Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature-dependent thermophysical properties

This paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature-dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.     

Optimal Homotopy Asymptotic Solutions for Nonlinear Ordinary Differential Equations Arising in Flow and Heat Transfer due to Nonlinear Stretching Sheet

Optimal homotopy asymptotic method (OHAM) is used to obtain solutions for nonlinear ordinary differential equations (ODEs) arising in fluid flow and heat transfer at a nonlinear stretching sheet. The solutions for skin friction and temperature gradient for some special cases are tabulated and compared with the available numerical results in the literature. Moreover, OHAM is found to be very easy to use and the technique could be used for solving coupled nonlinear systems of ordinary differential equations arising in science and engineering.     

Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition

The investigations on the flow of non-Newtonian fluids are becoming one of the major topics in the research field. These liquids have substantial applications in industrial and engineering fields such as drilling rigs, food processing, paint and adhesives, nuclear reactors and cooling systems. On the other hand, hybrid nanofluids play a major role in the heat transfer process. Keeping this in mind, the motion of Casson hybrid nanofluid squeezing flow between two parallel plates with the effect of heat source and thermophoretic particle deposition is examined here. The partial differential equations that govern fluid flow are converted into ordinary differential equations using appropriate similarity variables and those equations are numerically solved using the Runge–Kutta–Fehlberg fourth–fifth-order method by implementing the shooting scheme. The graphs depict the effects of a number of key parameters on fluid profiles in the absence and presence of the Casson parameter. These graphs show that fluid velocity enhances with the augmentation of the local porosity parameter. Thermal dispersal upsurges for enhancement of heat source/sink parameter and the concentration profile escalates for an upsurge of the thermophoretic parameter. Skin friction enhances with enhancement in the local porosity parameter.     

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.     

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

The bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring‐Powell fluid over an oscillatory stretching sheet embedded in a non‐Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The fluid properties, namely the fluid viscosity, thermal conductivity, and mass diffusivity, are assumed to vary with temperature. It is assumed that the first‐order chemical reaction with heat generation/absorption takes place in the flow. The flow domain is subject to uniform transverse magnetic field perpendicular to the stretching surface. The transformed flow equations are solved numerically using BSQLM on overlapping grids. The convergence properties and accuracy of the method are assessed. The proposed method is computationally efficient, and it gives stable and highly accurate results after few iterations and using few grid points in each subinterval. The improved accuracy rests upon the use of the overlapping grid, which produces sparse coefficient matrices that are easy to invert and have small condition numbers. The effects of physical parameters on the flow fields, local skin friction, the Nusselt number, and the Sherwood number are exhibited through graphs and tables. Amongst other findings, we found that the amplitude of the fluid flow along with flow characteristics may efficiently improve through the utilization of variable fluid viscosity. Heat and mass transportation processes enhance with the inclusion of nonlinear radiative heat flux, temperature‐dependent thermal conductivity, and mass diffusion coefficient, whereas they diminish with the increase in the local inertia coefficient. The current flow analysis can be useful in various engineering applications including paper production, polymer solution, glass blowing, extrusion of thermal system manufacturing process, and heat transportation enhancement.     

Approximate Analytical Solution of Stagnation Point Flow and Heat Transfer over an Exponential Stretching Sheet with Convective Boundary Condition

This study is concerned with the stagnation point flow and heat transfer over an exponential stretching sheet via an approximate analytical method known as optimal homotopy asymptotic method (OHAM). The governing partial differential equations are converted into ordinary nonlinear differential equations using similarity transformations available in the literature. The heat transfer problem is modeled using two‐point convective boundary condition. These equations are then solved using the OHAM approach. The effects of controlling parameters on the dimensionless velocity, temperature, friction factor, and heat transfer rate are analyzed and discussed through graphs and tables. It is found that the OHAM results match well with numerical results obtained by Runge–Kutta Fehlberg fourth‐fifth order method for different assigned values of parameters. The rate of heat transfer increases with the stretching parameter. It is also found that the stretching parameter reduces the hydrodynamic boundary layer thickness whereas the Prandtl number reduces the thermal boundary layer thickness.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating

Present research article investigate the heat and mass transfer characteristics of unsteady magnetohydrodynamic Casson nanofluid flow between two parallel plates under the influence of viscous dissipation and first order homogeneous chemical reaction effects. The impacts of thermophoresis and Brownian motion are accounted in the nanofluid model to disclose the salient features of heat and mass transport phenomena. The present physical problem is examined under the presence of Lorentz forces to investigate the effects of magnetic field. Further, the viscous and Joule dissipation effects are considered to describe the heat transfer process. The non‐Newtonian behaviour of Casson nanofluid is distinguished from those of Newtonian fluids by considering the well‐established rheological Casson fluid model. The two‐dimensional partial differential equations governing the unsteady squeezing flow of Casson nanofluid are coupled and highly nonlinear in nature. Thus, similarity transformations are imposed on the conservation laws to obtain the nonlinear ordinary differential equations. Runge‐Kutta fourth order integration scheme with shooting method and bvp4c techniques have been used to solve the resulting nonlinear flow equations. Numerical results have been obtained and presented in the form of graphs and tables for various values of physical parameters. It is noticed from present investigation that, the concentration field is a decreasing function of thermophoresis parameter. Also, concentration profile enhances with raising Brownian motion parameter. Further, the present numerical results are compared with the analytical and semianalytical results and found to be in good agreement.     

Micropolar flow in a porous channel with high mass transfer

In this research the injective micropolar flow in a porous channel is investigated. The flow is driven by suction or injection on the channel walls, and the micropolar model is used to describe the working fluid. This problem is mapped into the system of nonlinear coupled differential equations by using Berman's similarity transformation. These are solved for large mass transfer via Optimal Homotopy Asymptotic Method (OHAM). Also the numerical method is used for the validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results. Trusting this validity, effects of some other parameters are discussed.     

Magnetohydrodynamic mixed convection in a non-Newtonian third-grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

Buoyancy assisted and buoyancy opposed mixed convection of a third-grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third-grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non-Newtonian third-grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.     

Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer

We consider one of the newest analytical methods, the Optimal Homotopy Asymptotic Method (OHAM), to solve nonlinear equations arising in heat transfer. Two specific applications are considered: cooling of a lumped system with variable specific heat and the temperature distribution equation in a thick rectangular fin radiation to free space. Results obtained by OHAM, which does not need small parameters are compared with numerical results and a very good agreement was found. This method provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. The results reveal that the proposed method is explicit, effective and easy to use.     

Entropy generation analysis of free convection radiative MHD Eyring–Powell fluid flow between porous parallel plates with Soret and Dufour effects

In this present study, we have investigated the entropy generation analysis and Dufour and Soret impacts on unsteady incompressible free convective radiative MHD Eyring–Powell fluid flow between parallel plates with periodic injection and suction. The governing PDEs are converted into nondimensional coupled nonlinear ordinary differential equations by using similarity variables then numerically solved by Runge–Kutta fourth-order scheme with shooting technique. The results are discussed in detail for different flow, mass, and heat transfer profiles corresponding to various active parameters and presented in tables and graphs. Also, it is noticed that the temperature profiles are enhanced with the fluid parameter, whereas the concentration profiles are decreased with the Prandtl number. The validations of present results with the existing outcomes for the viscous case of skin friction are included and have found to be in good agreement. The present numerical study is useful for the enhancement of heat transfer in various industrial and chemical processes.     

Convective Heat Transfer of an Air Bubble in Water With Variable Thermophysical Properties

A numerical study of convective heat transfer of an air bubble in water with variable thermophysical properties is considered. Two-dimensional simulations of multifluid flows with heat transfer include the Navier–Stokes, energy, and volume of fluid (VOF) advection equations. The solver computes the flow field and temperature by solving the systems of Navier–Stokes equations and the energy equation using the finite–volume method with the SIMPLE algorithm and tracks the position of interface between two fluids with different fluid properties by the VOF method with piecewise linear interface construction technique. Empirical correlations in terms of temperature for thermophysical properties are considered in the simulations. The convective heat transfer model is assessed with a benchmark problem of cooling of water and compared with previous literature data showing good agreement. Finally, a numerical study of the effect of the bubble diameter in the range from 2 mm to 3 mm on heat transfer is performed.     

Thermochemistry and viscous heat dissipative effects on unsteady upper-convected Maxwell fluid flow past a stretching vertical plate with thermophysical variables

In this paper, unsteady upper-convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature-dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature-dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence.     

Second law analysis for chemically reacting natural convective second‐grade fluid flow between porous parallel plates with Hall and Ion slip

In this article, we performed the entropy generation of free convective chemically reacting second‐grade fluid confined between parallel plates in the influence of the Hall and Ion slip with heat and mass fluxes. Let there be a periodic suction/injection along with the plates, the governing flow field equations are reduced as a set of coupled nonlinear ordinary differential equations by using appropriate similarity transformations then solved numerically with shooting method based on Runge‐Kutta 4th order scheme. The results are analyzed for velocity in axial and radial directions, temperature distribution, concentration distribution, entropy generation number, Bejan number, mass and heat transfer rates with respect to distinct geometric, and fluid parameters and shown graphically and tables. It is observed that the entropy generation is enhanced with Prandtl number, whereas decreases with a second‐grade parameter, the effects of Hall and Ion slip parameters on velocity components, temperature and entropy generation number are the same. The entropy generation number the fluid is enhanced with the suction‐injection parameter whereas, the concentration of the fluid decreases with the increasing of chemical reaction parameter.     

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

The thermodynamics modeling of a Reiner–Philippoff-type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear-thinning, Newtonian, or shear-thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature- and concentration-induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral-based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature-dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.     

Transient electromagnetohydrodynamic radiative squeezing flow between two parallel Riga plates using a spectral local linearization approach

This article addresses transient electromagnetohydrodynamic radiative squeezing flow due to convectively heated electromagnetic actuator. The transport analysis of heat and mass is explored considering the heat generation/absorption and destructive species homogeneous reaction. Suitable transformations are applied on the mathematical model developed to convert governing partial differential equations to ordinary differential equations (ODEs). Spectral local linearization method (SLLM) is employed on the resultant nonlinear coupled ODEs to compute the numerical results. Influence of sundry physical quantities on heat mass transfer of squeezing flow characteristics are determined using graphs and tabular results. SLLM results exhibit that momentum and temperature improved with rise in squeezing and heat source parameters correspondingly. Momentum enhances at lower plate and detracts with rise in modified Hartmann number. For improved heat source parameter, the rate of heat transfer diminishes and is more significant for higher Prandtl number values. This investigation has relevance in disk style magnetic clutches, rolling elements, food processing, bearings, squeezing film pressure sensors, and flow rheostats.     

Second law analysis in radiative mixed convective squeezing flow of Casson fluid between parallel disks with Soret and Dufour effects

The present communication deals the entropy generation by cause of heat and mass transform in an unsteady mixed convective radiative squeezing flow of a Casson fluid confined between two parallel disks in the presence of diffusion‐thermo and thermal‐diffusion effects and temperature jump. The lower disk is taken to be porous and the upper one is impermeable. The governing PDE is converted as nonlinear ordinary differential equations (ODE) by using well‐established similarity transformations; then, the reduced nonlinear ODE are solved by shooting method with Runge‐Kutta fourth‐order approach. The influence of distinct nondimensional fluid and geometric‐related parameters on the velocity profiles, temperature, concentration, entropy generation number, and Bejan number are studied in detail and represented in the form of graphs. The entropy of the Casson fluid is increased with the Eckert number, whereas the concentration profile is decreased by squeezing Reynolds number. The current results are correlated with existing results for the viscous case and found to be in better agreement.     

Chebyshev Spectral Collocation Method for Unsteady Mhd Flow and Heat Transfer of a Dusty Fluid Between Parallel Plates

The unsteady magnetohydrodynamic flow of a dusty fluid and heat transfer between parallel plates in which the electrically conducting fluid has temperature-dependent viscosity is studied. Both the fluid and the dust particles are governed by the coupled set of momentum and energy equations. The Chebyshev spectral method in space and implicit backward difference in time procedure is presented, introducing physically Navier-slip conditions for both the fluid and dust particle velocities. The Hartmann number, viscosity parameter, and Navier-slip parameter influences on the flow and temperature are simulated.     

Bioconvection in a squeezing flow of a micropolar fluid in a horizontal channel

The bioconvection flow of an incompressible micropolar fluid containing microorganisms between two infinite stretchable parallel plates is considered. A mathematical model, with a fully coupled nonlinear system of equations describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms is presented. The governing equations are reduced to a set of nonlinear ordinary differential equations with the help of suitable transformations. The resulting nonlinear ordinary differential equations are linearized using successive linearization method, and the resulting system of linear equations is solved using the Chebyshev collocation method. The detailed analysis illustrating the influences of various physical parameters, such as the micropolar coupling number, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number, and bioconvection Peclet number on the velocity, microrotation, temperature, concentration and motile microorganism distributions, skin friction coefficient, Nusselt number, Sherwood number, and density number of motile microorganism, is examined. The influence of the squeezing parameter is to increase the dimensionless velocities and temperature and to decrease the local Nusselt number and local Sherwood number. The density number of motile microorganism is decreasing with squeezing parameter, bioconvection Lewis number, bioconvection Peclet number, and bioconvection Schmidt number.