristics of heat transportations are formulated and investigated through viscous dissipation and heat generation. The reduced non-linear governing expressions are solved analytically by homotopic technique. Analysis of velocity and temperature are comprehensively demonstrated through graphs. Further, rate of heat transfer and drag force are computed graphically via various parameters. It is concluded that inclination and magnetic parameters diminish the flow velocity gradually. Further, temperature field intensifies when Biot number is enlarged while it decays with increasing thermal stratification. It is hoped that the present study will help us to form the homogeneous mixtures of fluids at industrial and biomedical levels especially in food liquids, medical syrups, and medicines.

Purpose: The physical dynamic and impact of many problems is successfully attributed via fractional approach. The fractional models more effectively present the insight of many problems which maintain the memory effects. Owing to excellent thermal activities and alters, the nanoparticles are more superior contrasting to base liquids. Different dynamic of nanoparticles are reported in the heating transmission systems, engineering processes and industrial framework. Design/methodology/approach: Present study elucidates the heat transfer distribution in Oldroyd-B nanofluid which is decomposition of copper nanoparticles with blood base fluid. The variable thermal conductivity function is assumed to treat the nanofluid problem. Furthermore, the viscous dissipation consequences are utilized in order to modifying the problem. The modeling is based on Caputo fractional forms. The finite difference simulations are performed to computing the numerical results. Thermal results for nanofluid model are physical claimed with variation of flow parameters 0≤Ha≤5,1≤Gr≤3,0.01≤φ≤0.2,0≤ϵ≤1,0≤Ec≤1 and α=β∈(0,1].. Findings: The claimed results verify that boosted thermal phenomenon is associated under the variable thermal conductivity assumptions. The increasing volume fractional parameter role is noted for temperature profile. The heat transfer pattern is increasing function of nanoparticles volume fraction while controlling results are noted for fractional parameter. Based on reported results, it is claimed that current solution approach can be further implemented to different physical problems.

Heat transfer in burners, combustion engines and energy consumption through nuclear explosions is significantly influenced by radiations. In missile nozzles, nuclear power plants for aerospace uses, and gaseous-core nuclear rocket systems, the radiations are considered for evaluating heating significance. The significance of present study is to compute heat and magnetic flux behavior across various angles π/6, π/4, π/3, π/2, π and 3π/2 of gravity-driven magnetized cylinder under gravity modulation, thermal radiation and viscous dissipation. The aim of this research is to examine wave oscillations in heat and current density along magnetic-driven circular cylinder. The computational and mathematical model is evaluated in terms of coupled periodic partial differential equations (PDE). The appropriate dimensionless variables are used to convert governing periodic model into non-dimensional form. The dimensionless formulations are transformed into steady and oscillatory form. To explore physical and numerical findings, the finite difference method with primitive formulations is applied for smooth algorithm in FORTRAN language. The significant results are explored for various pertinent parameters. The oscillatory magnetic flux and heat transmission are plotted by using steady state temperature and magnetic boundary layers. It is found that the prominent amplitude in velocity increases as reduced gravity increases at each angle. The maximum oscillating amplitude in heat transfer enhances at each angle as viscous dissipations and solar radiation increases.

The heat transfer in the fluids over a disk occurs in several industrial applications. Thermal and cooling systems, spray coating, heat exchangers, and automobiles are sectors where heat transfer is encountered. In view of these applications, the present investigation is carried out. Therefore, the theoretical study related to heat transfer enhancement has significance. The governing laws are used to formulate the problems. For numerical formulations, the finite element method (FEM) is used. This method has proven to be a very good numerical scheme for complex models, along with complex mathematical corelations for involved thermo-physical properties. Accuracy and convergence are ensured, and mesh-free analysis is performed. The present results for their special case are compared with published data, and an excellent agreement is found between the present results and already published data. Hence, authenticity is ensured. The strongest effects of shear rate-dependent viscosity in the case of ternary nanofluids are seen. The highest wall heat flux is noticed in the case of a ternary nanofluid. The viscous dissipation results in a remarkable decrease in the wall heat flux. The highest viscous dissipation is noticed in the case of ternary nanofluids. The ternary nanofluid generates the most heat when it is subjected to thermal changes. However, the fluid with a single type of nanoparticles generates the least heat. The strongest effects of shear rate-dependent viscosity in the case of ternary nanofluids are seen. The viscous dissipation results in a remarkable decrease in the wall heat flux. Thus, the fluid should be less viscous and dissipative if the highest wall heat flux is required in any industrial application. The highest wall shear stress is noticed in the case of ternary nanofluids, whereas the smallest values of wall shear stress are noted in the case of monofluids. Therefore, sufficient strength of the wall over which ternary nanofluid flows should be ensured in order to avoid failure or breakage of the setup where ternary nanofluid is used.

Character of activation energy and nanofluids has a prominent significance in the field of oil reservoir, chemical engineering, geothermal engineering, heat exchanger, food processing, heat and mass transportation and cooling devices. The aim of current study is to present the mathematical modeling and numerical solutions of three dimensional flow of Sutterby nanofluid past a bidirectional moving surface under the influences of mixed convection, binary chemical reactions, viscous dissipation and activation energy. Boundary layer theory is abduced to model the physical problem in the form of partial differential equations. The obtained partial differential system is metamorphosed into ordinary differential system by operating appropriate conversion. Fehlberg Runge Kutta scheme is applied to derive the numerical simulations of reduced non-dimensional differential model. It is gripping to explore that fluid velocities f′(η) and g′(η) have opposite behavior due to the enrichment of Sutterby fluid parameter β₁. Additionally, higher approximation of chemical reaction parameter and activation energy parameter has reverse trends on nanoparticle concentration.

Nanofluids have shown tremendous potential in the heat intensification of several manufacturing industries and have been utilized extensively in energy technologies in recent years. The goal of this exploratory paper is to examine the impact of double stratification on steady two-dimensional MHD Casson nanofluid flow over an exponentially porous stretching sheet. Thermophoresis and Brownian impact of the nanofluid model is described. In addition, the influence of joule heating, viscous dissipation, and heat generation are considered. The governing partial differential equations are converted into nonlinear coupled ordinary differential equations using similarity transformation, and they are then resolved using the Homotopy analysis method. The established nonlinear expressions have been solved analytically using the homotopic concept. Graphs demonstrate the influence of non-dimensional limitations on fluid momentum, thermal, and concentration. The drag force coefficient factor, Nusselt number and Sherwood number for various controlled factors on the Casson nanofluid properties are examined and tabulated. Researchers interested in the thermal science of liquid drifts are drawn to the mutual interaction of double stratification in MHD drift regimes since it affects various thermal engineering viewpoints in daily life.

In this analysis, Sutterby fluid flow of induced magnetic hydrodynamic at a stretchable cylinder is deliberated. The viscous dissipation impacts with temperature-dependent properties are applied on the fluid flow. The governing equations are developed using boundary layer approximation in terms of differential equations. The differential equations are dimensionless by means of suitable transformation. The dimensionless system is elucidated by the numerical procedure. Governing physical parameters influences are offered through graphs as well as tabular form. The curves of the velocity function show to enhance due to an increment in the decay-resistant parameter. The curves of the velocity function increased due to higher values of the magnetic field parameter. The sponginess parameter and velocity have inverse relation presented in graph. Temperature augmented due to increasing values of ε. The variable thermal conductivity and temperature have direct relation. Due to this relation, temperature boosted up by boosting the thermal conductivity.

Analysis of a steady flow of a viscous Casson fluid subject to Ohmic dissipation and an induced magnetic field is the main goal here. Through a stretched vertical sheet, the flow is managed. The energy equation is explained in a thermodynamical system along with Ohmic heating. By making the assumption that the viscosity and thermal conductivity are temperature-dependent as described here, an accurate assessment of the heat transfer rate may be carried out. Our research also addresses the effect of slip velocity. There are many applications for thermal flow fields subject to limited spaces and heated walls, including electronic cooling systems, furnaces, cooling towers, and thermal individualities in buildings and rooms, to highlight a few. The governing equations of the current model are generated mathematically in the form of partial differential equations by applying the boundary layer approximations along with these assumptions. Through appropriate transformations, a nonlinear system of differential equations is produced. The approximate solution is then obtained by using the Chebyshev spectral collocation method. The proposed problem is reduced to a nonlinear system of algebraic equations with the help of the properties of Chebyshev polynomials of the third-kind. Diagrams are therefore used to illustrate the significant impact of all controlling parameters on the fluid flow. Further, the local Nusselt number and the skin-friction coefficients’ numerical values are also computed and examined. Results show that the Casson fluid motion is strengthened by the electric and mixed convection characteristics, whereas the magnetic, the slip velocity and viscosity parameters impede the flow motion. Also, the distribution of temperature is amplified by a larger Eckert number.

Owing to its bounteous applications in engineering and advanced industrial processes magnetized hybrid Nano fluid influenced by suspended Nano-size particles got unusual consideration. The prime focus of current study rely on the meaningful investigation of the proposed phenomena with the utilization of buoyancy and viscous dissipation influence in the hybrid fluid. Numerical approach appertaining to three-dimensional hybrid Nano fluid flow configured by horizontal stretched surface is developed in the contemporary study. Magneto hydrodynamic viscous flow demeanor of hybrid traditionally water-based Nano fluid is contemplated in current report. Heat transmission phenomenon is taken into consideration on account of suspended Nano-scale size particles namely Magnesium-oxide (MgO) and Titanium-oxide (TiO2). Furthermore, Viscous dissipation along with thermal radiation impacts are also opted for the optimization of energy. Velocity profile along x-component and y-component is observed under buoyancy effects. Cartesian coordinates system have been accounted to mathematically model the proffered nonlinear system of PDEs by invoking appropriate similarity approach. An esteemed and prominent Runge-Kutta (4th - order) established on shooting technique is employed for the determination of velocity as well as temperature distributions. Multifarious parameters influence is sketched graphically. Velocity profile along horizontal components demonstrates the strengthening behavior for the growing values of magnetic parameter M and also buoyancy parameter λb while demonstrates depreciating behavior for the enhanced values of slip parameter K and also rotation parameter λ. Moreover, velocity profile along the vertical components is observed under the consequences of varying values of magnetic parameter M, rotation parameter λ, and slip parameter K and for buoyancy parameter λb.We noticed that horizontal component depicts enhanced demeanor for magnetic parameter M, slip parameter K whilst decaying demeanor for the upshot vales of rotation parameter λ. Local Skin-friction and also Nusselt number influence is reported via tables and found in excellent accuracy. The final outcomes will be validated numerically by aiding suitable techniques (R–K 4th order based Shooting Method). Our findings will be validated through graphs. This research provides significant field of study and will play an extensive role in field of fluid mechanics.

A theoretical study is conducted in order to scrutinize the thermodynamic first law of the MHD nanofluid flow with an inclined magnetic field, radiation, heat source/sink, viscous dissipation, Joule heating, concentration power-law exponent, and the chemical reaction on a porous stretching surface immersed within a permeable Darcian medium. Cobalt ferrite nanoparticles (CoFe2O4) have been combined with pure water to form a nanofluid called CoFe2O4/H2O. The controlling mathematical equations for MHD nanofluid flow are transformed through similarity transformation into non-dimensional equations. The exact solutions for the energy and mass transfer equations are provided in terms of confluent hypergeometric function. The effects of controlling parameters on the velocity, temperature, and concentration profiles are discussed and illustrated with figures and tables. According to the results, increasing the concentration power-law exponent yields a rise in the Sherwood number (PSC) magnitude and the wall concentration (PMF). Furthermore, the 3-D plots showed that the skin friction coefficient is directly related to the Hartmann number, suction parameter, and nanoparticle volume fraction parameter.

To improve heat transfer, this work provides a unique theoretical mathematical model of ternary hybrid nanofluid. In this analysis, the tri-hybrid nanoparticles TiO2, Al2O3, and AA7072 are submerged in ethylene glycol (EG), resulting in the mixture TiO2+Al2O3+AA7072/EG. The tri hybridity nanofluid is considered 3-D flowing via a rotate permeable cone embedded in Darcy-Forchheimer porousness material in the existence of fluctuating temperature generating (sink) and current radiate fluxing. The Keller box scheme (KBS) is exploited to resolve the liquid flowing and temperature equations numerically after converting them to ordinary differential equations employing similarity transformations. The results are graphed, and it is shown that the tri-hybrid nanofluid (THNF) has superior thermal conductance to the hybrid nanofluid (HNF) and that the fluid's velocity and temperature develop as a consequence of enlargement in thermal radiative fluxing and variable thermal conductivity effects. Raising values of De and Fr decline drag friction but drag friction coefficient values are improved as a result of positive variation in M, Re, ς, and λ. It is apparent that the rate of heat transference amplifies owing to magnification in QT, QE and Rd but the heat transfer rate diminishes due to magnification in Re and Fr. Incremental change in volume fraction of nanoparticles φ=0.005 to 0.03 delivers more heat in the case of tri-HNFs TiO2+Al2O3+AA7072 in contrast to ethylene glycol based TiO2+Al2O3 fluid. The optimal percentage error diminishes for the drag friction phenomenon from 1.4% up to 1.1% by adopting De from 1 to 1.5 and λ=0.5. The percentage error in terms of heat transfer rate is getting smaller from 3.6% to 3.0% because of a positive change in QT by keeping Rd=1.5.

In the current investigation, it is examined numerically entropy generation (EG) on inherent irreversibility motion of couple stress cold liquid with porous medium via Horizontal channel in presence of viscous dissipation. Present work was studied heat generation on couple stress liquid with porous channel. This work considerable importance in many industrial applications like “Control Mechanism in Material Manufacturing”, “Manufactures of Electronic Chips”, “Crystal Formation”, “Scientific Treatment Problems of Irrigation”, “Soil Erosion and tile drainage” are the present focus of development of channel motion. The formulated physical liquid equations are subsequently calculated by shooting technique with R-K-F (“Runge-Kutta Fehlberg”) scheme. The velocity, temperature as predicted via graphically. we found the velocity dwindle, temperature high production by an escalating statistical value of K (“Couple Stress Parameter”), Ec (“Eckert number”) and Q (“Heat Generation parameter”) respectively. Gradient constraint in addition to improve by an enhancement into Bejan number for various values of “pressure gradient parameter”.

The improvement of heat transfer is the focus of this paper's innovative theoretical ternary hybridity nanofluid (HNF) prototype. In this examination, blood is employed as the conventional liquid, and the tri-hybrid nanomolecules Au, Ag, and TiO2 are submerged in it. The extension has been made in the conventional Tiwari and Das hybrid nanofluid model to transform it for the case of a trihybrid nanofluid. By consuming resemblance variables and the Keller box methodology (KBM) to resolve the ordinary differential equations (ODEs) resulting from the conversion of the liquid flowing and temperature formulas. The results are graphed, and it is shown that the tri-hybridity nanofluid (THNF) has greater thermal conductance than the HNF. The heat transference rate increases in the situation of an augmentation in thermal conduction and radiation effect which helps remove the toxic plaque from the blood flowing through arteries. This additional heat produced because of amplification in thermal radiative fluxing is used to open rigid arteries through which the blood is flow.

A novel EMHD dissipative second-grade nanofluid flow model is proposed exclusively in this numerical inspection for radiating copper-based ethylene glycol nanofluids to reveal the dynamical and thermal aspects of the studied homogeneous mixture during its unsteady two-dimensional stagnation point flow towards a horizontal electromagnetic actuator. Based on admissible physical assumptions and authenticated experimental correlations, the governing PDEs and BCs are derived appropriately for the nanofluid flow problem under consideration. After numerous rearrangements and non-dimensionalization treatments, the resulting ODEs and BCs are handled computationally with the help of a robust GDQ algorithm under the parametric control of several influencing factors, whose strengthening magnitudes affect probably the flow control process and heat transport mechanism. In this context, it proved graphically that the nanoparticles’ loading process exhibits dissimilar dynamical and thermal impacts as compared with the influences of the nanoparticles’ diameter size. Besides, the resistive dynamical effect of the utilized electromagnetic actuator reinforces thermally the enhancing role of the thermal radiative heat flux and Joule’s heating process within the nanofluidic medium.

Apart from the Buongiorno concept, no study was published that sufficiently examined the impact of nanoparticles on the extendable surface of the third-grade fluid prototype. The third grade nanofluid (3GNF) model's liquid simulation needs for Tiwari and Das are theoretically evaluated in the current work utilizing motor oil as the standard base liquid. Tiwari and Das' model look at the volume portion of nanoparticles for heat transfer enhancement as opposed to the Buongiorno concept, which primarily relies on thermophoretic and Brownian dispersion impacts. This analysis takes into consideration the Biot quantity, thermal radiative viscous flowing, slippage variable, Joule heating, and magneto variable, which are all thermal features of 3GNF. The Galerkin finite element methodology (G-FEM) mathematical structure is used to produce the computer solution. Copper/engine oil (Cu-EO) and titanium dioxide/engine oil (TiO2-EO) are considered. TiO2-EO nanofluid has a greater thermodynamic representation than Cu-EO nanofluid in the same conditions. The following rate range: 1.9%–43%, demonstrates Cu-advantage EO over TiO2-EO in terms of thermal conductivity. Additionally, the porous materials boundary's function is to increase the speed outlines whilst lowering the heating transduction rate. At the end of the day, the Reynolds and Brinkman values increase entropy.

Stoke's problems significantly impact several domains, including industrial manufacturing, geophysical flows, chemical engineering, and heat conduction. Stoke's second problem deals with the movement of a semi-infinite viscous incompressible fluid caused by an oscillating flat plate. Thus, this work examines Stoke's second problem for an unsteady hydromagnetic surface-driven flow along an infinite flat plate in the presence of thermal radiation and heat dissipation. The governing momentum and energy equations form an emerging nonlinear system of partial differential equations through dimensionless proxies. MAPLE 2022 is employed to solve the resulting system of nonlinear partial differential equations that control the flow both analytically and numerically in specific situations. The analytical solutions are displayed graphically, along with variations of skin friction and Nusselt number at the plate. It has been observed that momentum and thermal slips significantly diminished the flow characteristics to cause damping flow rate and temperature distributions. Rising the values of Magnetic and velocity slip parameters, an oscillatory motion is observed in skin friction. This is due to the periodic and wavy nature of the boundary wall. Furthermore, a rise in the Prandtl number and radiation value correspondingly boosted the wall heat gradient profiles. Finally, this study will assist industry and engineering in understanding the sensitivity of their working fluids to parameter variations and for the exact prediction of their base fluids.

Research is conducted on parametric heat transfer and fluid flow solutions under the influencing factors of the porous stretching cylinder, magnetic field, curvature, permeable media, radiation, Joule heating, viscous dissipation, and heat generation/absorption. High non-linear coupled PDEs are solved and result in high non-linear coupled ODEs. The confluent hypergeometric function solves the energy equation with the PHF (prescribed heat flux) boundary condition. An analysis of physical parameters' effects is presented as tables and figures. According to the results, the variation of radiation parameters and Eckert numbers for the local Nusselt number in the injection area is negligible, while the variation of the heat source/sink parameters is considerable. The suction/injection and curvature parameters directly affect the local skin friction coefficient and Nusselt number. The porous stretching cylinder has a higher skin friction coefficient and heat transfer rate when compared to the porous stretching sheet.