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

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

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

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

Owing to valuable significance of bioconvective transport phenomenon in interaction of nanoparticles, different applications are suggested in field of bio-technology, bio-fuels, fertilizers and soil sciences. It is well emphasized fact that thermal outcomes of nanofluids can be boosted under the consideration of various thermal sources. The aim of current research is to test the induction of induced magnetic force in bioconvective transport of non-Newtonian nanofluid. The rheological impact of non-Newtonian materials is observed by using Casson fluid with suspension of microorganisms. The chemical reaction effected are interpreted. The thermal conductivity of material is assumed to be fluctuated with temperature fluctuation. The flow pattern is endorsed by stretching surface following the stagnation point flow. Under the defined flow assumptions, the problem is formulated. A computational software with shooting technique is used to present the simulations. A comprehensive analysis for problem is presented. It is claimed that the interpretation of induced magnetic force exclusively enhanced the thermal phenomenon. [ABSTRACT FROM AUTHOR]

The article focuses on studying the effect of variable thermal conductivity on the reflection of waves propagating through a medium. Considered solid is half space with semiconductor properties. Additionally, we have also introduced the concept of non-local thermoelasticity to develop a stress-strain relation. Using the Helmholtz decomposition principal, we have determined that three longitudinal waves and one transverse wave propagate through the medium after reflection. To account for the thermal signals generated by the elastic vibration, we have used a three-phase lag (3PL) heat conduction model. The numerical computation of the theoretical results is presented graphically for a specific medium. The study of elastic waves passing through the human body is used for diagnosis and treatment. Nature and characteristics of the materials can also be detected by evaluating the behavior of waves reflected and transmitted through them. [ABSTRACT FROM AUTHOR]

This paper addresses the melting of phase change solid sphere, which motivates researchers to develop new thermal energy storage (TES) systems techniques. Phase change materials can store or release large amounts of heat in short intervals of time, thus improving the thermal performance of cooling and heating systems in buildings and regulate the temperature of PV systems, batteries and other electronic components. We have considered a convective spherical Stefan problem with thermal conductivity as a function of time and temperature. The heat balance integral method (HBIM) is used to find the problem's solution numerically. The temperature profile is approximated by using n degree polynomial. The influence of governing parameters on the location of melting front and temperature profile is discussed thoroughly. The parameters depict that transition from solid to liquid phase becomes fast for higher values of Stefan number while the transition rate slows down for larger values of Peclet number. The melting rate increases from 20% to 80% when Stefan number rises from 0.1 to 1.0 at a particular time. Moreover, a comparative study of the proposed model with some existing models is being done. It is observed that moving melting front for the assumed problem undergoes a fast melting process. [ABSTRACT FROM AUTHOR]

Slip condition plays a significant role in many heat transfer phenomena such as cleaning microheat exchangers, mechanical heart valve cleaning, and inner cavity polishing. The present study is carried out on the numerical analysis of steady mixed convection (SWCNT + MWCNT/ H2O) hybrid nanofluid flow with slip boundary conditions in the presence of variable thermal conductivity, heat generation and thermal radiation via an exponentially extending sheet. By using the proper exponential similarity transformations, a nonlinear coupled ordinary system is obtained from the coupled partial differential system. The generated ordinary differential systems are resolved using the MATLAB software. Physical characteristics, such as the mixed convection parameter (λ), the velocity slip (A), the thermal slip (B), and the heat generation (QH), that have an impact on temperature, Nusselt number, and velocity field, are shown in graphical and tabular representations. The enhancement of suction and velocity slip causes a reduction in the velocity profile. The findings of the thermal slip test against stretching sheet show that hybrid nanofluid improves the rate of heat transmission by 4.33% when compared to nanofluid. [ABSTRACT FROM AUTHOR]

The importance of thermal efficiency in major industrial and engineering sectors cannot be overstated. Numerous processes within these domains require substantial heat transfer, and conventional fluids often fall short in generating the necessary amount of heat for these operations. Recognizing this limitation, there arose a need to enhance the thermal conductivity of ordinary liquids. In response to this challenge, researchers and scientists proposed a groundbreaking idea: the introduction of metallic and non-metallic nano additives into the base fluid to improve its thermal effectiveness. This innovative approach gave rise to a new category of liquids known as hybrid nanofluids. In this article, we delve into the analysis of the 2D steady flow of SWCNT-Fe3O4/H2O and MWCNT-Cu/H2O-based hybrid nanofluid over a stretching and shrinking sheet, taking into account factors such as suction/injection and thermophysical impacts. The utilization of similarity variables enables the reduction of partial differential equations to a more manageable system of ordinary differential equations. To solve these transformed ordinary differential equations, a numerical technique, specifically the shooting algorithm with the bvp4c solver, is employed. The results are presented and elucidated through graphical representations, providing valuable insights into the behavior of the system under consideration. [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]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This research investigates the unsteady flow of rotating Casson tetra hybrid nanofluid with dual stratification, examining the impact of variable thermal conductivity and thermal stratification on heat transfer. This study shows the unsteady behavior of tetra and ternary hybrid nanofluid flow over two different surfaces, i.e., linear and exponential surfaces. The thermophysical properties of the tetra nanoparticles, i.e., Ag,Cu,SWCNTs,andMWCNTs\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{Ag}},\;{\text{Cu}},\;{\text{SWCNTs}},\,\,{\text{and}}\,\,{\text{MWCNTs}}$$\end{document}, comprise in C2H6O2–H2O (50–50%) base fluid. Similarity constraints are applied to convert the flow model equations into a system of coupled ordinary differential equations, which are then solved using MATLAB’s iteration-based bvp4c code. Results show that rotation and stretching significantly affect the velocity and temperature profiles. A comparison with existing literature indicates strong agreement, validating the current findings. Additionally, response surface methodology (RSM) for multiple linear regression is used to statistically analyze the impact of relevant parameters on the drag coefficient and rate of energy transfer of fluid over the linear elongated surface, including 3D plots illustrating these effects. Thermal stratification is utilized in energy-efficient buildings to maintain comfortable temperatures by keeping warmer air near the ceiling and cooler air near the floor. It is also employed in water reservoirs to optimize energy storage and distribution. [ABSTRACT FROM AUTHOR]

Prior research suggests that the use of nanotechnology may greatly improve the efficiency of enhanced oil recovery methods, especially hot fluid injection. The thermophysical characteristics of the nanofluid may have an enormous effect on how well the injection process works. However, it takes both time and resources to conduct laboratory analyses of the effects of thermophysical characteristics on the effectiveness of nanofluid-based improved oil recovery methods. Computational models can effectively forecast the thermophysical characteristics of nanofluids and how they affect oil recovery efficiency, which helps overcome this difficulty. The current study investigates the flow of vacuum residue (VR) fluid, which generates entropy when suspended graphene oxide (GO) nanoparticles. When mixed convection and variable thermal conductivity are present, a static/moving wedge allows the nanofluid to propagate. The continuity, energy, entropy, and momentum equations form the foundation of the governing model. We use certain similarity variables to simplify the suggested mathematical formulations into forms for nonlinear differential equations (DEs). We show the results of the reduced equations using the Chebyshev collocation method. We present the graphical and numerical results for all the emerging parameters. For enhanced oil recovery applications, the current results are beneficial. [ABSTRACT FROM AUTHOR]

The current work presents a theoretical framework to analyze the nonlocal thermoelastic model with a general kernel function for memory-based derivatives by incorporating two-time delays. The introduced model aims at studying the thermomechanical response of rotating size-dependent nanobeams. The nonlocal elasticity theory and the generalized heat conduction model with phase delays are utilized to formulate the problem. In the proposed model, the thermal conductivity is expected to vary linearly with temperature and the system is excited by a variable harmonic heat source by considering the time-dependent exponential decaying load. To this end, the semi-analytical solutions for the transverse and axial displacements, thermodynamic temperature and bending moment are examined using the Laplace transform method. The effects of the nonlocal parameter and various loading conditions are also investigated and discussed. Finally, it is demonstrated that how the linear variation of thermal conductivity could affect the performance of the considered system. [ABSTRACT FROM AUTHOR]

The pioneer motivations for current flow model are to study the rheological aspects of chemical reactive Williamson nano-material with utilization of gyrotactic microorganisms. The peak theme of activation energy and variable thermal conductivity are also incorporated. Unlike typical investigations, current flow model is formulated with employment of slip consequences with higher order relations. The induced flow is caused by a porous stretched surface additionally impact by magnetic force. The flow equations are transmuted into dimensionless form first for which numerical simulations are performed using famous finite difference approximations. The results are verified for limiting cases by comparing with various investigations and found excellent accuracy. The physical insight of all flow parameters are graphically underlined with interesting physical appliances. Furthermore, the numerical calculation for heat transfer enhancement, change in mass flux and motile density simulations are also evaluated in tabular form. The stream line and contour plots are also prepared. [ABSTRACT FROM AUTHOR]

Design of an optimal extended surface having functionally graded material is significant in cooling performance of hot attached structures in technological applications. The present endeavor is to search for axially variable thermal conductivity formula for a prescribed longitudinal fin shape of rectangular or triangular cross section. Heat transfer is presumed to take place through conductive, convective and radiative effects. The well-known fact is that it is not possible to solve in closed-form the highly nonlinear heat transfer equation under such considerations in general, unless some effects are ignored. Temperature or spatial dependence of material properties of the fin make the problem even harder to treat without numerical simulations. To help designer to avoid such simulations, prescribed temperature distributions in the form of elementary polynomial functions involving some shape parameters are utilized. Under operative geometric and thermal parameters such as the Biot number and the radiation parameter, exact solution formulae for the pertinent thermal conductivity distribution along the functionally graded extended surface are then obtained. The price to pay is only to work out the domain of definition of physical parameters acting on the loaded temperature profile.Designer can benefit from the advantage of the presented elementary solutions while analyzing the efficiency of convecting-radiating longitudinal fins of rectangular, triangular or a more general tapered longitudinal fin class cross sections and control/adjust the physical parameters to the desired temperature/material conditions. With a preloaded temperature profile to the energy equation, the tip temperature can be adjusted so as to enhance the heat transfer rate by increasing/decreasing the governing fin parameters. Such promising inverse problem of extracting axial thermal conductivity distribution from a prescribed temperature solution can also be utilized in other kinds of fin profiles without resorting to the numerical simulations. [ABSTRACT FROM AUTHOR]

Phase change materials (PCM) are substances that release and absorb sufficient energy at phase transition to provide useful heat or cooling. Stefan problems including PCM have many applications in science and engineering. Since an exact solution for this type of Stefan problem does not exist, tracking the moving boundary and obtaining accurate temperature distribution are still challenging issues in mathematical aspects. Therefore, in this paper, a new approach based on combining the cubic B-spline and a fourth-order compact finite difference scheme is developed to capture the behavior of the one-dimensional Stefan problem including moving PCM, variable thermal conductivity and periodic boundary condition. The proposed combined method in space and the Crank–Nicolson method in time are applied to the model after the moving domain is transformed into the fixed domain by the boundary immobilization method. The comparative results have seen a good agreement for a particular case. Besides, the stability of the scheme and the effect of the model parameters on the numerical solution are analyzed. The computations reveal that the new combined method is seen to pull up the accuracy of the model solutions and presents an efficient alternative solution to the model. [ABSTRACT FROM AUTHOR]

This paper deals with an unsteady magnetohydrodynamic (MHD) two-dimensional (2D) second-grade fluid flow towards a permeable exponentially stretching surface with homogeneous–heterogeneous reactions. The non-uniform heat source/sink, variable thermal conductivity and thermal radiation are considered to analyse the thermal attributes. The velocity slip effect is also taken into consideration at the boundary of the surface. The modelled equations of motions and energy are transformed into non-linear ODEs by suitable transformations. The Matlab Bvp4c approach is employed for the numerical solution of the equations. The impacts of various parameters are scrutinised using graphs. The physical quantities of interests such as Sherwood number, Nusselt number and skin friction are presented in the form of graphs and tables and discussed. The velocity profile diminishes by enhancing the values of the parameter of the porous medium. The temperature field rises with larger values of thermal radiation parameters. Decay in concentration profile is noted when the influence of homogeneous–heterogeneous reactions becomes larger. By increasing the values of the second-grade fluid parameter, the magnetic field parameter and the porous medium, the coefficient of skin friction increases, while it reduces by enhancing the values of the unsteady parameter. [ABSTRACT FROM AUTHOR]

We consider a stochastic heat equation with variable thermal conductivity, on infinite domain, with both deterministic and stochastic source and with stochastic initial data. The stochastic source appears in the form of multiplicative generalized stochastic process. The generalized stochastic process appearing in the equation could be a generalized smoothed white noise process or any other generalized stochastic process of a certain growth. In our solving procedure we use regularized derivatives and the theory of generalized uniformly continuous semigroups of operators. We establish and prove the result concerning the existence and uniqueness of solution within certain generalized function space. We justify our procedure by proving that, under certain conditions, the operators of non-regularized and the corresponding regularized problems are associated. [ABSTRACT FROM AUTHOR]

Researchers have commonly known non-Newtonian materials for their extensive technical and industrial uses including coal slurries, clay mixture, food dispensing, paper manufacturing, nutritional preparation, wiring coatings, polymers, cosmetics, oil recovery, rubber, crystal growth and plastic sheeting. The goal of presented research is to analyze bioconvectional second-grade nanoliquid flow with implications of thermal conductivity and motile microorganism across three-dimensional sheet. A transmuted construction is formed in the ordinary differential method by the use of suitable similarity functions. Governing relations of present flow problem are presented graphically and solved numerically by utilizing built-in MATLAB computational tool with the help of the famed numerical shooting method bvp4c (Lobatto IIIa Formula). The influences of physical parameters like activation energy parameter, bioconvection Lewis number, Lewis number, Peclet number, thermophoresis number, mixed convective number, buoyancy ratio number and Brownian motion number via the velocity profile, temperature concentration, volumetric concentration and motile concentration are discussed in detail. The current research has major applications in medical, contemporary aerospace technologies and importance to energy systems. The results designate that x-component of skin friction is enhanced for larger values of bioconvection Rayleigh number by 25%. The y-component of skin friction is enhanced for larger values of mixed convection parameter by 10%. Furthermore, local Nusselt number is upgraded for growing values of thermal Biot parameter by 57%. [ABSTRACT FROM AUTHOR]

The porous fin of radial profile is considered in the current analysis along with the radiation and thermal-dependent internal heat generation condition. In addition, two different cases have been examined based on the linear dependency and exponential dependency of thermal conductivity on temperature. The Darcy's law is used to study the porous nature of fin. The modeled governing equation is a second-order nonlinear ordinary differential equation and is solved via Runge–Kutta–Fehlberg fourth–fifth-order method. The important terms are grouped as dimensionless parameters and discussed their influence on the heat transfer rate and thermal stresses of the fin. The thermal stresses like radial stress and tangential stress are addressed comprehensively and interpreted graphically. Also, the fin efficiency is defined and discussed graphically. It is found that the tangential stress shows higher compression near fin base region and larger tensile stress near tip radius. [ABSTRACT FROM AUTHOR]

In this work, we present a new thermoelasticity model in the context of the new theory of fractional order strain thermoelasticity with variable thermal conductivity. The thermoelastic properties of a semi-infinite homogeneous isotropic medium with variable thermal conductivity were investigated. The governing equations have been derived and we use the direct method to obtain the solutions of the field functions in the Laplace domain. The medium is subjected to ramp type thermal loading. To obtain the different inverse field functions numerically we used a complex inversion formula of Laplace transform based on a Fourier expansion. The effects of different parameters on the conductive temperature, the thermodynamical temperature, the displacement the stress and on the strain distribution are presented graphically. Comparison between each field function with constant and variable thermal conductivity are also presented graphically and discussed. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, the boundary layer flow around a thin needle is examined. Non-constant thermal conductivity as well as viscosity is the art of present study. Governing equations are modeled in the presence of frictional heating and are simplified by utilizing boundary layer assumptions. To obtain a self-similar solution, boundary layer equations are further transformed into dimensionless forms by utilizing axisymmetric similarity variables. For further investigation of the problem, attained self-similar nonlinear equations with suitable boundary conditions are solved numerically using MATLAB bvp5c. A comparative study with existing findings is carried out. Impact of velocity ratio parameter, size of the needle, variable viscosity parameter, Prandtl number, fluid friction and variable thermal conductivity parameters on dimensionless velocity, skin friction coefficient, temperature and local Nusselt number are investigated through graphical analysis. It is observed that flow with variable viscosity and thermal conductivity is significantly different and realistic in comparison with constant properties-based flow. It is also noted that the temperature of the fluid and the thickness of the thermal boundary layer are related directly to reduction in needle size. Further, considerable enhancement is observed in heat transfer rate for the variable properties case. [ABSTRACT FROM AUTHOR]

The rheological features of an incompressible axi-symmetric Casson-Maxwell nanofluid flow between two stationary disks are examined. The lower permeable disk is located at z = −a, while the upper disk is placed at z = a. Both the disks are porous and subjected to uniform injection. The fluid properties such as thermal conductivity vary with temperature. The Cattaneo-Christov thermal expression is implemented along with the Buongiorno nanofluid theory. By operating the similarity functions, the reduced form of the fluid model in terms of ordinary differential equations is obtained and solved by the bvp4c numerical technique. The physical quantities are demonstrated graphically on the velocity and temperature fields. Three-dimensional flow arrangements and two-dimensional contour patterns against several dimensionless variables are also sketched. The numerical values of the local Nusselt and Sherwood numbers for various quantities are presented in tabular set-up. The intensity of the linear relationship between the Nusselt and Sherwood numbers is assessed through Pearson's product-moment correlation technique. The statistical implication of the linear association between variables is also examined by the t-test statistic approach. [ABSTRACT FROM AUTHOR]

Analysis of thermal and solutal energy transport phenomena in Maxwell fluid flow with the help of Cattaneo–Christov double diffusion theory is performed in this article. Unsteady 2D flow of Maxwell fluid with variable thermal conductivity over the stretching cylinder is considered here. We formulate the partial differential equations (PDEs) under given assumptions for the governing physical problem of heat and mass transport in Maxwell fluid by using double diffusion of Cattaneo–Christov model rather than classical Fourier's and Fick's law. Numerical technique bvp4c is employed for the solution of ordinary differential equations (ODEs) which are obtained from governing PDEs under the appropriate similarity transformations. In the view of acquired results, we observed that for convenient results the values of unsteadiness parameter should be less than one. The higher values of Maxwell parameter declines the flow field but increase the energy transport in the fluid flow. Both temperature and concentration distributions in Maxwell liquid decline for higher values of thermal and concentration relaxation time parameter. Moreover, small thermal conductivity parameter also enhances the temperature field. The validation of results is proved with the help of comparison Table 1 with previous articles. The present results are found with help of bvp4c scheme and homotopy analysis method (HAM). [ABSTRACT FROM AUTHOR]

The nature and properties of generalized Newtonian fluid flows are of the most significant phenomena applicable to engineering applications. But this particular portion of research work incorporates the importance of flow, heat and mass transfer analysis of non-homogeneous Sisko fluid transport model. The flow source in this study is assumed by the stretching and shrinking velocities of the sheet. Therefore, the influence of these two velocities creates a phenomenon of multiple solutions. The effect of magnetic field is another significant physical parameter in the flow analysis and has been considered in this study. Moreover, the impacts of variable thermal conductivity, mass diffusivity and suction/injection are also incorporated. The system of conservative governing partial differential equations are converted into a dimensionless system of equations by using the suitable transformations. The new system of equations along with the corresponding transformed boundary conditions are then solved numerically with the help of collocation method in Matlab. This method is a built-in approach for the solution of nonlinear boundary value problem. In comparison with other user-defined numerical approaches, this method is little bit fast and works accurately because this method uses finite difference method for modifying weak initial guess and the CPU timing is very small as compared to other built-in approaches. The present results are shown for the existence of multiple (upper branch and lower branch) solutions for a specific range of involved physical parameters. The critical values of shrinking parameter corresponding to suction parameter and Sisko fluid parameter are computed in the certain range of ( χ c < χ < 0 ). The behaviors of various dimensionless parameters on different profiles are discussed graphically. The increase in material parameter causes a reduction in skin friction for both cases, i.e., shear-thinning as well as shear-thickening fluids. The first and second solutions of temperature and concentration profiles, respectively, show increasing and decreasing trends for an increase in temperature and concentration time relaxation parameters. [ABSTRACT FROM AUTHOR]

Among the fabrication of the nano-biometerials, the bioconvection of nanoparticles attained the utmost importance in this decade. Therefore, this theoretical continuation is performed to utilize the bioconvected flow of Williamson nanofluid caused by an oscillatory stretching surface. The flow is generated due to periodic motion of the sheet. The energy equation is modified by variable thermal conductivity. The significance of present flow problem increases by utilizing the thermophoresis and Brownian movement factors. The available formulated partial differential equations are promoted into non-dimensional structure via similarity variables. The analytical solution is fulfilled using convergent technique. The implications of promising parameters on velocity, temperature profile, nanoparticles volume fraction and microorganisms profile are evaluated graphically. Locally constituted physically expressions such as Nusselt number, Sherwood number and motile density number are treated numerically as well as graphically. The presence of variable thermal conductivity, thermophoresis and Brownian motion effects are more frequent for enhancement of heat transfer. The detected observation can involve the theoretical significance in various engineering processes, bio-fuel cells, solar energy system and enhancement of extrusion systems. [ABSTRACT FROM AUTHOR]

In thoughtfulness of researchers and technologists in the arena of nanoscience and nanotechnology owing to reduced thermal properties of the usual base fluids, a new-fangled sort of fluids acknowledged as nanofluids have been established, which contains nanoparticles deferred in a hostfluid. For instance, nanofluids have superior heat transport enactment, because deferred nanoparticles have better thermal conductivity allied with base liquid. Here elaborated 3D flow of a Carreau nanoliquid is influenced by a bidirectional stretched surface. To visualize the properties of Brownian motion and thermophoresis on the Carreau nanoliquid, the Buongiorno's relation is exploited in a more proficient tactic. Variable thermal conductivity with the possessions of heat source/sink is pondered for heat transfer mechanisms. Suitable conversion is used to change the PDEs into non-linear ODEs. Numerically, bvp4c scheme is prompted to crack the resulting ODEs. The discrete behaviors for shear thinning/thickening of nanoliquid temperature and concentration field are described and deliberated in aspect for somatic parameters. It is exposed that the Carreau liquid temperature declines for Prandtl number and conflicting trends are being noted for Brownian and thermophoresis parameters. Moreover, heat transfer amount diminishes for higher Brownian and thermophoresis parameters. An assessment between two different approaches namely, bvp4c and homotopy analysis method, is also presented in tabular form which ensure that our outcomes are more precise. [ABSTRACT FROM AUTHOR]

The present work focused here is a mixed convective MHD flow of cross fluid in the presence of heat generation/absorption and variable thermal conductivity over a bidirectional stretchable sheet. To elaborate the mechanism of heat transfer is analyzed in view of non-Fourier heat flux based upon Cattaneo–Christov theory. The influence of a simple isothermal model of homogeneous–heterogeneous reactions is further used for solute concentration. As a result, the relevant Buongiorno fluid model is utilized in mathematical modeling and then it is simplified through lubrication technique. By using appropriate transformations, the raised PDEs initially converted to ODEs. Convergent solutions of ODEs are obtained by the implementation of the numerical procedure bvp4c technique. However, the velocity, temperature and concentration profiles have been sketched by distinct physical flow parameter. Drag coefficients and heat transport are also computed numerically. Our results reveal that temperature profile has an inverse relation between the relaxation parameter and variable thermal conductivity. [ABSTRACT FROM AUTHOR]

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the Green- Lindsay (G-L) theory, the coupled (CD) theory, and the Lord-Shulman (L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock. The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium. [ABSTRACT FROM AUTHOR]

We have explored multiple solutions for non-Newtonian Casson nanofluid flow past a moving extending sheet under the influence of variable thermal conductivity and nonlinear radiation through a permeable medium with convective boundary conditions. The governing equations are transformed to ODEs by similarity transformations and then solved numerically by the Chebyshev pseudospectral (CPS) method. Dual solutions are obtained for velocity, temperature and nanoparticle concentration distributions with different values of physical parameters. In the present analysis, it was found that, the nonlinearity formula for thermal radiation gives a realistic description of nanofluid mathematical model depending on the existence of nanoscale particles. Furthermore, the concentration of nanoparticles is highly influenced by nonlinear thermal radiation due to the sizes of nanofluid, where linear radiation has a weak effect on the concentration distributions of nanoparticles. These results are very important in medicine, and more specifically for reinforcing the delivery of drugs through the skin, as the nanoparticle entrapment of drugs enhances delivery to, or absorption by, target cells. The transdermal drug delivery system offers huge clinical advantages over other dosage forms. As transdermal drug delivery offers controlled as well as predetermined rate of release of the drug into the patient, it can keep up steady-state nanofluid concentration. [ABSTRACT FROM AUTHOR]

A novel model of variable thermal conductivity of semiconductor medium in two-temperature theory is studied. The Photothermal excitation due to laser pulses is investigated. The governing equations have been studied under three theories in generalized thermoelasticity during Photothermal transport process. Taken into consideration the linearity of thermal conductivity, in which depend on temperature. The normal mode method is used to obtain the exact expressions of some physical fields analytically, in the context of the recombination between thermal-elastic-plasma waves. The silicon (Si) material is used to the numerical simulation. Some comparisons between the results are made as the influence of thermoelectric coupling parameter, variable thermal conductivity and two-temperature parameter of physical fields. The numerical calculations have been discussed and illustrated graphically. [ABSTRACT FROM AUTHOR]

White crystalline powder (aluminum oxide-Al2O3) and water are the products often formed after the heating of aluminum hydroxide. In this report, boundary layer flow of two different nanofluids (i.e., 36 nm Al2O3-water and 47 nm Al2O3-water) over an upper horizontal surface of a paraboloid of revolution under the influence of magnetic field is presented. The combined influence of magnetic field strength, electric current density, electric charge, electron collision time, and the mass of an electron in the flows are considered in the governing equations. Three-dimensional transport phenomenon was considered due to the influence of the Lorentz force (F→) along the z-direction as in the case of Hall currents. In this study, the dynamic viscosity and density of the nanofluids are assumed to vary with the volume fraction ϕ. The dimensional governing equations were non-dimensionalization and parametrization using similarity variables. The corresponding boundary value problem was transformed into initial value problem using the method of superposition and solved numerically using fourth-order Runge-Kutta method with shooting technique (RK4SM). Magnetic field parameter is seen to have dual effects on the cross-flow velocity profiles of both nanofluids. The maximum cross-flow velocity is attained within the fluid domain when 36 nm nanoparticles alumina is used. The cross-flow velocity gradient at the wall increases with magnetic field parameter (M) and also increases significantly with Hall parameter at larger values of M. [ABSTRACT FROM AUTHOR]

An analysis is introduced to investigate the salient features of nonlinear convective flow of thixotropic fluid in the version of Cattaneo-Christov heat flux theory. The stagnation point flow is present. The flow phenomenon is by an impermeable stretching sheet. The energy expression is modeled through the theory of Cattaneo-Christov heat flux. Characteristics of heat transfer phenomenon are described within the frame of variable thermal conductivity. Suitable variables reduced to the nonlinear partial differential expressions to the ordinary differential expressions. Series solutions of resulting systems are acquired within the frame of homotopy theory. Convergence analysis is achieved and suitable values are determined by capturing the so-called ℏ−curves. Graphical results for velocity and temperature are displayed and argued for sundry physical variables. Expression of skin friction coefficient is calculated through numerical values. Higher values of mixed convection parameter, Prandtl number, and thermal relaxation time lead to decay the temperature and layer thickness. [ABSTRACT FROM AUTHOR]

The objective here is to examine the characteristics of non-Fourier flux theory in flow induced by a nonlinear stretched surface. Constitutive expression for an incompressible Walter-B liquid is taken into account. Consideration of thermal stratification and variable thermal conductivity characterizes the heat transfer process. The concept of boundary layer is adopted for the formulation purpose. Modern methodology for the computational process is implemented. Surface drag force is computed and discussed. Salient features of significant variables on the physical quantities are reported graphically. It is explored that velocity is enhanced for a larger ratio of rate constants. The increasing values of thermal relaxation factor correspond to less temperature. [ABSTRACT FROM AUTHOR]

Of concern in this work is an investigation of the heat and mass transfer mechanisms in the presence of first-order chemical reaction for an incompressible flow of non-Newtonian Carreau fluid model past a wedge. The hydromagnetic effects are also incorporated in the present study alongside the momentum, thermal, and solutal slips on the surface of the wedge. In addition to it, the impact of variable thermal conductivity is taken into account to explore the heat transfer characteristics of the flow field. The principal equations corresponding to the physical situation are transformed over to an arrangement of non-dimensional ordinary differential equations through local similarity variables. The numerical solutions of non-dimensional systems are acquired by enforcing fifth-order Runge-Kutta integration scheme and Newton’s method with the assistance of broadly utilized computer software MATLAB. The curiosity of present investigation is that the shear stress and the fluid velocity are substantially raised by the magnetic parameter, while the temperature and concentration profiles are decelerated. Another interesting result is that the thermal slip parameter prompts the lessening of fluid temperature together with the rate of heat transfer. Furthermore, the present computations reveal that the concentration of the chemical reaction is observed to be a decreasing function of the Schmidt number and solutal slip parameter. Moreover, the suitable validations are presented to confirm the achieved results accuracy. [ABSTRACT FROM AUTHOR]

Influence of temperature-dependent thermal conductivity on MHD flow of Cross nanoliquid bounded by a stretched sheet is explored. The combined feature of Brownian motion and thermophoresis in nanoliquid modeling is retained. In addition, the attributes of zero mass flux at sheet are imposed. First-order chemical reaction is retained. The resulting problems are numerically computed. Plots and tabulated values are presented and examined. It is figured out that larger thermophoretic diffusion and thermal conductivity significantly rise the thermal field, whereas opposite situation is seen for heat transfer rate. [ABSTRACT FROM AUTHOR]

The present article explores the influence of variable fluid properties on nanofluid flow over a wedge. The flow analysis has been considered under the effect of surface slip. It is supposed to have fluid viscosity and thermal conductivity as an inverse function and linear function of temperature, respectively. The resulting nonlinear ordinary differential equations are solved numerically using RK-4 method together with shooting procedure. The consequence of involved pertinent parameters on the flow province has been discussed through graphs and tables coupled with required discussion. Our analysis conveys that the fluid temperature is higher in the presence of variable viscosity parameter and thermal conductivity parameter. It is also observed that the wall stress decreases with increasing velocity slip parameter. [ABSTRACT FROM AUTHOR]

Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The constitutive equations of Carreau fluid are modeled in the form of partial differential equations (PDEs). Concerning boundary conditions available, the PDEs are converted to ordinary differential equations (ODEs) by means of similarity transformation. The homotopy analysis method (HAM) is used for solution of the system of nonlinear problems. The effects of various parameters such as Weissenberg number $\mathit{We}^{2}$ , magnetic parameter $M^{2}$ , power law index n, porosity parameter D, wall thickness parameter α, power index parameter m, slip parameter λ, thermal conductivity parameter ε, radiation parameter R and Prandtl number on velocity and temperature profiles are analyzed and studied graphically. [ABSTRACT FROM AUTHOR]

Two-dimensional squeezing flow of second grade fluid between two parallel plates is addressed. The lower plate is stretched while the upper plate is either moving away or towards the lower one. Temperature-dependent thermal conductivity is considered. Further, heat source/sink is present. Unlike the classical situation, the heat flux by Cattaneo-Christov theory is adopted instead of Fourier's heat conduction law. Homotopic convergent solutions of velocity and temperature are developed and analyzed. Reduction in the thermal layer thickness is observed for Cattaneo-Christov heat flux model when compared with that of Fourier's law of heat conduction. It is observed that velocity profile is enhanced by increasing the squeezing parameter. Also, a positive squeezing parameter enhances the thermal field due to a higher squeezing force applied on the fluid. [ABSTRACT FROM AUTHOR]

Steady mixed convection micropolar fluid flow towards stagnation point formed on horizontal linearly stretchable melting surface is studied. The vortex viscosity of micropolar fluid along a melting surface is proposed as a constant function of temperature while dynamic viscosity and thermal conductivity are temperature dependent due to the influence of internal heat source on the fluid. Similarity transformations were used to convert the governing equation into non-linear ODE and solved numerically. A parametric study is conducted. An analysis of the results obtained shows that the flow-field is influenced appreciably by heat source, melting, velocity ratio, variable viscosity and thermal conductivity. [ABSTRACT FROM AUTHOR]

In the present work, the hydromagnetic boundary layer flow and heat transfer of Casson fluid in a thin liquid film over an unsteady stretching sheet in the presence of variable thermal conductivity, thermal radiation, and viscous dissipation is investigated numerically. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. Similarity equations are derived and then solved numerically by using a shooting method with fourth order Runge-Kutta integration scheme. Comparisons with previous literature are accomplished and obtained an excellent agreement. The influences of parameters governing a thin liquid film of Casson fluid and heat transfer characteristics are presented graphically and analyzed. It is observed that the heat transfer rate diminishes with a rise in thermal conductivity parameter and Eckert number. Further, the opposite influence is found with an increase in radiation parameter. [ABSTRACT FROM AUTHOR]

This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper is devoted to introduce a numerical simulation with a theoretical study for flow of a Newtonian fluid over an impermeable stretching sheet which embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that proposed method is powerful mathematical tool and it can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering. [ABSTRACT FROM AUTHOR]

This article is devoted to describe the boundary layer flow and heat transfer for non-Newtonian Powell-Eyring fluid over an exponentially stretching continuous impermeable surface with an exponential temperature distribution taking into account variable thermal conductivity. The fluid thermal conductivity is assumed to vary as a linear function of temperature . The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with numerical technique using appropriate boundary conditions for various physical parameters . The numerical solution for the governing non-linear boundary value problem is based on applying Chebyshev spectral method over the entire range of physical parameters. The effects of governing parameters like the thermal conductivity parameter and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are computed and discussed through graphs and tables. In this work, a special attention is given to investigate the effect of the variable thermal conductivity parameter on the temperature field above the stretching sheet. [ABSTRACT FROM AUTHOR]

The steady flow and heat transfer of a couple stress fluid due to an inclined stretching cylinder are analyzed. The thermal conductivity is assumed to be temperature dependent. The governing equations for the flow and heat transfer are transformed into ordinary differential equations. Series solutions of the resulting problem are computed. The effects of various interested parameters, e.g., the couple stress parameter, the angle of inclination, the mixed convection parameter, the Prandtl number, the Reynolds number, the radiation parameter, and the variable thermal conductivity parameter, are illustrated. The skin friction coefficient and the local Nusselt number are computed and analyzed. It is observed that the heat transfer rate at the surface increases while the velocity and the shear stress decrease when the couple stress parameter and the Reynolds number increase. The temperature increases when the Reynolds number increases. [ABSTRACT FROM AUTHOR]

In this work, we consider the 1D problem for an infinitely long hollow cylinder in the context of the theory of generalized thermoelasticity with one relaxation time. The material is assumed to have variable thermal conductivity depending on the temperature. Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained using a numerical technique based on Fourier expansion. Numerical results are represented graphically and in table format. [ABSTRACT FROM AUTHOR]