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Thermal analysis of serrated fins which are consist of annular and plain sections are investigated. Serrated fin's thermal conductivity is assumed to change linearly with temperature. Nonlinear differential equations are obtained by applying the energy balance equation for both sections of the serrated fin and these equations are solved by applying homotopy perturbation method. Insulated fin tip, constant fin base temperature and common boundary conditions between the interface of two sections are considered. Serrated fin radii ratio (𝜀), segment height ratio (𝛿), thermo-geometric fin parameter (𝜓) and thermal conductivity parameter (𝛽) effecting the thermal performance and temperature distribution are investigated. The results showed that the homotopy perturbation is a reliable method for the solutions of such nonlinear differential equations. A very good agreement with the homotopy perturbation method and the numerical finite difference method are obtained. It is seen that, serrated fin efficiency lays between annular and rectangular fins and increases with the increase of segment height ratio and thermal conductivity parameter. Such as, fin efficiency values under the condition of 𝜀 = 2, 𝜓1 = 1.0 and 𝛽 = 0 for 𝛿 = 0, 0.5, and 1 are 0.692, 0.718, and 0.762, respectively. [ABSTRACT FROM AUTHOR]

In this paper, hybrid nanofluid flow with mediated compressions and dilations subject to the temperature-dependent viscosity/ thermal conductivity and inclined magnetic field is considered. In medical science, the flow mediated dilation of the artery exists when the blood flow is enhanced in the artery. The compressed/ dilated type flow can be utilized in food processing, hot plate welding, rheological testing, cardiovascular drugs, measurement of brachial artery dilation, blood vessel damage caused by cigarette smoke. The volume of the dilated flow is maintained by injecting the same fluid into the flow field through the exponentially permeable and stretchable walls of the channel. This phenomenon is modeled mathematically and solved by Chebyshev pseudo-spectral method utilizing quasi-linearization approach. It is interestingly analyzed that squeezing/ dilating forces generate two points of inflection in the flow field where the magnitude of permeable fluid velocity is enhanced by 17.21% in the mid portion of the channel by the increase of dilating forces, however it is reduced by 20.35% due to the strengthening of the compressing forces of the channel. The reported flow mediated dilation/ contraction of the study can be used in targeted drug delivery (especially cardiovascular drugs), assessment of endothelial function, measurement of brachial artery dilation and blood vessel damage. The angled magnetic field can be utilized to successfully control the environmental skin-friction and heat transfer. [ABSTRACT FROM AUTHOR]

In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth. [ABSTRACT FROM AUTHOR]

Abstract The purpose of this research is to investigate the thermophoretic diffusion and chemical reaction on steady magnetized Williamson fluid flow, heat, and mass transfer along a Riga surface in the presence of variable thermal properties. By imposing the appropriate similarity technique, the system of higher-order formulas has been transformed from partial order into ordinary order. An efficient numerical technique named the classical Keller box scheme has been incorporated to solve these dimensionless coupled non-linear ordinary differential equations. The obtained results are visualized graphically with physical justification. In addition to that, we validated the obtained outcomes by comparing them to earlier literature, and we identified an excellent match, supporting the reliability of the present method. We discovered from our analysis that acceleration in the values of Williamson fluid and viscosity leads to enhancement in both velocity plots. Also, the material and stretching parameters have a major role in the fluid flow control process. [ABSTRACT FROM AUTHOR]

This investigation concentrated on the A g − M o S 2 /water hybrid nanofluid to solve the problem of heat-mass transmission across a permeable stretching/contracting sheet with the impacts of radiant heat and inclined magnetic force field. Here, we additionally take into account hybrid nanofluids with variable thermal conductivity, variable mass diffusivity, Joule dissipation, binary chemical reactions with velocity, and thermal and solutal slip conditions. Before being numerically solved by the MATLAB function bvp4c, the controlling PDE is converted into nonlinear coupled ordinary differential equations by appropriate similarity transformation. The findings also point to the presence of dual solutions in the stretching/contracting sheet region for a given value of the mass suction parameter, with stable upper branch solution and unstable lower branch solution. As a result of the velocity and temperature gradients, the entropy generation equation is constructed. The effects of the selected parameters are discussed and visually displayed for the velocity, temperature, concentration, skin friction coefficient, local Nusselt number, and Sherwood number. Due to some selected flow parameters, the pattern of entropy formation and assessment of the Bejan number are anticipated. Furthermore, it is discovered that when the volume percentage of M o S 2 nanoparticles increases, the Sherwood number decreases, and the skin friction coefficient increases with the rate of heat transmission. The Bejan number and entropy generation rate both increase with the volume proportion of nanoparticles and the radiant heat parameter, according to the visual simulations created using the present model. [ABSTRACT FROM AUTHOR]

This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius's kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (R a) values and decreases with increasing variable viscosity ( β 1 ) and material parameter ( W e ) values. [ABSTRACT FROM AUTHOR]

The objective of this article is to investigate how the properties of a non-Newtonian Williamson nanofluid flow, which occurs due to an exponential stretching sheet placed in a porous medium, are influenced by heat generation, viscous dissipation, and magnetic field. This study focuses on analyzing the heat transfer process by considering the impact of temperature on the thermal conductivity and viscosity of Williamson nanofluids. Additionally, the research significantly contributes by investigating the flow characteristics of these nanofluids when influenced by slip velocity. Using the spectral collocation method (SCM), the equations that describe the current problem are transformed into a collection of ordinary differential equations and then solved. The SCM proposed here basically depends on the properties of the Appell-type Changhee polynomials (ACPs). First, with the aid of ACPs, we give an approximate formula of the derivatives for the approximated functions. Through this procedure, the provided model is transformed into a nonlinear set of algebraic equations. Physical factors of interest, such as skin friction, the Nusselt number, and the Sherwood number, are explained using tabular expressions. Data are displayed as graphs for the nanofluid's velocity, temperature, and concentration. The primary findings showed that increasing the Williamson, magnetic, thermal conductivity, and Brownian parameters significantly improves the thermal field. Finally, testing the suggested method with specific cases from some past literature-based publications reveal a good degree of agreement. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the analysis of the reflection of waves through a thermoelastic medium with diffusion and mechanical force. The problem is discussed within memory-dependent derivatives in the context of the dual-phase-lag model and Lord and Shulman theory. The harmonic representation of waves method is used to find the solution of the reflection coefficients. On the basis of the solution, it is concluded that after reflection four quasi-waves (qP, qT, qN, qSV) propagate through the medium. Comparisons are made with the amplitude ratios of the reflected waves for different values of the magnetic field and gravity. Comparisons are made with the amplitude ratios of the reflected waves for different values of the mechanical force and thermal conductivity. The amplitude ratios of various reflected waves are significantly influenced by thermal conductivity, the angle of incidence and the gravity field. [ABSTRACT FROM AUTHOR]

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In this analysis, Sutterby nanofluid flow with an induced magnetic field at a nonlinear stretching cylinder is deliberated. The effects of variable thermal conductivity, Darcy resistance, and viscous dissipation are discussed. Thermal radiation and chemical reaction are considered to analyze the impact on the nonlinear stretching cylinder. The governing model of the flow problem is developed under the boundary layer approximation in terms of partial differential equations. Partial differential equations are transformed into ordinary differential equations by performing the suitable transformations. A numerical structure is applied to explain ordinary differential equations. The impact of each governing physical parameters on the temperature, concentration, skin friction, Sherwood, and Nusselt number is presented in graphs and tabular form. Increment in Prandtl number, which declined the curves of the temperature function. Temperature declined because the Prandtl number declined the thermal thickness as well as reduce the temperature of the fluid. Temperature curves showed improvement as Eckert number values increased because the Eckert number is a ratio of kinetic energy to the specific enthalpy difference between the wall and the fluid. As a result, increasing the Eckert number causes the transformation of kinetic energy into internal energy via work done against viscous fluid stresses.

This article aims to demonstrate the formation of entropy due to variable thermal conductivity, radiation, and fluid friction irreversibilities for a three-dimensional upper-convected Maxwell (UCM) fluid. The fluid motion occurs as a result of exponential stretching sheets. Separate discussions are held regarding the entropy generation related to the prescribed surface temperature and prescribed surface heat flux. Additionally, the heat transport mechanism is examined in the presence of thermal radiation. The governing physical situation is first modeled and then solved by using the homotopy analysis method to acquire the solution. The physical importance of relevant flow parameters is shown graphically and in tabular form. It is noted that the entropy generated is reduced with an increase in the thermal radiation parameter. Streamline patterns are also drawn for two- and three-dimensional UCM fluid models. Finally, the current analytical solution is found to be in agreement with the solutions in the literature.

This investigation deals with the effect of variable thermal conductivity in a micropolar thermoelastic medium without energy dissipation with cubic symmetry. The normal mode technique is employed for obtaining components of physical quantities such as displacement, stress, temperature distribution and microrotation.

In the current analysis, steady incompressible Sutterby fluid flows over a stretching cylinder are studied. The influence of variable thermal conductivity is considered in the presence of thermal slip, Darcy resistance, and sponginess. The impact of the induced magnetic field is considered to analyze the results at the cylindrical surface. The governing equations are established as partial differential equations using the boundary layer approximation. Appropriate transformations are used to convert partial differential equations into ordinary differential equations. The numerical technique, namely (bvp4c), is applied to ordinary differential equations to develop the results. The numerical results, such as heat transfer rate and skin friction, are revealed by tabular form to demonstrate the physical impact of governing factors. The physical impact of governing factors on induced magnetic hydrodynamic, velocity, and temperature profiles is presented through various graphs. The velocity function deteriorated due to the augmentation of the Sutterby fluid parameter.

Micropolar fluid flow in a channel with variable viscosity, variable thermal conductivity and activation energy is examined numerically using the Runge–Kutta Fehlberg method in this article. Two different boundary conditions are postulated in this study namely Prescribed Surface Temperature (PST) and Newtonian Heating (NH). The numerical outcomes are compared to check the precision of the suggested problem. Significant metrics like Reynolds number, Peclet number for heat and mass transfer, Schmidt number, Activation energy and chemical reaction parameter are graphically described. The influence of the parameters like spin gradient viscosity, vortex viscosity, micro-inertia density on the flow fields are discussed and shown. According to the graphic data, the velocity increases as the viscosity parameter increases whereas the temperature decays for larger values of variable thermal conductivity and also, activation energy enhances the concentration profile. The variation in viscosity parameter shows a significant effect on thermal distribution. The viscosity variation parameter enhances the shear stress and the couple stress. The Peclet number for heat transmission displays a changing effect for high and low Biot numbers regardless of the effect of variable thermal conductivity. This analysis tabulates the link between Nusselt number and Sherwood number over a Peclet number for heat and mass transfer. The skin friction coefficient increases with the viscosity parameter ∊ whereas enhancement in the thermal conductivity parameter decreases the Nusselt number. Furthermore, sensitivity analysis is carried here by developing RSM in order to identify the variations in the input values for the parameters Peh,Pem and N1. The response surface equation is created by using the software package MINITAB-16 by design of experiments. The regression model’s quality of fit is assessed by using the Analysis of Variance.

The current work is devoted to introduce a novel thermoelastic heat conduction model where the Moore-Gibson-Thompson (MGT) equation describes the heat equation. The constructed model is characterized by allowing limited velocities of heat wave propagation within the material, consistent with physical phenomena. The Green–Naghdi Type III model is improved by introducing the delay factor into the modified Fourier law. Also, from the presented model, some other models of thermoelasticity can be derived at specific states. Based on the suggested model, an infinite orthotropic material with a cylindrical hole exposed to time-dependent temperature variation was studied. It has also been considered that the coefficient of thermal conductivity varies with temperature, unlike in many other cases where this value is considered constant. The viscoelastic material of the investigated medium was assumed to be of the Kelvin–Voigt type. The Laplace transform method provides general solutions to the studied field variables equations. The effects of viscosity and thermal variability parameters on these fields are discussed and graphically presented. In addition, the numerical results were presented in tables, and a comparison with previous models was made to ensure the accuracy of the results of the proposed model.

In this study, influence of non-Fourier's heat flux in 2D Darcy Forchheimer flow of modified Eyring–Powell for a stretching sheet is discussed. Here, thermal conductivity of modified Eyring–Powell model depends upon temperature and porosity variable as well as Cattaneo–Christov heat-mass flux effects are also considered. By means of some suitable similarity transformations and simple BCs, coupled PDEs are transformed into a set of coupled ODEs. Resulting ODEs are solved by using bvp4c technique. The graphical results are obtained via MATLAB. The pictorial outcomes of some physical parameters are displayed. The acquired outcomes disclosed that temperature gradient decreases with the growing values of thermal relaxation parameter Prandtl number, while the concentration profile decreases for higher Lewis number. [ABSTRACT FROM AUTHOR]

In this paper, the effects of various fluid properties on two-dimensional unsteady biomagnetic fluid flow (blood) and heat transfer over a stretching sheet under the appearance of a magnetic dipole is investigated. The governing boundary layer equations are simplified via suitable transformation which are then solved using the bvp4c function approach in MATLAB software. The results indicate that fluid velocity and temperature are greatly influenced by the ferromagnetic interaction parameter. With increasing ferromagnetic number, fluid velocity drops but temperature increases. It is also found that the coefficient of skin friction and Nusselt number increase with an increase in values of thermal conductivity parameter. For certain parameter values, the results are also compared with previously published studies and they are found to be in acceptable agreement. [ABSTRACT FROM AUTHOR]

The mixed convection MHD boundary layer flow, heat and mass transfer of a Newtonian fluid mixture across an exponentially stretched permeable sheet in porous medium with Soret and Dufour effects subject to temperature-dependent fluid properties have been investigated numerically. The distribution of temperature and concentration at the surface is supposed to grow exponentially. Temperature is considered to affect fluid viscosity and thermal conductivity. The guiding partial differential equations with appropriate boundary conditions are converted into coupled, nonlinear ordinary differential equations with variable coefficients via a similarity transformation. Matlab's built in solver bvp4c is used to find numerical solutions. Using a graphical approach, the effects of several emerging physical parameters on velocity, temperature and concentration distributions on a flow field of a chemically nonreacting fluid mixture are examined and discussed. Results are compared to earlier literature available and found to be in good agreement. Furthermore, this research demonstrates that flow, heat and mass transmission are greatly influenced by mixed convection parameters, magnetic field, Prandtl number, viscosity, conductivity, permeability, and Schmidt number. Skin friction grows for mixed convection parameter, magnetic, viscosity. Highest growths of wall temperature and wall concentration gradients are observed for Prandtl number and Schmidt number, respectively. Heat and mass transfer rates increase with higher values of mixed convection parameters and Darcy parameter. To reduce heat transfer rate magnetic field may be used. Fluid with lower thermal conductivity and with higher Prandtl number may be employed to boost the cooling rate in conducting flows. Higher Schmidt enhances mass transfer rates. Suction stabilizes boundary layer growth. Soret effect can be used to separate light and medium molecular weight components from a fluid mixture and hence can be used for control of air pollution. [ABSTRACT FROM AUTHOR]

The primary interest of this study is to investigate the results of magnetohydrodynamics Casson and Carreau fluid heat via a porous medium at the aspect of a stretching sheet. Variable thermal physical phenomena and suction/injection parameter results are also taken into account. Similarity transformations are applied to convert the governing equations of the magnetohydrodynamics Casson and Carreau fluid glide model into dimensionless non-linear normal differential equations. The results on velocity, concentration, temperature profiles, surface drag, Nusselt number, and Sherwood number are discussed for various flow parameters and presented the results through plots and tables. The fluid flow is analyzed for every suction and injection case. From the analysis it is noted that the velocity profile reduces by increasing the magnetic parameter and the reverse trend is observed for increasing values of Weissenberg number in the case of suction and injection. The temperature space and heat transfer rate enhances by increasing the variable thermal conductivity and more in the case of suction. [ABSTRACT FROM AUTHOR]

The generalized thermo-viscoelastic theory without energy dissipation is used in this work to investigate the transfer of bioheat and the mechanical heat-induced response in a human skin plane tissue with variable thermal and rheological properties. Integral transformations are used for Laplace and Fourier. In the scheme of two-dimensional equations, the exponential matrix procedure, which forms the basis of the state-space approach of modern control theory, is applied. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Comparisons between computational measurements and Penne's experimental verification indicate that the Green–Naghdi (II) bioheat mathematical model is an effective method for estimating the transition of bioheat to viscoelastic skin tissue. The influences of variable thermal conductivity and volume materials properties on all fields are examined. [ABSTRACT FROM AUTHOR]

The present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo‐elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase. [ABSTRACT FROM AUTHOR]

This article aims to demonstrate the formation of entropy due to variable thermal conductivity, radiation, and fluid friction irreversibilities for a three-dimensional upper-convected Maxwell (UCM) fluid. The fluid motion occurs as a result of exponential stretching sheets. Separate discussions are held regarding the entropy generation related to the prescribed surface temperature and prescribed surface heat flux. Additionally, the heat transport mechanism is examined in the presence of thermal radiation. The governing physical situation is first modeled and then solved by using the homotopy analysis method to acquire the solution. The physical importance of relevant flow parameters is shown graphically and in tabular form. It is noted that the entropy generated is reduced with an increase in the thermal radiation parameter. Streamline patterns are also drawn for two- and three-dimensional UCM fluid models. Finally, the current analytical solution is found to be in agreement with the solutions in the literature. [ABSTRACT FROM AUTHOR]

In this analysis, Sutterby nanofluid flow with an induced magnetic field at a nonlinear stretching cylinder is deliberated. The effects of variable thermal conductivity, Darcy resistance, and viscous dissipation are discussed. Thermal radiation and chemical reaction are considered to analyze the impact on the nonlinear stretching cylinder. The governing model of the flow problem is developed under the boundary layer approximation in terms of partial differential equations. Partial differential equations are transformed into ordinary differential equations by performing the suitable transformations. A numerical structure is applied to explain ordinary differential equations. The impact of each governing physical parameters on the temperature, concentration, skin friction, Sherwood, and Nusselt number is presented in graphs and tabular form. Increment in Prandtl number, which declined the curves of the temperature function. Temperature declined because the Prandtl number declined the thermal thickness as well as reduce the temperature of the fluid. Temperature curves showed improvement as Eckert number values increased because the Eckert number is a ratio of kinetic energy to the specific enthalpy difference between the wall and the fluid. As a result, increasing the Eckert number causes the transformation of kinetic energy into internal energy via work done against viscous fluid stresses. [ABSTRACT FROM AUTHOR]

In the current analysis, steady incompressible Sutterby fluid flows over a stretching cylinder are studied. The influence of variable thermal conductivity is considered in the presence of thermal slip, Darcy resistance, and sponginess. The impact of the induced magnetic field is considered to analyze the results at the cylindrical surface. The governing equations are established as partial differential equations using the boundary layer approximation. Appropriate transformations are used to convert partial differential equations into ordinary differential equations. The numerical technique, namely (bvp4c), is applied to ordinary differential equations to develop the results. The numerical results, such as heat transfer rate and skin friction, are revealed by tabular form to demonstrate the physical impact of governing factors. The physical impact of governing factors on induced magnetic hydrodynamic, velocity, and temperature profiles is presented through various graphs. The velocity function deteriorated due to the augmentation of the Sutterby fluid parameter. [ABSTRACT FROM AUTHOR]

The key challenge in the design of thermal appliances is to degrade entropy production with maximal energy dissipation to improve system efficiency in a variety of engineering applications, such as nozzle design, converging die, and rocket design. Due to the existence of both tangential and radial components, which have a significant impact on the fluid movement, coupled transport rates, and entropy development in an inclined channel presents a greater challenge. The current inquiry intended to address the combined impacts of Cattaneo-Christove (C-C) heat flux and classical theory on thermal dissipation, along with irreversibility distribution in a tilted porous media. The Carreau nanofluid confined between two finite intersecting plates in the presence of a porous Darcy-Forchheimer medium is examined. The C-C heat flux, variable thermal conductivity, and mass diffusivity are all used to investigate heat transport. The flow originates from a source located at the intersection of the plates and constitutes the momentum conservation. The investigation includes entropy and Bejan analysis. The premises guide the mathematical modelling of the flow field. Through bvp4c techniques, numerical solutions are attained. Converging section velocity increases in response to increased porosity and the Forchheimer number. Variation in temperature is significant when classical heat flux is reverted. Higher thermophoretic and porosity parameters result in a higher rate of entropy formation, while the Darcy parameter promotes drastic increase. Bejan is an escalating function of Brownian and Darcy parameters, while the porosity parameter causes it to fall. Porosity and the Forchheimer number regulate skin friction.

This study investigates heat transfer in a hybrid nanofluid that flows due to a rotating disk. The nanofluid contains copper and dioxide nanoparticles in water and is affected by a constant magnetic field. The study accounts for heat generation/absorption and thermal radiation and solves the governing equations using similarity transformations and the Shooting Method. The research reveals that the higher nanoparticle concentration in a fluid result in increased radial and azimuthal velocities due to improved convective heat transfer. This leads to higher fluid velocity and lower local skin friction coefficient. Heat generation/absorption and thermal radiation have a strong influence on the heat transfer process. Higher nanoparticle concentration, variable thermal conductivity parameter, and radiation parameter cause an increase in the temperature of the hybrid nanofluid. The local Nusselt number increases with an increase in the variable thermal conductivity parameter but decreases with nanoparticle concentration while increases with the thermal radiation parameter. Results from a special case analysis, which excluded certain parameters, closely agree with previous studies, confirming the validity of the solution. These findings can be useful in understanding heat transfer in similar scenarios, especially in energy engineering and thermal management.

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

With impressive thermal outcomes, the nanofluids present multidisciplinary applications in the cooling processes, thermal systems, extrusion processes, heat storage devices and many more. The aim of current research is to inspect thermal impact of Jeffrey fluid with tiny particles under the assumptions of variable thermal conductivity. The problem is supported with applications of chemical reaction, activation energy and magnetic force. For heat and mass transfer phenomenon, Cattaneo-Christov diffusion theories have been implemented. The formulated model is solved by using the homotopy analysis method (HAM) with excellent accuracy. The graphical analysis is performed with specified range of parameters like 0.2⩽H⩽0.8, 0.1⩽ϖ⩽1.7, 0.0⩽N⩽1.5, 0.0⩽Π⩽3.1, 0.3⩽γ⩽0.6, 0.6⩽Ψ⩽3.2, 0.5⩽Ω⩽2.0, 0.0⩽Σ⩽1.5, 0.2⩽Nt⩽1.7, 1.0⩽Pr⩽1.9, 0.5⩽Sc⩽1.4,0.3⩽β⩽1.5, 0.1⩽ε⩽1.0, 0.2⩽Nb⩽1.7. The assessment of flow parameters is graphically evaluated. It is observed that both velocity profiles periodically enhance for Deborah number while temperature, microorganisms and concentration distributions decelerate. The greater estimates of variable thermal conductivity and heat generation improve the temperature distribution while conflicting scenario ensures for thermic relaxation constant.

In this article, we study moving longitudinal and exponential fins with variable thermal conductivity, thermal emissivity, and heat transfer coefficient. The problem is solved numerically using shooting technique. To compare the performance of trapezoidal fins with exponential fins, we introduce a novel idea of volume adjusted fin heat transfer rate, fin effectiveness, and fin efficiency. The result shows that heat transfer from the exponential fin is higher than from the trapezoidal fin. It is observed that the capability of an exponential fin is higher than the trapezoidal fin. With increasing thermal conductivity and radiation-conduction number as well as convection-conduction number, the fin’s efficiency increases. The results illustrate the effect of heat transfer coefficient, thermal emissivity, radiation-conduction and convection-conduction parameters, dimensionless radiation, and convection sink temperatures on the fin’s performance.

The most important condition of modern industrial activities is excellent refrigeration performance for conventional buildings. The Buongiorno relation assessment identifies nanofluid's thermal and mass efficiency, which inspires us to specify different properties of random motion and thermophoretic diffusion. Non-Newtonian nanofluids are used in a variety of fields, including thermal exchangers, solar liquid boiler, and heat control in vehicles. Nanoparticles can significantly enhance a fluid's thermal conductivity and heat transfer properties. This makes nanofluids attractive in cooling systems for electronic devices, such as computer chips and LED lights, and in various industrial applications where efficient heat transfer is important. The proposed thermos-electric system depends on nanomaterial heat flow, fractional volume of nanomaterial, density, and motile microorganisms. Because of their numerous applications, ferromagnetic nanoparticles have become extremely popular in biotechnology. Numerous mathematical and technical constraints are considered to generate more useful data. Using the shooting scheme, evaluating numerically by MATLAB function bvp4c to transform expressions. Some observations about the bio-convection procedure its different exclusive characteristics are elaborated in the literature. The graphs show how multiple flows influence non-dimensional quantities. The present theoretical model could be applied to engineering methods, heat transfer improvements, and thermal energy.

The study on heat and mass transportation play a noteworthy role in the liquid atmosphere wherever nearby is considerable temperature and deposition of diffusion transport in a stirring wedge. Heat and mass transport on fluids discoveries prominence in development of manufacturing and industrial processes such as petroleum reservoirs, nuclear waste disposal, heat exchanger devices, etc. By taking this into, the present study exhibited here to consider the impact of variable fluid properties on nanofluid flow over a wedge. The analysis of the flow has been analyzed consisting with the influences of heat generation/absorption and chemical reaction. It is accepted to have fluid viscosity and thermal conductivity as an opposite capability and conventional capacity of temperature, separately. The succeeding nonlinear ordinary differential circumstances are measured numerically utilizing the fourth order of the Runge-Kutta technique jointly with the shooting method. The consequence of the suitable parameters concerning the flow has been explained through graphs and tables, together with the necessary contentions/conversation. The accompanying investigation exhibits that the fluid temperature is higher within the view of a variable viscosity and heat generation parameters. It is additionally seen that the wall stress diminishes with expanding velocity slip.

Hybrid nanofluids (HNFs) are a new breed of nanofluids that possess numerous tempting applications encompassing microfluidics, transportation, defense, medical, etc. The objective of this novel exploration is to inspect the behavior of Hamilton–Crosser (H-C) and Yamada–Ota (Y-O) HNF flow models past a stretching cylinder. The H-C model is also used to gauge which particle shape (blade, platelet, cylinder, brick) is more effective in the improvement of the heat transfer rate. The envisioned flow is influenced by the Hall current, Cattaneo–Christov (C-C) heat flux and variable thermal conductivity (TC). The uniqueness of the projected model is the notion of a heterogeneous reaction sprouting on the surface of the cylinder in the presence of an absorbent medium. Owing to this supposition, the chemical reaction occurs in the least possible time. The proposed model's novelty lies in the consideration of the surface catalyzed reaction in the HNF flow models past a stretching cylinder amalgamated with the unique impacts of the Hall current, C-C heat flux and variable TC. The thermal performance of the two renowned models H-C and Y-O is also evaluated. The MATLAB software bvp4c technique is used for numerical outcomes of this coupled system. The analysis depicts that the performance of the Y-O HNF flow model is far above the H-C HNF flow model. It is also inferred from the results that blade-shaped nanoparticles possess higher TC than the other nanoparticles. The heat transfer rate for blade-shaped nanoparticles is stronger than the other nanoparticles. The fluid concentration reduces for higher surface-catalyzed reaction parameter. The corroboration of the proposed model is also given in this study. The comparative results disclosed that in the case of the magnetic parameter M , the minimum error percentage is 0.015% for M = 0. 5 , and permeability parameter λ , the least error percentage is 0.037% for λ = 1. 0. [ABSTRACT FROM AUTHOR]

The main objective of this study is to examine an unsteady swirling flow of a non-Newtonian Eyring-Powell fluid between two coaxial disks. The lower and upper disks are considered to rotate with different angular velocities. The three-dimensional axisymmetric flow phenomenon and heat transfer mechanism are observed with the consequences of the magnetic field and variable thermal conductivity of the fluid. The variable thermal conductivity is taken to be dependent on the fluid temperature. The implementation of the Von Karman similarity transformations on the constituting equations of the flow phenomenon yields the dimensionless system of the non-linear equations. An optimal homotopy analysis technique is adopted to obtain analytical solutions for highly non-linear equations. In view of the same and opposite directions of disks rotation, the various aspects of the flow system corresponding to the pertinent parameters are discussed with physical significance. The obtained results indicate that both radial and axial fields are the escalating functions of the Eyring-Powell fluid parameter. Moreover, the heat transfer rate enhances with the improving variable thermal conductivity parameter. [ABSTRACT FROM AUTHOR]

Objective of the present investigation is intended to study the MHD Casson fluids flow through an exponentially stretching surface. This free convective flow is investigated in thermally stratified porous medium. Also viscosity along with thermal conductivity is varying with temperature. With the exponential decay for the internal heat generation in the region and buoyancy force, the natural-convection is induced. Then the transformed set of equations of the flow after applying suitable similarity solutions were encountered by Shooting Technique in conjunction with the fourth ordered Runge-Kutta method. Outputs illustrates that with increased viscosity parameter an increasing velocity profile is noticed but a decrement is observed for temperature field in entire domain and near the wall for temperature gradient profile. Also with increased Casson fluids parameter decreasing velocity profile is noticed but an increment is observed for temperature field in entire domain and for temperature gradient profile near the wall. [ABSTRACT FROM AUTHOR]

The quintessence of this article encompasses the effect of diffusiophoresis, chemical reaction, and varying viscosity as well as thermal conductivity on a fully developed dissipative flow through an upright channel. The fluid is electrically conducting undergoing mixed convection. The governing equations, after transfiguring into dimensionless formation, are solved through a numerical procedure for boundary value problems incorporating MATLAB solver. Imperative scrutiny is made to visualize associative impacts of flow parameters, namely, magnetic parameter, the Brinkmann number, the Schmidt number, variable viscosity parameter, variable thermal conductivity parameter, chemical reaction parameter, diffusiophoretic parameter, and particle diffusion parameter, on the flow. The velocity field, the temperature field, the solute concentration field, the particle concentration field, the skin friction, the Nusselt number, the Sherwood number, and the particle concentration gradient are assessed in view of alteration of the aforesaid parameters with the help of visual illustrations in graphical form and tabular form. Solute mass transposition and colloidal particle locomotion are the fresh inclusions to the scrutiny of upright channel flow in light of solving scheme of bvp4c. Chemical reaction engulfs both solute and particle concentration. Growing viscosity hinders the fluid velocity and heats up the flow encouraging interlayer friction. [ABSTRACT FROM AUTHOR]

The free convective flow of an incompressible viscous fluid over an isothermal vertical cone with variable viscosity and variable thermal conductivity is examined in the presence of the Soret and Dufour effects. As thermal and solutal boundary conditions at the cone's surface, the constant temperature and concentration (WTC) and constant heat and mass flux (HMF) cases are taken into account. The successive linearization method is applied to linearize a system of nonlinear differential equations that describes the flow under investigation. The numerical solution for the resulting linear equations is attained by means of the Chebyshev spectral method. The obtained numerical results are compared and found to be in good agreement with previously published results. The impact of significant parameters on the heat and mass transfer rates is evaluated and presented graphically for the WTC and HMF situations. In both cases, the Soret number increases the skin friction coefficient and rate of heat transfer while decreasing the Sherwood number. With an increase in the Dufour parameter, the coefficient of skin friction and Sherwood numbers increase while the heat transmission rate decreases. [ABSTRACT FROM AUTHOR]

The aspects of activation energy in magnetized Maxwell nanofluid flow with Brownian movement and thermophoretic diffusion have been elaborated here. Furthermore, Joule heating, variable conductivity and chemical reaction are scrutinized. The Buongiorno nanofluid thought is ratify to incorporate the importance of thermophoretic and Brownian diffusion. The attained ODEs have been solved via homotopic algorithm. The performance of operational variables is inspected. The Maxwell temperature field for Eckert number and variable conductivity factor have similar trend. The fluid concentration exaggerates for activation energy and decelerates for Brownian motion parameter. Furthermore, the brilliant outcomes attained and associated with possible existing prose accurately. [ABSTRACT FROM AUTHOR]

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and air conditioning. Because of this impetus, we investigated non-Newtonian fluid flow regimes from the perspectives of both heat and mass transfer aspects. In this study, heat transfer of electrical MHD non-Newtonian flow of Casson nanofluid over the flat plate is investigated under the effects of variable thermal conductivity and mass diffusivity. Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. The shown problem can be recast as a set of ordinary differential equations by making the necessary changes. A modified finite element method is adopted to solve the obtained set of ODEs. The numerical method is based on Galerkin weighted residual approach, and Gauss–Legendre numerical integration is adopted in the modified finite element method application procedure. To clarify the obtained results, another numerical technique is employed to solve the reduced ODEs. With the help of error tables and the flowing behavior of complicated physical parameters on estimated solutions, this study graphically and tabulatively explains the convergence of analytic solutions. Comparing some of the obtained results with those given in past research is also done. From the obtained results, it is observed that the velocity profile escalates by improving the electric parameter. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures. [ABSTRACT FROM AUTHOR]

This article addresses a thermoelastic problem under varying thermal conductivity with and without Kirchhoff's transforms. The temperature increment, displacement, and thermal stresses in an orthotropic material with spherical cavities are studied. The inner surface of the hole is constrained and heated by thermal shock. The numerical solutions are derived using the finite element technique in the setting of the generalized thermoelasticity model with one thermal delay time. The thermal conductivity of the material is supposed to be temperature-dependent without Kirchhoff's transformation. Due to the difficulty of nonlinear formulations, the finite element approach is used to solve the problem without using Kirchhoff's transformation. The solution is determined using the Laplace transform and the eigenvalues technique when employing Kirchhoff's transformation in a linear example. Variable thermal conductivity is addressed and compared with and without Kirchhoff's transformation. The numerical result for the investigated fields is graphically represented. According to the numerical analysis results, the varying thermal conductivity provides a limited speed for the propagations of both mechanical and thermal waves. [ABSTRACT FROM AUTHOR]

The study of electro-osmosis, peristalsis and heat transfer with numerous slips, such as velocity slip, thermal slip and concentration slip, may be used to construct biomimetic thermal pumping systems at the microscale of interest in physiological transport phenomena. A mathematical model has been developed to investigate magnetohydro-dynamics non-Newtonian (Carreau fluid) flow induced by the forces to produce a pressure gradient. The walls of the microchannels erode as they expand. The Poisson and Nernst–Planck equations are used to model electro-osmotic processes. This procedure results in Boltzmann circulation of the electric potential across the electric double layer. The governing equations are simplified by approximations such as a low Reynolds number and a long wavelength. The ND Solver in Mathematica simulates and compares simplified coupled nonlinear governing equations. We investigate novel physical parameters affecting flow, heat transfer and pumping. Additionally, a fundamental peristaltic pumping phenomenon known as trapping is graphically provided and briefly discussed. The model's findings show that the velocity increases as the electric field intensifies, implying that electro-osmosis may improve peristaltic flow. [ABSTRACT FROM AUTHOR]

In the present work, the 2D problem of a magneto-micropolar thermoelastic medium in the context of the dual-phase-lag model with the frame of the memory-dependent derivative is established. Normal mode analysis and an eigenvalue expansion technique are used to solve the resulting non-dimensional coupled governing equations. The variations of the physical quantities with the vertical distance are illustrated graphically. The effects of the time-delay parameter, magnetic field, rotation, and the variable thermal conductivity on the variations of different field quantities inside the half-space are analyzed graphically. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the numerical analysis of an innovative model containing, bioconvection phenomena with a gyrotactic motile microorganism of magnetohydrodynamics Williamson nanofluids flow along with heat and mass transfer past a stretched surface. The effect of thickness variation and thermal conductivity feature is employed in the model. Bioconvection in nanofluid helps in bioscience such as in blood flow, drug delivery, micro-enzyme, biosensors, nanomedicine, for content detection, etc. For simulation procedure, the mathematical partial differential equations are converted into dimensionless systems owing to dimensionless variations such as magnetic field, power index velocity, Williamson parameter, wall thickness parameter, thermal conductivity variation, Prandtl number, thermal radiation, Brownian motion, Lewis number, Peclet number, and different concentration parameter, etc. For numerical simulation, New Iterative Technique (NIM) numerical algorithm is adopted and employed for the linear regression planned for the proposed model. For comparison purposes, the homotopy technique is employed on the flow model. Close agreement is seen between both methods revealing the accuracy and consistency of NIM numerical technique. Many features of no-scale constraints are evaluated through graphical data for a key profile of the flow model. Results show that microorganism concentration is heavy due to the magnetic effect and Hall current.

An investigation is carried out to study MHD boundary layer flow, heat and mass transfer of an incompressible viscous fluid past a continuously moving nonlinear stretching porous sheet in porous medium with temperature dependent fluid properties subject to heat source, viscous dissipation, chemical reaction and suction. The fluid viscosity and the thermal conductivity are assumed to vary as an inverse function and linear function of temperature respectively. The governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations by using similarity transformations and solved numerically by the Matlab’s built in solver bvp4c. The numerical results are presented graphically for velocity, temperature and concentration distributions. The skin friction, wall temperature and wall concentration gradients are tabulated for emerging parameters. It is arrived at a good agreement on comparing the present numerical results with previously published results. It is found that skin friction rises but wall temperature and wall concentration gradients fall with growing viscosity, magnetic field, stretching parameter and Darcy parameter respectively. The thermal conductivity parameter diminishes wall temperature gradient while the Schmidt number and chemical reaction parameter enhance wall concentration gradient.

It is well consensus among researchers affiliated with the field of thermal engineering that the thermophysical characteristics of heat transfer in fluid science own abundant applications like thermal distillation systems, heat exchangers, steam-electric power generation, electronic cooling, solar collectors, refrigeration systems and spacecraft thermal protection are to mention just a few. Considering such importance we offer a thermal case study on thermophysical aspects in a thermally magnetized non-Newtonian fluid along with a first-order chemical reaction effect. The flow field is carried with the following thermophysical effects namely, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent variable thermal conductivity. We have offered comparative analysis for temperature and Nusselt number by considering thermally radiative and non-radiative thermal flow fields. The thermal outcomes on temperature and Nusselt number are also reported for both the absence and presence of the heat generation effect. For both radiative and non-radiative Casson flow, the temperature shows an inciting nature towards Casson and variable thermal conductivity parameters. The magnitude of the Nusselt number towards Eckert, Prandt numbers, curvature, heat generation, and Casson fluid parameters is higher for the presence of thermal radiations while the opposite is the case for positive variation in the thermal conductivity parameter.

This article investigates the peristaltic flow of a hyperbolic tangent fluid with variable viscosity and thermal conductivity through a vertical asymmetric channel. Consideration is given to the effects of viscous dissipation, chemical reactions, and convection heat at the channel walls. The relevant mathematical modeling incorporates lubrication approximation. The resulting system of highly non-linear differential equations is converted non-dimensional via suitable quantities. The non-dimensional parameters formed in viscosity or thermal conductivity are treated as variables. This treatment is the fundamental recommendation of the current study to avoid obtaining unrealistic results. Using the built-in package (ParametricNDSolve) in the computing program Mathematica, the analysis is performed numerically, and the results for temperature and concentration profiles in addition to the trapping phenomenon are shown through graphs. The major findings show that an increase in temperature is associated with a decrease in viscosity, whereas the opposite (unrealistic) behavior is maintained when the variable parameters are treated as constants. Results also indicate that the thermal conductivity at relatively low temperatures is enhanced, whereas the opposite trend is noted at higher temperature values. Potential applications for the current work include cooling techniques used in medical and industrial applications, food processing, and blood flow in microvessels.