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Fluid flow across a Riga Plate is a specialized phenomenon studied in boundary layer flow and magnetohydrodynamic (MHD) applications. The Riga Plate is a magnetized surface used to manipulate boundary layer characteristics and control fluid flow properties. Understanding the behavior of fluid flow over a Riga Plate is critical in many applications, including aerodynamics, industrial, and heat transfer operations. The unsteady Micropolar nanofluid (UMNF) flow across a vertically oriented, nonlinearly stretchable Riga sheet is examined in the present study. The effects of variable thermal conductivity, thermophoretic force, and Brownian diffusion on flow and heat transfer are analyzed. The fluid flow has been expressed in the form of a nonlinear system of PDEs (partial differential equations), which are reduced into the non-dimensional form of ordinary differential (ODEs) by employing the similarity transformation approach. The dataset for training the ANNs using the Levenberg–Marquardt backpropagation (LMBP) technique is generated using numerical simulation methods. The influence of physical constraints on the dimensionless temperature, concentration, microrotation, and velocity distributions are graphically displayed and discussed. Numerical results for skin friction, Sherwood, and Nusselt numbers are presented in tabular form. The numerical outcomes are compared to both published numerical and experimental results for validity purposes. It can be noticed that the flow rate is enhanced with the rising influence of the Hartmann number, buoyancy force, and velocity slip parameter. The UMNF flow model is validated, tested, and trained with an average numerical error of 10−9, ensuring high accuracy in energy, velocity, microorganism motility, and concentration predictions. [ABSTRACT FROM AUTHOR]

The aim of this study is to perform analysis of nonlinear mixed convection flow of Carreau fluid due to curved stretched surface with slip condition. Furthermore, the effect of Darcy–Forchheimer and MHD is taken into consideration. The energy equation is modified by considering the variable thermal conductivity with Joule heating effect. The governing equations of the problem are highly nonlinear partial differential equations subjected to boundary conditions. Similarity transformations are used to transform nonlinear PDEs into ODEs. The numerical technique is used to solve this problem via bvp4c. The main outcomes of this research are that the impact of Forchheimer and porosity parameter tends to decrease the fluid velocity for shear thickening case. The velocity slip condition increases the fluid velocity only near the surface but the fluid velocity away from the surface does not get affected. The changing thermal conductivity raises the temperature of the fluid near the boundary. Furthermore, the impacts of various parameters on the velocity and temperature profiles are demonstrated. The values of local Nusselt number and skin friction for a different parameter are provided. [ABSTRACT FROM AUTHOR]

Synovial fluid is found in synovial joints, which act as a lubricant and shock absorber, that is crucial for the detection and treatment of diseases and injuries associated with the joints. It is significant for enhancing joint health diagnostics and treatment, improving drug delivery systems and advancing the understanding of complex fluid behavior and particle transport mechanisms in biomedical and engineering applications. The biological field utilizes complex analyses of condyloid, hinge, pivot and shoulder joints for current development. This work uses two viscosity models to examine the impact of activation energy and nonlinear heat source on the synovial fluid (SF) with thermophoretic particle deposition. The current model shows how the viscosity of an SF is affected by concentration and deformation. The impact of MHD and variable thermal conductivity on a heated disc is also investigated. The flow has been examined using the Arrhenius equation, which offers a mathematical explanation of how activation energy works in our system. PDEs are transformed into ODEs by employing the similarity transformation. The problem is solved by using the modified shooting method (bvp4c). This study focuses on the velocity, temperature and concentration profiles while presenting the physical significance of all the fluid parameters involved. These profiles are thoroughly described and shown graphically. The results show that when the magnetic parameter rises, the temperature profile rises and the velocity profile declines. The concentration profile decreases with higher values of the reaction rate parameter and the thermophoretic parameter and also increases with a higher value of the activation energy parameter. The flow of SF for model-I is significantly larger than that for model-II. [ABSTRACT FROM AUTHOR]

The present research focuses on the MHD second-grade nanofluid flow with induced magnetic field and viscous dissipation over an exponentially stretching surface. The solutal and thermal energy equations are analyzed in the presence of thermophoretic effect and variable thermal conductivity. The solutal and thermal slip boundary conditions are imposed on the surface of the sheet. In the mathematical modeling, the Brownian motion, and thermophoresis consequences are also discussed. The physical appearance of the induced magnetic field on the second-grade nanofluid is the central aim of this investigation. The mathematical flow model which is in the form of nonlinear PDEs is transformed into the system of couple ODEs by the usage of suitable similarity variables. These couple equations are tackled numerically with the help Bvp4c Matlab approach. The illustration of parameters on the flow model is discussed via graphs and tables. It is noted that the induced magnetic field profile and velocity of fluid intensify for the stronger values of second-grade parameter. Further, the numerical result shows that skin friction rate boosts via greater estimation of second-grade parameter and it reduces for magnetic Prandtl number. [ABSTRACT FROM AUTHOR]

The goal of this article is to examine the heat and mass transportation of a Maxwell fluid flow in the rotating frame with double stratification and porous medium through a linear stretching surface. The heat transfer scrutiny has been presented in the existence of Cattaneo-Christov theory and variable thermal conductivity. The suitable transformation is considered to modify the flow model into the nonlinear system of ordinary differential equations. The numerical computation for the nonlinear system of equations is built-in by the Bvp4c MATLAB approach. It is found that both rotation and stretching have a noteworthy impact on temperature and the velocity profile. Thermal stratification enhances the heat transfer rate as well as higher estimations of rotation parameter condense the heat flux. The novel idea of the present problem is to analyze the heat transfer and Maxwell fluid flow into the rotating frame along Cattaneo-Christov theory induced by the stretching sheet. A relative analysis of current computations with prevailing literature revealed an exceptional agreement. [ABSTRACT FROM AUTHOR]

The present work is implicated with the investigation of wave propagation in a homogeneous, isotropic, non-local microelongated viscothermoelastic solid half space with variable thermal conductivity under the dual phase lag (DPL) model. It is found analytically that three coupled longitudinal waves and one independent transverse wave exist in the medium which travel with distinct speeds. Reflection coefficients and energy ratios of various reflected waves are obtained analytically and presented graphically for aluminum epoxy-like material. The variations of these reflection coefficients are analyzed for different values of non-local parameter, microelongational parameter, viscosity and variable thermal conductivity. The expressions of energy ratios acquired in explicit form are also represented graphically as functions of the angle of incidence in accordance with the defined rule of conservation of energy. [ABSTRACT FROM AUTHOR]

Significance of magnetohydrodynamic effect on a viscous (temperature‐dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter S $S$ lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are θr ${\theta }_{r}$ [0.0, 1.0], Nr $Nr$ [0.0, 2.0], Pr $Pr$ [0.8, 1.5], Sc $Sc$ [0.5, 2.0], B* ${B}^{* }$ [0.0, 1.0], k1 ${k}_{1}$ [0.2, 3.0], fw ${f}_{w}$ [1.0, 2.0], M $M$ [0.0, 3.0], Du $Du$ [0.4, 1.0], and Sr $Sr$ [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement. [ABSTRACT FROM AUTHOR]

A mathematical model is analyzed to study the effect of various physical parameters related to non-isothermal flow of third grade fluid in the presence of thermal radiation through a porous medium. Hence, the objective of this paper is to investigate the combined impacts of magnetic field, viscous dissipation, thermal radiation, varying thermal conductivity and viscosity on non-isothermal flow of a third grade fluid with thermal radiation through a porous medium. The Galerkin weighted residual method was used to solve the resulting non-linear ordinary differential equations numerically. The graphic representation and discussion of the effect of various significant parameters on the flow system are presented. The investigation of this problem leads to the conclusion that the thermal radiation parameter, the variable thermal conductivity and viscosity parameters have a significant impact on the mass flow and the energy transfer phenomena in the system. [ABSTRACT FROM AUTHOR]

Mixed convection flows across the revolving bodies have eminent applications in science and technology, such as fibre coating, polymer deposition, centrifugal blood pumps, rotatory machinery, and so forth. In the current work, magnetohydrodynamic (MHD) flow and heat transfer characteristics of Casson hybrid nanofluid (Ag/MgO as nanoparticles) over the rotating sphere at the stagnation zone are being studied. Moreover, an analysis of heat transmission is conducted by considering the influence of thermal radiation, temperature‐dependent thermal conductivity, magnetic field, and viscous dissipation. The relevant partial differential equations are reformed into ordinary differential equations by appropriate transformations, which are solved using the successive linearization method (SLM). The thermal field, velocity components in x and z directions, heat transfer rate, and skin friction coefficient are computed for various physical quantities like rotation parameter mixed convection parameter, radiation parameter, Eckert number, Casson parameter, magnetic parameter, variable thermal conductivity parameter, and so forth. The current findings align well with the literature in a limiting sense. Thermal enhancement in hybrid nanofluid is observed for the viscous dissipation parameter (Ec), thermal conductivity parameter (ε), and radiation parameter (Rd). The degree of heat transfer rises from 12.8% to 20% when the Casson parameter's value (β0) increases. Also, a decrease of approximately 33% is depicted between the peak values of the velocity magnitude with an increase in rotation parameter. [ABSTRACT FROM AUTHOR]

The current work analyzes the role of various thermophysical variables in examining the Jeffrey model bioconvection phenomena in a stretched Darcy-Forchheimer medium. The non-Newtonian Jeffrey fluid model is significant because of its enormous applicability in the production of industrial fields, such as paints, oils, gels, and adhesives. Continuing measurements of the non-Newtonian model's flow dynamics and heat transfer shows complex fluctuations in the mass and heat flux rates. These observations, made under various physical conditions, help to clarify what its actual behavior is. The governing equations are converted to nonlinear ordinary differential equations utilizing a similarity transform and then solving analytically using the BVPh2.0 tool designed for optimal homotopic procedure in Mathematica. The temperature, velocity, concentration, and bioconvection microorganism analytical findings are generated and visually shown. Our investigation found that fluid velocity increased in the case of Jeffrey's fluid increase. Collisions between fluid particles produce Brownian motion, which increases fluid kinetic energy and nanoparticle activity and raises temperature; an increased Nt increases thermophoretic force, which pushes tiny particles far from the heated surface and produces a counter flow. By increasing the values of β and the velocity profile increases. The profile of velocity is greater for the boundary layer with thickness η = 0 without dimensions and then sharply decreases along the stretching sheet to zero. In the absence of magnetic fields, the profile of velocity is maximum, and in the presence of magnetic fields, it drops. By using the Jefferey model to investigate bioconvection in Darcy-medium, this work has practical implications that go beyond theoretical domains. These include groundwater management in environmental engineering and bioreactor optimization in biotechnology. Heat exchangers, distillation towers, cancer therapy, magnetic field-assisted wound healing, MHD Jeffrey fluid with porous media, and hyperthermia are just some of this fluid's industrial and medicinal uses. [ABSTRACT FROM AUTHOR]

This study presents a novel model for variable fluid properties of a ternary hybrid nanofluid with base fluid polymer suspended on a three-dimensional stretching sheet under the influence of magnetohydrodynamic forces. Viscosity and thermal conductivity are temperature-dependent. This model has potential for use in nanotechnology, particularly in the shaping and design of surfaces for devices that can stretch or contract, wrap, and paint. The nonlinear equations in charge of this physical problem are derived by using similarity transformations. The fluid behavior is examined using the Reynolds viscosity model. The coupled nonlinear governing equations and the necessary boundary conditions are solved using the shooting technique with RK-4. The numerical calculations, including velocity and temperature profiles, are presented graphically to give the results a physical interpretation. The table discusses skin friction and Nusselt numbers at various physical parameters. The study’s findings show that changing the stretching parameter causes a significant change in the flow characteristics. Particularly, the thickness of the boundary layer decreases as the volume fraction of nanoparticles rises. Furthermore, because temperature-dependent viscosity is taken into account, as the viscosity parameter increases, so does the temperature. Key results specify that the Nusselt number Nu{\rm{Nu}} increases with the increase in temperature-dependent viscosity α\alpha , while decreases with the increase in thermal conductivity ϵ\epsilon parameters. Impact of α\alpha shows more convective heat transfer. Greater values of ϵ\epsilon reduce the effectiveness of heat transfer.

Abstract The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

This article investigates the effect of activation energy on Carreau fluid flow in the presence of variable thermal conductivity, inclined magnetic field, melting heat transfer, and Soret and Dufour phenomena. A set of suitable similarity transformations is applied for transforming the governing partial differential equations (PDEs) considered for the physical phenomena into non-linear ordinary differential equations (ODEs). We obtained the results by solving the non-linear ODEs numerically which describe the behavior of the velocity, temperature, and concentration profiles of the fluid against the governing parameters and illustrated these graphically. The velocity distribution decreases for angle of inclination while it is increasing against higher melting parameter. The temperature distribution enhances with higher modified Dufour parameter and Prandtl number while it declines for thermal conductivity, activation energy, and melting parameters. The concentration distribution increases for melting parameter, Soret number, and activation energy parameter while decreasing for temperature difference parameter, Schmidt number, and reaction rate parameter. Skin friction, Nusselt and Sherwood numbers are evaluated numerically against the various governing parameters. Accuracy of the present work is illustrated and established through comparison carried out for skin friction versus magnetic parameter with existing results in the literature. [ABSTRACT FROM AUTHOR]

The solar radiations are absorbed in the form of heat energy by using the solar centering systems in solar collectors, this energy is then transmitted to nanofluid. This study concerns the production of entropy in a Maxwell nanofluid passed over an infinite horizontal surface. Then the non-linear stretching of the surface causes a flow in parabolic trough solar collector (PTSC). The similarity transformations are employed to transmute the system of PDEs into a system of solvable ODEs provided with the boundary conditions. Eventually, the classical Keller box scheme is applied to find the numerical solutions of transmutes ODEs. The analysis of two distinct nanofluids including copper-engine oil (Cu-EO) and zirconium dioxide-engine oil ZrO2-EO is taken into account and the results for both of them are discussed. The extracted results demonstrate a decline in Nusselt number with growing permeable media parameter and augmentation for increasing values of skin friction coefficient. A recent study is presented to provide information related to the enhancement of heat collector in the PTSC with Maxwell nanofluid. The minimal level of efficiency of Cu-EO over ZrO2-EO is 7.1% and the maximum level is up to 18.7%. [ABSTRACT FROM AUTHOR]

Purpose: The problem is concerned with the analysis of the reflection of the waves through a fiber-reinforced thermoelastic medium under the effect of the magnetic field, gravity, and the initial stress. The problem is discussed in the context of the three-phase-lag model and Green-Naghdi theory of type II and III with the memory-dependent derivative and variable thermal conductivity. Methods: The harmonic representation of waves is used to find the solution to the problem. Based on the solution, it is concluded that after reflection three quasi-waves propagate through the medium. Results: Numerical computations were performed using MATLAB software. The reflection coefficient ratio variations with the angle of the incident are shown graphically. Conclusion: Comparisons are made with the results predicted for different values of the thermal conductivity parameter, two-temperature parameter, initial stress, gravity field, and different values of the magnetic field. [ABSTRACT FROM AUTHOR]

This paper investigates the Magnetohydrodynamics (MHD) convective flow over a cone with the influence of viscous dissipation, variable viscosity, chemical reaction and variable thermal conductivity effects. Related equations are tackled by the Homotopy analysis method (HAM). The impacts of physical variables on concentration, velocity and temperature are presented through numerical tables and graphs. It is noticed that the heat transfer rate (Nusselt number) increases against Prandtl number. Similarly, the mass transfer rate (Sherwood number) increases against Schmidt number. Also, it is seen that skin friction in tangential and azimuthal direction increases against the buoyancy forces ratio parameter. Current results are validated with previous literature work. [ABSTRACT FROM AUTHOR]

Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow. [ABSTRACT FROM AUTHOR]

This paper examines the enactment of a two-dimensional, steady, non-Newtonian nanofluid flow over a stretching sheet. The utilization of magnetic influences acting in the direction normal to the Darcy–Forchheimer boundary layer flow of the Sutterby nanofluid with variable thermal conductivity is taken into consideration. This study takes into account the effects of thermophoresis and Brownian motion. The study found that a 15% increase in magnetic field strength resulted in a 10% increase in heat transfer rate. Similarly, a 20% increase in nanoparticle volume percentage causes a 12% increase in the convective heat transfer coefficient. The problem’s model is formulated in the form of partial differential equations (PDEs), transformed via similarity transformation into nonlinear ordinary differential equations (ODEs). Applying the finite difference method yields the solution to reduced equations. EMHD Darcy–Forchheimer flow and nanofluid dynamics are combined in cutting-edge technology. This is important for many industrial and technical applications. Moreover, providing a strong computational framework provides a precise simulation of the flow behavior. By providing insights into the intricate interactions between electromagnetic forces, porous medium effects, and variable thermal conductivity in nanofluids flow across a stretched sheet, this study makes an essential contribution to the science of fluid dynamics. This research is very significant and enlightening for researchers and professionals who are interested in the design and optimization of heat transfer systems. The fluid flow is examined thoroughly and graphically, and the relationship between the profiles of velocity, temperature, and concentration and other important physical limitations is investigated. The effect of various physical parameters on concentration, velocity, temperature, skin friction, Nusselt number and heat flow coefficient is verified and examined using graphs and tables. [ABSTRACT FROM AUTHOR]

In the fluid transport processes extent of irreversibility causes entropy generation that leads to degrading the life span of any engineering system. The main objective of this investigation is to enhance the span of the system by analyzing the effects of various physical parameters. A nanofluid flow over an inclined stretching cylinder is studied to measure entropy generation due to thermal conductivity, Soret and Dufour effects along with viscous dissipation and internal heat source. Buongiorno model is considered as a base structure. The mathematical equations so formed are solved by shooting technique with Gill's fourth order method. Numerical results are validated with Homotopy analysis method through Bvph2.0. Effects of various parameters have been investigated on transport processes like axial velocity, temperature profile, and nanofluid concentration profiles. It seems that higher intensity of the applied magnetic field (M = 0, 1, 2), variable thermal conductivity (ε = 0.1, 0.3, 0.5), and Brinkman number (Br = 0.35) generates more entropy that degrades the system's life. Magnetic parameter and group parameter (1 ≤ Br/Ω1 ≤ 3), changing thermal conductivity all leads to a rise in entropy. In the study, group parameter reducing Bejan number that makes system more sustainable that full fills the aim of the study. Such physical situations generate more entropy must be reduced or avoided to make the system more efficient and long-lasting. [ABSTRACT FROM AUTHOR]

Peristalsis of non-Newtonian nanofluid via a non-uniform conduit has several applications in physiology and industry. This study proposes a mathematical model as well as exploration of the impacts of entropy generation for peristalsis of magneto nanofluid with temperature-dependent thermal conductivity via an expanding asymmetric channel. Buongiorno's model for study of nanofluid flow has been adopted. Rheological aspects are accounted using the Carreau–Yasuda model due to its experimentally validated significance. Impacts of applied electric and magnetic fields have been taken into account. Thermophoresis, ohmic heating, viscous heating and Brownian motion effects are incorporated in the model. Numerical method is used via NDSolve in Mathematica after implementing the lubrication approach and Debye–Huckel linearization. The effects of embedded parameters on the flow, heat transfer, entropy generation and Bejan number are studied using graphical depictions. Outcomes indicate that a rise in electroosmotic parameter enhances heat transfer rate, whereas it reduces entropy generation and mass transfer rate at the boundary. Therefore, this study can provide basics to study nanofluidic systems which has applications in drug delivery. Increasing trends for temperature, heat transfer rate and entropy generation, while declining trends in the concentration of the particles are noted for higher joule heating. [ABSTRACT FROM AUTHOR]

AbstractOwing to the improved thermal applications of nanomaterials, various applications have been suggested in various era of engineering including heat transfer devices, chemical processes, thermal management devices, electronic cooling etc. The aim of current investigation is to presents the bioconvective flow of nanofluid with applications of multiple slip effects. The motivations for considering the slip effects for heat and mass transfer analysis are associated to its significance in the petroleum sciences, extrusion processes, oil recovery and plasma physics. The nonlinear thermal radiation effects and chemical reaction consequences have been attributed. In contrast to traditional investigations, the thermal conductivity of nanofluid have been assumed to be temperature dependent. Following the assumptions of dimensionless variables, a system of nonlinear differential equations is obtained. The shooting technique is employed for computing the numerical simulations. The accuracy of solution is ensured. The physical assessment of problem is incorporated in view of involved parameter. It has been claimed that interaction of slip effects enhances the heat and mass transfer effects. Change in microbes density slip parameter leads to improvement in the microorganisms profile. Moreover, local Nusselt number and Sherwood number reduces for slip parameters. Current results present significance in heat transfer systems, thermal engineering, chemical engineering, fertilizers, biofuels etc. [ABSTRACT FROM AUTHOR]

In engineering and industrial processes, hybrid nanofluids, an advanced form of nanofluid, are used to improve thermal efficiency. Hybrid nanofluids have various uses in refrigeration, tumor treatments, power stations, cooling systems, food processing, biomedical devices, and solar thermal systems. Thus, the major purpose of this article is to examine the heat transport features of a hybrid nanofluid on the dynamics of Zn-Ti6Al4V/H2O. The flow phenomenon of such fluid is produced by a shrinking disk when momentum and the thermal phenomenon are maintained. The classical transformation is employed to alter the flow model of a hybrid nanofluid in the form of non-linear ODEs. The produced model is tackled numerically through the MATLAB solver bvp4c function. The aspects of different emerging physical constraints on the flow field, fluid temperature, drag friction, and Nusselt number are exemplified thoroughly. The study finding reveals that the addition of a hybrid nanofluid in a flow system shows a promising increase in thermal transportation rate. The friction drags coefficient and thermal transportation rate show an upsurge in both solution branches for an increment in the suction parameter. Furthermore, higher values of the thermal conductivity parameter show an enhancement in fluid temperature for both branches.

The current investigation delves into the tangent hyperbolic Williamson hybrid nanofluid flow featuring varying thermal conductivity through the Darcy–Forchheimer medium across an exponentially stretching cylinder. Incorporating the activation energy and chemical reaction effects into consideration also strengthens the mathematical model's vitality. The considered hybrid nanofluid comprises silver and molybdenum disulfide nanoparticles submerged in the water. The highly non-linear system of equations is solved utilizing the MATLAB bvp4c approach. The influences of the leading variables versus involved fields are demonstrated through graphical delineations and tables. The core findings demonstrated that a strong Weissenberg number and Darcy-Forchheimer factor decay the velocity curve and strengthen the thermal curve. Also, the fluid concentration is enhanced for escalating activation energy and tangent hyperbolic factor. Additionally, the hybrid nanofluid betokens substantially enhance the thermal transportation rate of up to 8.8 % in contrast to nanofluid. Also, in contrast to the nanofluid and Williamson hybrid nanofluid, the hybrid nanofluid exhibits notably higher mass and thermal transport rate. This study is a noteworthy advancement in the disciplines of fluid dynamics and nanofluid research, as it provides promising potential for optimizing the transfer of mass and heat in a wide range of engineering and industrial contexts. The findings exhibit good agreement when contrasted with previously published work.

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.

This paper investigates the characteristics of ternary-hybrid nanoliquid for time-dependent Darcy-Forchheimer flow. Formulation is based for mixture of water subject to ternary nanoparticles with different shapes like (platelet, spherical and cylindrical). Heat transfer consists of convective condition, radiation and heat generation. Appropriate variables are used to generate dimensionless nonlinear system. Analysis is carried out for Cattaneo-Christov heat flux and variable thermal conductivity. Finite difference method (FDM) is utilized to construct solutions. Salient characteristics of sundry variables are discussed. Analysis is carried out for Nusselt number and skin friction. Present results may have relevance in renewable energy process, polymer extrusion and metallurgy.

A mathematical model is analyzed to study the effect of various physical parameters related to non-isothermal flow of third grade fluid in the presence of thermal radiation through a porous medium. Hence, the objective of this paper is to investigate the combined impacts of magnetic field, viscous dissipation, thermal radiation, varying thermal conductivity and viscosity on non-isothermal flow of a third grade fluid with thermal radiation through a porous medium. The Galerkin weighted residual method was used to solve the resulting non-linear ordinary differential equations numerically. The graphic representation and discussion of the effect of various significant parameters on the flow system are presented. The investigation of this problem leads to the conclusion that the thermal radiation parameter, the variable thermal conductivity and viscosity parameters have a significant impact on the mass flow and the energy transfer phenomena in the system.

The study of nanofluids is important due to valuable applications in drug delivery systems, thermal processes, solar management systems, microfluidic devices, extrusion phenomenon, chemical processes etc. The objective of current analysis is to investigates the enhanced thermal performances of magnetized Casson nanofluid with suspension of microorganisms. An unsteady periodically oscillating flow due to bidirectional moving porous surface have been considered. The analysis is subject to assumptions of variable thermal conductivity. The modelled problem is based on implementation of modified Fourier theories. The Buongiorno nanofluid model is used to predicts the significance of Brownian motion and thermophoresis effects. Chemical reaction species are also attributed. For solution methodology, homotopy analysis scheme is implemented. The convergence region is specified. The physical impact of problem is visualized. The significant applications of parameters have been focused. The claimed results offer significance in cooling systems, chemical reactions, air conditioning, solar thermal systems, automotive radiators, heat exchangers in power plants etc.

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature.

In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.

AbstractThis paper analyzes the flow of the Reiner-Rivlin hybrid nanofluid, considering the magnetic field and varying thermal conductivity between two spinning disks. Appropriate similarity variables are used to transform all dimensional equations into dimensionless form. A semi-analytical homotopy analysis approach applied to solve dimensionless equations and velocity profiles, temperature distribution, Nusselt number, skin friction, entropy generation, and Bejan number are presented graphically. Some key outcomes include that axial and tangential velocities decreases when porosity parameters increase. Additionally, higher Eckert number when varying from 1 to 1.3, increases the temperature near the center of the two disks from 1.02 to 1.18. The heat transfer rate goes up from 10.2767 to 10.3043 when thermal conductivity rises from 0.1 to 0.7. The entropy generation grows in proportion to the Brinkman number, Reynolds number, and the porosity parameter values. This research might enhance cooling, lubrication, and thermal management in automotive, aerospace, and biomedical industries. [ABSTRACT FROM AUTHOR]

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced. [ABSTRACT FROM AUTHOR]

In this study, we have investigated magnetohydrodynamic Couette flow across a deformable porous regime with entropy generation having equal suction and injection velocities. The aim of this work is to analyze the novel impact of thermophoresis deposition, activation energy, and magnetic effect by considering viscosity and thermal conductivity as dependent on temperature in a deformable porous regime. The dimensional equations are turned into nonlinear ordinary differential equations (ODEs) through proper similarity variables. To solve these ODEs, we utilized the MATLAB bvp4c approach. Graphs are used to study the behavior of many physical parameters such as skin friction, Bejan number, velocity, displacement, entropy generation, concentration, and temperature. It is found that the viscosity parameter reduces the solid displacement, whereas it enhances the fluid concentration. Due to the impact of suction/injection and drag parameters, fluid velocity becomes reduced. The thermal conductivity parameter raises entropy generation and temperature, but it decays the Bejan number. The volume fraction parameter plays an interesting behavior in skin friction. Moreover, the current work is compared with prior research work while neglecting the newly introduced effects, and the results remain consistent. [ABSTRACT FROM AUTHOR]

This research investigated the impact of Sorret and Dufour on the flow of Sutterby nanofluid over a stretchable Riga sheet while considering the variable thermal conductivity. The analysis was based on the Buongiorno nanofluid model, and nonlinear partial differential equations were formulated using the governing laws and applying the boundary layer approximations. These equations were transformed into ordinary differential equations using appropriate similarity variables. The bvp4c numerical scheme in MATLAB was used to calculate numerical and graphical results. The figures show how various parameters affect the velocity, temperature, and concentration profiles. Additionally, numerical results of the skin friction, Nusselt number, and Sherwood number for various parameters were presented in tables. The velocity distribution profile decreases with an increase in the Sutterby fluid parameter value but increases with the modified Hartmann number. The temperature profile rises with increased Dufour number and thermal conductivity. The concentration profile decreases with an increase in the Schmidt number and chemical reaction but increases with an increase in the Soret number. [ABSTRACT FROM AUTHOR]

The suspension nanoparticles in non-Newtonian materials convey different applications in the thermal systems, engineering processes, industrial energy developments, extrusion systems, solar system, etc. It is commonly observed that the thermal properties in the various base materials fluctuated and cannot be assumed to be constants. A decomposition of nanofluids is fluctuated and cannot considered as a constant. The objective of this communication is to inspect the thermal mechanism of non-Newtonian nanofluids due to accelerated frame in view of variable thermal conductivity. The modified mathematical relations for Fourier and Fick theories are utilized to model the problem. The nanofluids contain the microorganisms to ensure the thermal stability. The problem is modeled in nonlinear partial differential system which is further communicated via HAM. The convergent analysis is ensured and later on physical illustrations to problem in view of parameters are discussed. It is observed that thermal phenomenon controls due to mixed convection parameter while increasing impact for Williamson fluid parameter is observed. The magnitude of oscillation of Nusselt number due to Prandtl number is enhanced without any phase difference. The obtained results may convey different engineering applications like extrusion systems, chemical processes, thermal management systems, heating and cooling application, plasma, manufacturing processes. [ABSTRACT FROM AUTHOR]

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature. [ABSTRACT FROM AUTHOR]

Presently, due to its extraordinary mechanical, thermal, electrical and biomedical facets nanofluids deliver several prospects to exaggerate the propensity of isothermal systems by augmenting the conductivity features of the host fluids. In various areas of the energy partition, nanoparticles show a remarkable measure in energy storage, energy variation, and energy convertible, i.e. thermoelectric plans, petroleum cells, supercapacitors, stellar cells, rechargeable batteries, light-radiating diode and carbon-based light-radiating diode, smart coatings. In this current conversation, we anticipated an unsteady 3D flow of the Sutterby nanofluid consequence of a bidirectional extended surface. To envision the thermophoresis and Brownian motion properties in Sutterby's nanofluid, the Buongiorno association is utilized in an additional refined technique. Variable thermal conductivity with heat source/sink property occurred deliberated considering heat transmission techniques. The appropriate transformation is applied for transposing the PDEs into nonlinear ODEs. For numerical results, the bvp4c programmed is prerequisite for elucidating the subsequent Ordinary differential equations. The distinct performance of the Sutterby nanofluid temperature and the concentration field are designated and discussed in the physical parameter's aspect. It is clear that the temperature of the Sutterby fluid decreases with respect to the ratio of stretching rates parameter and similar developments are observed for the thermophoresis and Brownian motion parameters. Furthermore, the concentration profile declines for sophisticated estimates of the Lewis number and thermophoresis parameters. [ABSTRACT FROM AUTHOR]

The present numerical investigation uncovers the flow, heat, and mass transfer of ethylene glycol-based nanofluid (BN-EG) led by the combined impacts of peristaltic pumping and electroosmosis. The thermal conductivity of carrier liquid is deemed to change with temperature. Further, the features of electric field, Ohmic heating, radiative heat flux, mixed convection, and magnetic field are taken. Mathematical modeling is conducted under the assumption of lubrication theory. The nonlinear-coupled equations are addressed numerically by implementing Shooting method. The effective results of all physical constraints linked with the flow model are vigilantly studied and highlighted through various curves. The observations obtained from current analysis reveal that temperature augments with higher electroosmotic parameter. However, the Joule heating parameter increases the rate of heat transmission, while a lower rate of heat transfer is perceived for the radiation parameter. An increment in Helmholtz–Smoluchowski velocity increases the velocity profile. Pressure gradient rises in a forward way when electrical field favors peristaltic flow. Concentration of nanomaterial considerably declines when concentration Grashoff number is assigned higher values. [ABSTRACT FROM AUTHOR]

Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations' model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of a / c = 0. 5 , while it depicted the counter behavior for a / c = 1. 5. The skin friction is heightened with improving values of Re because R e boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of M p cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of β. [ABSTRACT FROM AUTHOR]

Purpose: This paper demonstrates the way tangent hyperbolic nanofluid flow through a vertical cone is influenced by varying viscosity and varying thermal conductivity. This study also seeks to illustrate the impact of convective boundary conditions on a fluid. The mathematical modeling also takes the Darcy–Forchheimer effect into account.Methodology: Using the appropriate similarity transformation, the fluid problem is reduced into a set of nonlinear ordinary differential equations. These systems of differential equations are evaluated numerically by applying the Optimal Homotopy Asymptotic Method.Findings: The nature of emergent parameters is examined in relation to the temperature distribution, nanoparticle concentration profile, and velocity profile. An increase in variable viscosity corresponds to a decrease in fluid velocity, while enhanced thermal conductivity results in elevated fluid temperature. The skin friction coefficient, Sherwood, and Nusselt numbers are numerically examined for active concerned parameters. These findings can be put into practice in a variety of fields such as polymer cooling systems and medication.Originality: Existing literature has yet to explore the combination of tangent hyperbolic nanofluids with varying viscosity and thermal conductivity under convective boundary conditions. [ABSTRACT FROM AUTHOR]

AbstractIn this instigation, the heat and mass transfer pattern on Eyring-Powell nanofluid with suspension of dust particles is focused. For heat transfer phenomenon, the Eyring-Powell nanofluid capturing the variable thermal conductivity. Furthermore, the variable and mass diffusivity assumptions are entertained for summarizing the observations chemical reaction phenomenon. The flow is endorsed to magnetic force impact. The additional impact of Brownian motion and thermophoresis consequences have been adopted. The numerical computations with shooting technique are performed. The physical aspects of parameters have been observed graphically. Based on depicted observations, it is examined that the fluid velocity reduces due to interaction velocity parameter which reverse trend is noted for dust particles velocity. The temperature profile for dusty fluid particles enhanced due to interaction parameter for temperature. Furthermore, the concentration profile reduces due to concentration interaction parameter. Current results present applications in solar energy, thermal processes, heat transform devices cooling systems, plasma, manufacturing processes, energy systems, etc. [ABSTRACT FROM AUTHOR]

The influences of variable viscosity and thermal conductivity on a steady, laminar, viscous, incompressible, hydromagnetic flow passing through a channel filled with a porous medium are investigated. The effects of heat source, thermal radiation, thermophoretic deposition, and Soret and Dufour numbers are considered. The governing equations are solved by the MATLAB bvp4c solver. It is found that increases in the viscosity parameter, thermal conductivity parameter, and the thermophoretic coefficient reduce the fluid velocity, while increasing radiation parameter and Dufour number enhance it. An increase in the thermal conductivity parameter raises the concentration, but reduces the temperature. The influences of the relevant parameters on the skin friction and Sherwood and Nusselt numbers are presented in tabular form and analyzed. [ABSTRACT FROM AUTHOR]

Heat, mass transfer, and non-Newtonian fluid flow processes have gained significant interest in various industrial applications due to their substantial significance in the fields of technology, engineering, and science. The aforementioned processes hold significance in the context of polymer solutions, porous industrial materials, ceramic processing, oil recovery, and fluid beds. This study aims to investigate the impact of temperature-dependent viscosity and thermal conductivity on the cilia-driven flow of tangent hyperbolic fluid with mass and heat transfer. The objectives include analyzing how these variable properties affect the velocity, temperature, and concentration profiles within the fluid flow, thereby providing insights into potential applications in bioenergy systems and enhancing the understanding of non-Newtonian fluid dynamics. Viscous dissipation has been taken into consideration. Firstly, governing nonlinear coupled equations are solved in a fixed frame, and then the results are tracked in the wave frame. MATHEMATICA's NDSolve command is utilized to graphically discuss the findings for several different flow parameters. Analytically stated, solving a problem with such a coupled and nonlinear system is tough. The effect of new parameters is discussed on velocity and temperature profile and graphically shown. It has been observed that the thermal conductivity is improved at moderately low temperatures, whereas the opposite pattern is seen at comparatively high temperatures. On the other hand, the temperature distribution demonstrates a behaviour consistent with lowering as the number of heat Bolus increases. The findings that were provided offer beneficial insight into bioenergy systems and serve as a helpful benchmark for both experimental and extra-progressive computational Multiphysics models.