Cattaneo-Christov Heat Flux Model Research Articles

Numerical study of hybrid binary Al2O3-Cu-H2O nanofluid coating boundary layer flow from an exponentially stretching/shrinking perforated substrate with Cattaneo-Christov heat flux, heat source, suction and multiple slip effects

Modern coating systems are increasingly deploying nanomaterials which offer improved thermal performance. The optimization of these systems can benefit from more elegant fluid dynamic models of the coating process. Inspired by these advancements, the present investigation introduces a novel mathematical model to analyze the boundary layer transport in Al2O3-Cu-H2O hybrid binary nanofluid coating deposition on an exponentially stretching porous substrate (sheet). Lateral mass flux (suction) at the wall is also considered a heat source (generation) for hot spot manufacturing effects. To add further sophistication to the thermal conduction model, a non-Fourier approach is adopted which accurately incorporates thermal relaxation effects i.e. the Cattaneo-Christov heat flux (CCHF) model. The Tiwari-Das volume fraction nanoscale formulation is implemented for different combinations of Alumina (Al2O3) and Copper (Cu) metallic nanoparticles in an aqueous base fluid (H2O). Hydrodynamic wall and thermal slip are also included as they feature in coating processes. The fundamental equations governing mass, momentum, and energy conservation, along with the corresponding conditions at the wall (substrate) and free stream, are made dimensionless through suitable scaling similarity transformations. The resulting nonlinear coupled ordinary differential boundary value problem is subsequently addressed using the efficient MATLAB bvp4c routine. Special cases of the non-Fourier model are validated against published results, and the general model is further confirmed through validation using an Adams-Moulton 2-step predictor-corrector algorithm (AMPC). Furthermore, dual solutions of the generalized model are extracted and visualized. A comprehensive study of the effects of key thermophysical key parameters on momentum and thermal characteristics (velocity, temperature, skin friction and local Nusselt number) is conducted and solutions are visualized graphically. The computations show that higher temperatures are present with intensification in the thermal relaxation parameter (Cattaneo-Christov hyperbolic model parameter), which predicts therefore larger temperatures than the classical Parabolic heat conduction model using Fourier analysis. Effectively, thermal relaxation is responsible for finite heat wave propagation and produces more accurate estimations of heat transfer than the Fourier model. An increase in stretching parameter enhances the skin friction coefficient and elevates the local Nusselt number. As the thermal relaxation parameter increases, the temperature magnitudes corresponding to the first and second solutions are both enhanced as are thermal boundary layer thicknesses. An increase in wall suction induces an escalation in the first solution for velocity whereas it reduces the second solution velocity. Stronger wall suction suppresses temperatures. With increasing thermal slip, the boundary layer is cooled i.e. temperature plummets and thermal boundary layer thickness is decreased. Strong deceleration is induced with greater hydrodynamic (velocity) slip. Both first and second solutions for skin friction are elevated with shrinking whereas they are depressed with stretching. With greater velocity slip both the first and second solutions for skin friction are depleted with greater velocity slip for the shrinking case, whereas they are generally enhanced for the very strong stretching case. The computations offer some new insights into multi-physical thermal fluid dynamics of nanofluid-based coating systems.

Insight into the dynamics of bioconvective Walter’s-B nanofluid flow subjected to Cattaneo–Christov heat flux and activation energy

In order to study the implementation of the generalized magnetohydrodynamic (MHD) bioconvective aspects of the Walter’s-B fluid flows over a convectively heated stretched sheet in the presence of activation energy and numerous boundary conditions, the non-homogeneous nanofluid flow model is used. Here, the nonlinear differential equations illustrating the current nanofluid flow model of non-Newtonian fluid explicitly include the concentration of both motile microbes and solid nanoparticles. Furthermore, the associated temperature, impact of thermal radiation and the Cattaneo–Christov heat flux model are discussed. The similarity transformations are formally displayed to transfer the consequential reduction in the mathematical complexity of the existing physical situation by converting partial differential equations (PDEs) into a nonlinear associated framework of ordinary differential equations (ODEs). Furthermore, the homotopy analysis method (HAM) through the MATLAB tool is used to numerically solve the dimensionless similarity equations. The results are extremely well demonstrated. In this manner, the significant engineering procedures are more accurately and entirely estimated before being reported. The results of the fixed physical factors of velocity, temperature, concentration, and microbe concentration profiles are effectively demonstrated through multiple types of illustrations and comprehensive explanations. The principal assumption is that the greater significance of the bioconvection Lewis and Peclet numbers can lead to a drop in the microbe concentration profile. It is observed that the concentration profile is reduced with the greater value of the concentration relaxation parameter.

Pulsatile flow of blood and Cattaneo Christov heat flux model in diseased arteries with variable properties

ABSTRACT The current effort is executed to interpret the heat transmission of combined stenosis and aneurysm in an artery, taking into account variable properties such as viscous dissipation and thermal radiation. We reduced the two directional energy and momentum equations to unidirectional flow by normalizing them under the mild stenotic assumption. After that, a mathematical framework for the physical problem is developed. An intricate nonlinear set of partial differential equations results from this formulation. A suitable numerical method of finite difference is employed on consequent equations to solve them. Afterward, graphical results predict the region of flow and the influence of involved parameters is shown in pictorial form. Furthermore, these solutions are employed to test how certain parameters, like streamlines, flow rate, and wall shear stress, affect blood flow. Using streamlines, we will also observe the general behavior of blood flow patterns.

Magnetized water-based hybrid nanofluid flow over an exponentially stretching sheet with thermal convective and mass flux conditions: HAM solution

Abstract The boundary-layer flow on a shrinking/contracting sheet has abundant industrial applications, which include continuous glass casting, metal or polymer extrusions, and wire drawing. In this regard, the present analysis focuses the hybrid nanofluid flow on an exponentially extending sheet. The water-based hybrid nanofluid flow contains CoFe2O4 and TiO2 nanoparticles. Heat transfer rate analysis involves the utilization of the Cattaneo–Christov heat flux model. Moreover, the Brownian motion and thermophoresis effects are used in this novel work. The mathematical model is presented in the form of system of partial differential equations, which is then transformed into system of ordinary differential equations (ODEs) using the similarity variables. The system of ODEs is evaluated by homotopy analysis method. The variation in the flow profiles has been investigated using figures and tables. The conclusions demonstrate that the effect of magnetic parameter is 52% better for hybrid nanofluid flow than for the pure water. Conversely, the increasing magnetic parameter diminishes the thermal transfer rates for water, TiO2–H2O, CoFe2O4–H2O, and TiO2–CoFe2O4/H2O. The increasing thermophoresis parameter upsurges the thermal flow rate of nanofluids and hybrid nanofluid, while the increasing Brownian motion parameter lessens the thermal transfer rates of nanofluids and hybrid nanofluid. The increasing effect of thermophoresis parameter is 39% better for hybrid nanofluid than for the base fluid. However, the declining impression of Brownian motion factor is 48% greater for hybrid nanofluid related to pure water.

Non-Fourier Heat Flux Model for the Magnetohydrodynamic Casson Nanofluid Flow Past a Porous Stretching Sheet using the Akbari-Gangi Method

The Casson fluid flow with porous material in magnetohydrodynamics is examined in this work. Additional semi-analytical results are investigated using the Silver-Water nanofluid. The Akbari-Ganji Method (AGM) is used to solve the semi-analytical Cattaneo-Christov heat flux model after taking thermal radiation into account. With the use of appropriate parameters, such as the relaxation time parameter, Prandtl number, radiation parameter, magnetic parameter, and so on, the normalized shear stress at the wall, temperature profile, and rate of heat flux may be examined. This issue has numerous industrial applications and technical procedures, such as the extrusion of rubber sheets and the manufacture of glass fiber. The main physical application is the discovery that a rise in the thermal relaxation parameter and Prandtl number maintains a constant fluid temperature.

Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model

Abstract This study investigates the complex dynamics of a viscoelastic fluid subjected to magneto-hydrodynamics over a stretching sheet, incorporating the Cattaneo–Christov heat flux model. This model is especially advantageous for explaining heat transfer in materials possessing significant thermal conductivity, where the conventional Fourier’s law might not be precise. The investigation revolves around evaluating how the thermal relaxation time affects the boundary layer and how both thermal radiation and viscous dissipation influence the thermal field. The significance of this research lies in its contribution to understanding the intricate behavior of such fluids in the presence of magnetic fields and non-Fourier heat conduction. The primary objective is to analyze the impact of viscoelasticity, magnetohydrodynamics, and Cattaneo–Christov heat flux on the flow and heat transfer characteristics over the stretching sheet. The research methodology involves the application of mathematical models and numerical techniques, particularly the use of the shifted Chebyshev polynomials of the sixth-order approximation and spectral collocation technique. The major conclusion of the study underscores the significant influence of viscoelasticity, magnetic field, and Cattaneo–Christov heat flux on the transport properties of the fluid, providing valuable insights for applications in various engineering and industrial contexts. Certain notable results arising from the current issue indicate that heat transfer is more pronounced for the viscoelastic factor and magnetic parameter, whereas the thermal relaxation parameter exhibits the opposite trend. In addition, the inclusion of the Cattaneo–Christov term enhances our comprehension of thermal behavior.

Numerical illustration of diffusive flow of blood-based tri-hybrid nanofluid generated by a curved stretching sheet using law of porosity

The study of flow of blood through the blood vessels carries nanoparticles which opens new ways in the research. This study explores one such flow of trihybrid nanoparticles suspended in blood over a curved stretching surface which undergoes the Darcy-Forchheimer porosity model. The analysis employs Cattaneo-Christov heat flux model along with chemical reaction, linear heat source allowing the surface to slip with heat and mass convection. The trihybrid nanofluids consist of a mixture of titanium dioxide, iron oxide, and silica nanoparticles mixed with base fluid (blood) to generate TiO 2 - Fe 3 O 4 - SiO 2 /blood hybrid nanofluids. Runge-Kutta-Fehlberg 4th–5th order technique, a robust numerical technique, was employed to obtain mathematical solutions. Throughout the numerical process, all parameters, except those under examination, were kept at their default values. Additionally, various plots were generated based on numerical results to illustrate the obtained data. The findings indicate that an increase in the Forchheimer number and porosity results in a reduction in the velocity profile. Furthermore, an increase in the radiation parameter and thermal Biot number leads to an increase in the temperature profile, while the temperature profile decreases with an increase in the thermal relaxation parameter. Additionally, an increase in the chemical reaction parameter and concentration Biot number results in an increase in the concentration profile. Moreover, higher Brinkman and Prandtl numbers enhance the Nusselt number.

Evaluation of homogeneous-heterogeneous chemical response on Maxwell-fluid flow through spiraling disks with nonlinear thermal radiation using numerical and regularized machine learning methods

ABSTRACT The present study addresses the effects of nonlinear thermal radiation and heat fall/rise on the thermal radiated viscoelastic fluid flow through spiraling disks with a homogeneous and heterogeneous chemical response. The properties of the Cattaneo-Christov heat flux model, a revised model of conventional Fourier’s law that predicts thermal relaxation properties, are examined in detail. The rotation of both the disks in the same and opposite directions is evaluated. The effect of heterogeneous-homogeneous chemical reactions is also considered in the present communication, making the study reasonably adaptable. The coupled partial differential equations, such as energy, momentum, and concentration, are transformed into ordinary differential equations by von Kármán variables. The outcomes of the present work confirm that flow behavior is reversed due to stretching action. Velocity and pressure profiles are reduced with the impact of Deborah’s number. In addition, it is noticed that increasing heterogeneous-homogeneous reaction parameters decreases the fluid concentration. Numerically computed values are compared with the predicted results using L.R. regularized L.R. and regularized S.V.R. It is observed that the regularized L.R. method outperformed the other two machine learning methods. Graphical illustrations of axial, radial, and tangential flows and concentration and temperature profiles are illustrated in graphs.

Effects of MHD and thermal radiation on non-Newtonian fluid with Cattaneo–Christov heat over a stretching flow surface

In this study, we are investigating the flow of an incompressible Williamson fluid using a Cattaneo–Christov heat flux model, with consideration for a magnetic Reynolds number that is not high. This fluid flows over a linearly stretched 2-D surface and is affected by a magnetic field, thermal radiation-diffusion, and heat generation. To model the Williamson flow, we apply a boundary layer approximation and develop the ordinary differential equations. The system of differential equations is transformed into a system of ordinary differential equations using a suitable transformation. We utilize the Iterative Runge–Kutta fourth-order scheme to numerically solve the boundary conditions associated with the nonlinear, dimensionless ordinary differential equations. Graphical representations of the results are employed to analyze the impact of physical properties on velocity, temperature, and concentration, with the numerical results presented in tabular form. Upon comparing our findings with previously published results, we have found them to be in good agreement. The velocity decreases as the Williamson fluid factor gradually increases. Williamson fluids are recognized for their shear thinning behavior, wherein viscosity decreases as the shear rate increases. However, higher parameter values can lead to increased fluid viscosity, potentially reducing the degree of shear thinning. This phenomenon results in a more uniform viscosity profile across varying shear rates, contributing to a reduced velocity distribution within the fluid.

MHD flow of Carreau fluid over a curved stretching surface with Cattaneo–Christov heat flux model and chemical reaction

The numerical investigation of the mixed convection transport of Carreau fluid due to stretched sheet, along with the combined effect of MHD and first-order chemical reaction is taken into account. The energy equation is modified by considering the effect of the Cattaneo-Christov heat flux. The boundary layer equations of the problem are transformed into the structure of dimensionless coupled ordinary differential equations by utilizing the appropriate similarity variables. These equations of the problem are solved numerically via BVP4c. The main outcome of the problem is that the relaxation time enhanced the fluid temperature while the chemical parameter declined the concentration profile. Moreover, the mixed convection effect increases the fluid velocity of the stretching sheet. The physical quantities like fluid velocity, temperature, concentration, friction at the wall, mass, and heat flux for the variation of several pertinent parameters are discussed graphically and in tabular form.

Unsteady magnetohydrodynamic hybrid nanofluid flow over a rotating disk with viscous dissipation and Cattaneo–Christov heat flux model

This work addresses unsteady MHD flow of hybrid nanofluids (MWCNTs−Fe3O4)/H2O over a rotating disk with viscous dispassion and the Cattaneo–Christov heat flux model. The boundary layer flow-directing PDEs were converted into systems of dimensionless coupled nonlinear ODEs using the similarity conversion technique. Using the spectral quasilinearization method (SQLM), the resulting nonlinear momentum and energy equations were then numerically solved along with their boundary conditions. For the preparation of (MWCNTs−Fe3O4)/H2O hybrid nanofluid with shape factor n1=n2=3, it is specified that 5% of MWCNTs, 20% of Fe3O4, and 75% of H2O be taken. Using graphs and tables, the effects of more noticeable parameters on the thermal flow fields and velocity were thoroughly investigated. The results show that as the value of the unsteady parameter increased, the momentum and thermal boundary layer thickness decreased. The local heat transfer rate improves by nearly 20% as 0.2 volume of Fe3O4 nanoparticles dispersed in 0.1 volume of MWCNTs and 0.7 volume of H2O nanofluid. The finding of this study is noteworthy because it indicates that the (MWCNTs−Fe3O4)/H2O hybrid nanofluids exhibit superior flow distributions and good thermal property stability when compared to their mono counterparts.

Cattaneo-Christov heat and mass fluxes model of Casson fluid employing non-Fourier double diffusion theories with ion slip and Hall effects

It is vitally important to comprehend non-Newtonian fluids flow behaviour from an industrial perspective. Non-Newtonian fluids are needed for a number of industrial and technical processes, including the production of paper, photographic films, and polymer sheet extrusion. There are several industrial applications for heat and mass transfer. However, thermal and solute relaxation time phenomena can't be predicted by classical heat and mass transfer laws (Fourier and Fick laws). This work aims to apply the modified Ohm law to thermal and mass transfer which are based on Fick's and generalized Fourier principles, respectively. The current study examines the three-dimensional Darcy-Forchheimer flow of non-Newtonian fluid “Casson fluid” via porous medium with ion slip and Hall effects across a stretched sheet. Thermophoresis and Brownian motion aspects are also considered. The diffusion phenomena are modelled using the Boungrino model. The modified Buongiorno model (MBM) for nanofluids is used to investigate the enhancement of heat transport. Together with practical nanofluid properties, it covers the mechanics of thermo-migration and random motion of nanoparticles. By adding the appropriate similarity transformations, this collection of (PDEs) that reflect the mathematical model is transformed into an (ODEs) system, which it is subsequently resolved utilizing the Lobatto IIIA technique's powerful computing capabilities via Matlab software. Data visualisations and numerical examples are presented considering many physical restrictions affect the fluctuation of velocities, temperatures, concentration, dimensionless shear stress, Nusselt number, and Sherwood number. According to certain findings, the existence of Hall and ion slip effects, and other factors contribute to an increase in horizontal velocity distribution. Furthermore, Fourier's law produces a wider temperature distribution than the Cattaneo-Christov heat flux model.

Characteristics of sodium alginate-based hybrid nanofluid and darcy-forchheimer flow induced by stretching surface with thermal radiation and cattaneo–christov heat flux model

In today's industrial age, one of the most pressing challenges is to find an efficient heat transfer fluid because common fluids don't provide efficient heating and cooling in industries. This paper aims to explore the flow and heat transfer characteristics of (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluids in the presence of Cattaneo–Christov heat flux model and thermal radiation on a surface. To achieve this, we transform the modeled partial differential equations (PDEs) into ordinary differential equations (ODEs) using suitable similarity variables. These equations are then solved using MATLAB software (bvp4c) to illustrate the influence of important controlling parameters, presented in both tabular and graphical formats. It is noted that raising the Inertia coefficient parameter leads to a drop in the velocity distribution profile of the (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluid. Enhancing the rotation parameter of (SWCNT-Ag/ Sodium Alginate) and (MWCNT-Cu/ Sodium Alginate) based hybrid nanofluid decreases the velocity distribution profile. The increasing values of the thermal radiation parameter and Biot number increased the thermal distribution profile while the fall down for the enhancing values of the melting parameter. The convergence ranges of emerged flow parameters are listed here(0.1<β<1.4),(0.1<Γ<0.4), (0.1<P<1.3),(0.1<Fr<1.2), (0.01<ϕ1=ϕ2<0.04), (0.4<Me<1.0),(0.1<Bi<2.2),(0.1<Rd<1.2), and (0.4<Ωt<1.0). The key and fascinating aspect of this innovative study is that the heat transfer rate increases for all the parameters involved, aligning with the fundamental goal of utilizing nanofluids in nanotechnology for their promising applications.

Brownian motion and thermophoresis influence in magnetized Maxwell upper-convected stagnation point fluid flow via a stretching porous surface

This article focuses on the effects of Brownian motion and thermophoresis convection in the stagnation point flow of a Maxwell upper-convected fluid over a non-Darcian porous surface with slip conditions and a magnetic inclination effect. The Maxwell dissipative fluid accounts for Joule heating due to an imposed magnetic field and porous medium resistance. At the same time, the Cattaneo-Christov heat flux model represents thermal relaxation in contrast to the conventional Fourier law. The resulting nonlinear partial differential equations are transformed into ordinary differential equations (ODEs) using similarity variables. The analysis revealed the influence of dimensionless numbers, including Deborah, Eckert, Prandtl, chemical reaction, thermal relaxation, inclination and slip parameters. The findings were presented using graphs and tables. An increase in the thermophoresis parameter notably led to higher concentration and temperature profiles. In contrast, increasing Brownian motion (Nb) decreased the solutal boundary layer thickness but enhanced the thermal boundary layer.

Lubricated stagnation point flow of Walters-B nanofluid with Cattaneo-Christov heat flux model: Hybrid homotopy analysis simulations

Thermal mechanism of non-Newtonian nanofluid coated by lubricated power law material has been theoretically worked out. The slip interaction constraints has been proposed for inspecting the thermal transport. The modelling of heat transfer is processed via updated Cattaneo-Christov (CC) expressions. The rheological constraints of nonlinear model are observed by Walter B fluid. The flow phenomenon is governed by stagnation point flow. The differential system is associated to interaction of similarity variables. The solution technique is based on new developed hybrid homotopy analysis scheme. The hybrid homotopy algorithm is developed by combining the shooting technique and traditional HAM. The accuracy regarding the developed scheme is carefully inspected after making comparison of results with earlier claimed studies. The different physical aspect of transport phenomenon is attributed in view of parameters.

Heat and mass transport aspect on magnetised Jeffery fluid flow over a stretching cylinder with the Cattaneo–Christov heat flux model

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings.

Entropy Generation Optimization in an Unsteady Hybrid Nanofluid Flow Over a Flat Plate with Variable Viscosity: A Cattaneo-Christov Heat Flux Model

Nanofluids are a novel and intriguing class of heat transmission fluids that can be used in place of more conventional options. They have several applications, including fuel cells, heat exchangers, and the pharmaceutical industry. When it comes to heat transport, hybrid nanofluids much outperform their mono-fluid counterparts. These are being put to use in a wide variety of areas, from solar power to air conditioning. Unsteady flow characteristics of a hybrid nanofluid (Ethylene Glycol + ZnO + TiO2) over a flat plate at varied Lorentz forces, volume fraction of nanoparticles, and thermal radiation are unknown when variable viscosity is taken into account. Paper’s novelty is addressing this gap, which is to examine the impact of variable viscosity on the hybrid nanofluid flow by a flat plate under convective boundary condition when thermal radiation and magnetic field are significant. Cattaneo and Christov’s heat flux model is used to analyse the phenomenon of heat transfer. This paper also includes an analysis of irreversibility. The equations required to represent the problem have been turned into a system, and this system has been solved using the bvp4c solver. Validated the results (of engineering parameters including friction coefficient) obtained using the bar graphs by using Multiple linear regression. It has been observed that the thermal relaxation parameter (Γ) and the unsteady parameters (S) both have similar effects on the heat transmission rate. It is found that there is an increment of 0.001278 (when 0 ≤ Γ ≤ 0.6) and 0.103865 (when 0.4 ≤ S ≤ 1) in the Nusselt number. It is clear from a closer inspection that as magnetic field parameter (Mg) and viscosity parameters (δ) are raised, the friction factor declines. It is observed that, at 0 ≤ Mg ≤ 1.8, friction factor declines at a proportion of 0.08974. It is detected that higher Brinkman number values lead to a greater rate of entropy generation and an upsurge in the (temperature-dependent) viscosity parameter contributes to a decline in the same. As the viscosity parameter is amplified, it is also seen that the fluid’s velocity declines.

A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.

Non-linear thermal radiation and entropy generation on MHD Casson and Williamson hybrid nanofluids across a curved stretching sheet with Cattaneo-Christov heat flux model

This entire study aims to prove the impacts of non-linear thermal radiation and entropy generation on Casson and Williamson hybrid nanofluids through a comparative analysis of the magnetohydrodynamic flow in a porous, curved stretching sheet with the Cattaneo-Christov heat flux model. We used hybrid nanofluid blood based on gold (Au) and Aluminium oxide (Al2O3) nanoparticles. The governing non-linear coupled Partial Differential Equation (PDE) are transformed into non-linear coupled Ordinary Differential Equations (ODE) using the Maple software solver using the Homotopy Perturbation Method. The Homotopy Perturbation Method (HPM) results are compared with the Numerical Method (NM) results, and HPM gives reliable results. The results are provided through the table and graphical representations for several parameters such as velocity, temperature, entropy production, Bejan number, Nusselt number, and skin friction respectively. The velocity profile decreases for Williamson and Casson hybrid nanofluids over a curved stretching sheet while the magnetic field parameters increase. Due to magnetic force associated with Lorentz force, which is known as resistive force, velocity decreases. The Magnetic field on the entropy generation for Casson and Williamson hybrid nanofluids. As the Magnetic field increases, the entropy generation increases for Williamson and Casson hybrid nanofluids. This problem is used in various biomedical situations, including resistive impedance to flow, arteria wall shear stress, and heating impact owing to radiation throughout the surgical process by altering the strength of the applied magnetic field.

Entropy generation analysis on Darcy-Forchheimer Maxwell nanofluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model and Joule heating

This research paper inspects the flow characteristics of a magnetohydrodynamic (MHD) Maxwell nanofluid in the presence of a Darcy-Forchheimer (DF) model applied to a stretching sheet. Additionally, numerical analysis is performed to evaluate the findings, utilizing a nanofluid composed of copper (Cu) suspended in water. The energy equation in this study incorporates thermal radiation, viscous dissipation, the Cattaneo-Christov heat flux model, and joule heating. The entropy generation is then determined based on the obtained solutions for temperature and velocity, in compliance with the flow constraints. By applying suitable similarity transformations, the conservative equations of energy and momentum are transformed into nonlinear ordinary differential equations (ODEs). To solve these equations, a bvp4c method implemented through Matlab software is employed. By taking into account pertinent characteristics like the relaxation Prandtl number, magnetic parameter, time parameter, radiation parameter, and others, one can analyse the normalized shear stress at the wall, temperature profile, and rate of heat flux. For practical purposes, the local Nusselt and number of skin frictions are determined for various modified values of the physical constraints. This provides vital insights about the system's behavior under various settings. The graphical results indicate that the velocity profile exhibits a decrease as the volume fraction, magnetic parameter, Maxwell fluid parameter, and inertia coefficient parameter increase. The entropy generation demonstrates an increase with growing values of the Brinkman number and magnetic parameter. On the other hand, entropy generation declines with increasing values of the temperature ratio parameter. The Bejan number exhibits the opposite behavior of the entropy generation. Specifically, as the Bejan number increases, the entropy generation decreases, and vice versa.