Solutal Grashof Number Research Articles

Magnetohydrodynamic double-diffusive peristaltic flow of radiating fourth-grade nanofluid through a porous medium with viscous dissipation and heat generation/absorption

This article focuses on determining how to double diffusion affects the non-Newtonian fourth-grade nanofluids peristaltic motion within a symmetrical vertical elastic channel supported by a suitable porous medium as well as, concentrating on the impact of a few significant actual peculiarities on the development of the peristaltic liquid, such as rotation, initial pressure, non-linear thermal radiation, heat generation/absorption in the presence of viscous dissipation and joule heating with noting that the fluid inside the channel is subject to an externally induced magnetic field, giving it electromagnetic properties. Moreover, the constraints of the long-wavelength approximation and neglecting the wave number along with the low Reynolds number have been used to transform the nonlinear partial differential equations in two dimensions into a system of nonlinear ordinary differential equations in one dimension, which serve as the basic governing equations for fluid motion. The suitable numerical method for solving the new system of ordinary differential equations is the Runge–Kutta fourth-order numerical method with the shooting technique using the code MATLAB program. Using this code, a 2D and 3D graphical analysis was done to show how each physical parameter affected the distributions of axial velocity, temperature, nanoparticle volume fraction, solutal concentration, pressure gradients, induced magnetic field, magnetic forces, and finally the trapping phenomenon. Under the influence of rotation Omega, heat Grashof number {Gr}_{t}, solutal Grashof number {Gr}_{t}, and initial stress {P}^{*}, the axial velocity distribution u changes from increasing to decreasing, according to some of the study’s findings. On the other hand, increasing values of nonlinear thermal radiation R and temperature ratio {theta }_{w} have a negative impact on the temperature distribution theta but a positive impact on the distributions of nanoparticle volume fraction Phi and solutal concentration gamma. Darcy number Da and mean fluid rate F also had a positive effect on the distribution of pressure gradients, making it an increasing function.

Heat source and Joule heating effects on convective MHD stagnation point flow of Casson nanofluid through a porous medium with chemical reaction

This investigation explores the convective MHD stagnation point flow of Casson nanofluid over a stretching sheet in a porous medium with higher-order chemical reactions and multiple slips. The examination of heat transmission is carried out in the presence of radiation, Joule heating, viscous dissipation, and heat source. The system of governing equations was simplified by using appropriate transformations. The transformed equations are tackled numerically by a Runge-Kutta-based shooting technique with the bvp5c MATLAB package. The graphical and numerical results for different parametric values are discussed and presented through figures and tables. It is observed that an increase in the magnetic field, porosity, and Casson fluid parameter reduces the velocity whereas the opposite trend is seen in the case of the thermal Grashof number and the solutal Grashof number. Increasing values of radiation and Joule heating parameters, and the Eckert number, lead to an increase in the temperature. The chemical reaction, suction, and solutal slip were found to reduce the concentration. The friction factor was reduced due to the higher values of the thermal Grashof number, solutal Grashof number, and the velocity ratio parameter. Also, an increase in the Brownian motion and thermal slip parameters decreases the heat transfer rate. The computational results of the Nusselt number have been validated with published results in the literature and found good agreement. The results obtained in this investigation have applications to biomedical, engineering, and industrial sectors such as food processing, polymer manufacturing, glass, and fiber production, improving oil recovery, and material processing.

Impact of double diffusivity on the hyperbolic tangent model conveying nano fluid flow over the wedge

The significant thing in our analysis is to inspect the double-diffusivity convection for the hyperbolic tangent nanofluid model, under the spotlight effects of activation energy and viscosity over the wedge-shaped geometry. Activation energy enunciates chemical reaction and also Buongiorno model is applied to highlight the important features of the thermophoresis and Brownian diffusion coefficient. The convection of double diffusivity is illustrated through Soret and Dufour parameter. The mathematical modeling of demarcated flow produces a collection of non-linear partial differential equations, which are consequently transmuted into ordinary differential equations using suitable transformation. The graphical results for these ordinary differential equations are created using the Bvp4c approach. The effect of pertinent parameters on fluid flow, thermal variation, concentration and double diffusivity profiles are examined. The velocity field generally behaves as the decreasing function of thermal and nanofluid Grashof number but surges along the Solutal Grashof number. The Brownian diffusion coefficient surges the temperature profile and minors the concentration and double-diffusivity. Soret diffusivity surges the concentration distribution when fluid crosses the edge of the wedge. The nanofluid Lewis number particularly slows down the double-diffusivity profile. The graphical sketches of local skin friction, Nusselt number, Sherwood number, isothermal contour and streamlines flow elaborated our analyses more precisely.

Response surface optimization for the electromagnetohydrodynamic Cu-polyvinyl alcohol/water Jeffrey nanofluid flow with an exponential heat source

This article examines the sensitivity analysis of Jeffrey fluid flow in the presence of copper nanoparticles with polyvinyl alcohol water serving as the base fluid under the influence of source terms like Joule heating, viscous dissipation, exponential heat source, and Arrhenius activation energy via a non-linear vertically elongating surface of non-uniform thickness. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting coupled ODEs are converted into a system of first-order ODEs and then solved using the shooting iteration technique with the RK-4th order method. The remarkable impacts of numerous parameters like Deborah number, Hartmann number, electric field parameter, thermal and solutal Grashof number, Prandtl and Eckert numbers, exponential heat source parameter, Lewis number, chemical reaction parameter, and activation energy parameter associated with the flow properties are discussed graphically. The effects of various physical parameters and the dependence of the response factors on the input parameter are explored using an experimental design and sensitivity analysis based on Response Surface Methodology. Response Surface Methodology is utilized to determine the output response variables of model dependencies, such as the drag coefficient and Nusselt number on the independent input parameters, namely the electric field parameter and Deborah numbers for the drag coefficient, and electric field parameter, thermophoresis diffusion parameter, and exponential heat source parameter for the Nusselt number. Local Nusselt number enhances with increment in the electric field parameter and thermophoresis diffusion parameter values, whereas it decelerates with the rise in exponential heat source parameter. The non-Newtonian nanofluids have proven their great potential in thermal transportation which has a diverse range of applications in thermal energy technologies such as lubrication, natural gas networks, spray processes, and cooling of nuclear reactors, spinning of fibers, cryopreservation, drawing of copper wires, nano-drug delivery, electronics, and many more.

Non-Newtonian Mixed Convection Magnetized Flow with Heat Generation and Viscous Dissipation Effects: A Prediction Application of Artificial Intelligence

A non-Newtonian stagnation point fluid flow towards two different inclined heated surfaces is mathematically formulated with pertinent effects, namely mixed convection, viscous dissipation, thermal radiations, heat generation, and temperature-dependent thermal conductivity. Mass transfer is additionally considered by the use of a concentration equation. The flow narrating equations are solved numerically by using the shooting method along with the Runge–Kutta scheme. A total of 80 samples are considered for five different inputs, namely the velocities ratio parameter, temperature Grashof number, Casson fluid parameter, solutal Grashof number, and magnetic field parameter. A total of 70% of the data are used for training the network; 15% of the data are used for validation; and 15% of the data are used for testing. The skin friction coefficient (SFC) is the targeted output. Ten neurons are considered in the hidden layer. The artificial networking models are trained by using the Levenberg–Marquardt algorithm. The SFC values are predicted for cylindrical and flat surfaces by using developed artificial neural networking (ANN) models. SFC shows decline values for the velocity ratio parameter, concentration Grashof number, Casson fluid parameter, and solutal Grashof number. In an absolute sense, owning to a prediction by ANN models, we have seen that the SFC values are high in magnitude for the case of an inclined cylindrical surface in comparison with a flat surface. The present results will serve as a helpful source for future studies on the prediction of surface quantities by using artificial intelligence.

Entropy Generation and Thermal Radiation Analysis of EMHD Jeffrey Nanofluid Flow: Applications in Solar Energy.

This article examines the effects of entropy generation, heat transmission, and mass transfer on the flow of Jeffrey fluid under the influence of solar radiation in the presence of copper nanoparticles and gyrotactic microorganisms, with polyvinyl alcohol-water serving as the base fluid. The impact of source terms such as Joule heating, viscous dissipation, and the exponential heat source is analyzed via a nonlinear elongating surface of nonuniform thickness. The development of an efficient numerical model describing the flow and thermal characteristics of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in various devices continues to increase. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting higher-order coupled ODEs are converted into a system of first-order ODEs and then solved using the RK 4th-order method with shooting technique. The remarkable impacts of pertinent parameters such as Deborah number, magnetic field parameter, electric field parameter, Grashof number, solutal Grashof number, Prandtl number, Eckert number, exponential heat source parameter, Lewis number, chemical reaction parameter, bioconvection Lewis number, and Peclet number associated with the flow properties are discussed graphically. The increase in the radiation parameter and volume fraction of the nanoparticles enhances the temperature profile. The Bejan number and entropy generation rate increase with the rise in diffusion parameter and bioconvection diffusion parameter. The novelty of the present work is analyzing the entropy generation and solar radiation effects in the presence of motile gyrotactic microorganisms and copper nanoparticles with polyvinyl alcohol-water as the base fluid under the influence of the source terms, such as viscous dissipation, Ohmic heating, exponential heat source, and chemical reaction of the electromagnetohydrodynamic (EMHD) Jeffrey fluid flow. The non-Newtonian nanofluids have proven their great potential for heat transfer processes, which have various applications in cooling microchips, solar energy systems, and thermal energy technologies.

Mixed convective flow of Casson nanofluid in the microchannel with the effect of couple stresses: irreversibility analysis

ABSTRACT The current cutting-edge modelling involves mixed convection and couple stress influences on the velocity and thermal distribution of the flow of Casson nanomaterial in possession of microchannel. This study elucidates the mass and heat transport of Casson nanomaterial in the upright microchannel in the existence with non-linear thermal radiation, Brownian motion and thermophoresis. Along with the flow, the particle size effects are also taken into consideration. The channel walls facilitate the sucking/injecting the fluid into the microchannel. Viscous dissipation and buoyant forces are deliberated in the study. Slip regime and convective conditions are taken at the boundaries. By making use of velocity and thermal profile, the entropy produced and dominance of heat or fluid friction irreversibilities are analyzed. The obtained equations are non-dimensionalized using non-dimensional entities and further solved using Runge-Kutta Fehlberg 4–5th order procedure together with shooting technique. Illustrations of the graph exemplify the outcomes of the work. The impact of couple stress parameter depicts the depletion of velocity profile as the couple stress takes into consideration the size effect of the particle, which enhances viscosity and hence declines velocity of the flow. The irreversibility in the channel can be achieved to be least when the thermal and solutal Grashof number is kept low.

Convective Flow of Blood through a Constricted Cylinder and the Effect of Cholesterol Growth Rate on the Motion in the Presence of a Magnetic Field

An inflammatory disease resulting in the pathological constriction of the intima and media of the arterial system, such as the aorta, causes symptoms like stroke, heart attack, or angina; This research investigates the convective flow of blood through a constricted cylinder and the effect of cholesterol growth rate on the motion in the presence of a magnetic field by transforming the problem into a system of time-dependent partial differential equations. The governing partial differential equations (PDEs) were transformed into dimensionless ordinary differential equations (ODEs) and solved using the Laplace method. After obtaining the analytical solution, Wolfram Mathematica was used to perform the numerical computation where the various physical parameters such as Soret number, radiation number, solutal Grashof number, Schmidt number, and Prandtl number were varied to their impact studied. The study discovered that increasing the Soret number causes an increase in blood velocity, whereas decreasing the Solutal Grashof number decreases blood velocity. Furthermore, an increase in radiation parameter increases the blood velocity, but a Soret number increase results in a decrease in the concentration of cholesterol in the fluid, a Schmidt number, and oscillatory frequency increase, causing the temperature to decrease. This research is useful for clinicians and mathematical modellers who are trying to understand the flow of cholesterol saturated fluid in the human vascular system and how best to proffer analytical and numerical solutions in synergy with laboratory investigation.

Modify homotopy perturbation method using yang transform to study the effect of magnetic field with mass and heat transfer on pulsatile blood flow in tapered stenosis arteries

AbstractThe effect of a magnetic field on two‐dimensional pulsatile blood flow in tapered stenosis arteries was studied by employing the Yang transform homotopy perturbation method (YTHPM). The mathematical model which was solved by the researchers Liu and Liu, was successfully developed by adding the effect of a magnetic field for the blood flow in addition to the effect of mass and heat transfer on it. The impact of the angle of tapering, the Grashof number, the solutal Grashof number, and the magnetic field on the axial velocity, the wall shear stress, flow resistance, and the volumetric flow rate was investigated in two cases absence and presence of the magnetic field. The results prove that YTHPM is efficacious and highly accurate in finding the analytical approximate solution for pulsatile blood flow in tapered stenosis arteries under the influence of a magnetic field. The convergence of the new solutions is also discussed in the absence and presence of the magnetic field. Further, the graphs of these new solutions show the validity of, a necessity for, and utility of YTHPM, and are in line with results put forward by other studies.

Casson fluid flow in a vertical annulus through porous medium with heat transfer characteristics and chemical reaction: An exact solution

This study explores heat and mass transport in natural convection of Casson fluid in a vertical annulus via porous medium. Impacts of thermal radiation, heat source and chemical reaction are taken into consideration. The equations representing the model reduced into nondimensional ordinary differential equations under adequate transformations are solved analytically. Closed form solutions are obtained for the problem in terms of Bessel’s functions. Influences of various arising parameters such as porous medium parameter, heat generation, thermal radiation, thermal Grashof number, solutal Grashof number, etc. on flow, temperature and concentration fields are exhibited by graphs and discussed. Also, we have solved the problem numerically on MATLAB software employing the bvp4c technique along with shooting technique. The exact and numerical solutions compared found a good match. Moreover, the effects of numerous parameters on quantities of physical importance such as skin-friction coefficient, Nusselt number and Sherwood number are also portrayed and discussed. Heat exchangers, energy storage systems such as batteries and inverters, thermal storage and thermal protection systems are some examples of applications of the study.

The modified finite element method for heat and mass transfer of unsteady reacting flow with mixed convection

This study reveals the extension of a mathematical model of heat and mass transfer of fluid flow over a sheet by incorporating the effect of non-linear mixed convection. The governing equations of flow phenomena are expressed as partial differential equations (PDEs). Similarity transformations are employed to get a dimensionless set of boundary value problems. Most of the existing relevant literature employed some solver to solve a set of differential equations, but this study implements the finite element method to tackle the boundary value problems. The employed finite element method is based on the Galerkin approach. For verifications of the obtained results, a set of linear and non-linear boundary value problems is also solved with Matlab solverbvp4c. The results are displayed in graphs by varying Grashof number, modified (solutal) Grashof number, non-linear convection parameters in heat and mass transfer, radiation parameter, Prandtl number, Schmidt number, and reaction rate parameter. Also, numerical values for the friction at the wall and local Nusselt and Sherwood numbers are given in tables. The problem in PDEs form is also solved with software that implements the finite element method to solve problems. The simulations are also provided, which is the outcome of the software. It is shown that the velocity profile escalates by growing values of thermal and solutal Grashof numbers. Problem-solving techniques from this study may be used in future research to address other unsolved heat transfer fluid physics issues.

Modelling Blood Flow through a Sclerotic Artery and the Effect of Thermal Heat on Cholesterol Concentration in the Presence of a Magnetic Field

Blood flow through a sclerotic artery and the effect of thermal heat on cholesterol concentration in the presence of a magnetic field are modelled using mathematical models which represent the blood momentum coupled with buoyancy due to temperature, cholesterol concentration, porosity of the medium and magnetic field effect. The study involved the formulation of the geometry of atherosclerosis at a specific location with sclerosis over time in the arterial channel. The system of equations was solved using the Laplace method, where the blood velocity, cholesterol concentration and temperature profile were obtained with governing parameters such as magnetic field, Schmidt number, Soret number, Prandtl number, radiation parameter, chemical parameter, and oscillatory frequency, respectively. The result revealed that the blood velocity increases for different units of increase in Soret number, radiation parameter, and porosity parameter, while the velocity decreases for different values of solutal Grashof number, Schmidt number, Prandtl number, and magnetic field parameter. Furthermore, the cholesterol concentration decreases with an increase in Soret number, Schmidt number, and Prandtl number, respectively. The study also revealed that an increase in Prandtl number, radiation parameter, and oscillatory frequency parameter decreases the blood temperature.

Exponential space and thermal-dependent heat source effects on electro-magneto-hydrodynamic Jeffrey fluid flow over a vertical stretching surface

This paper deals with the study of an incompressible electro-magneto-hydrodynamic (EMHD) Jeffrey fluid flow over a vertical nonlinear stretching surface of variable thickness. Heat and mass transfer effects are analyzed by considering different source terms like viscous dissipation, Ohmic heating, thermophoresis, Brownian motion, thermal heat source, exponential heat source and activation energy. Governing equations for the flow system are converted into dimensionless forms using appropriate similarity transformations. The solution for the resulting governing equations is obtained by using the shooting technique with RK-4 method. The effects of various physical parameters such as magnetic field parameter [Formula: see text], Grashof number (Gr), solutal Grashof number [Formula: see text], Brownian diffusion parameter [Formula: see text], thermophoresis diffusion parameter [Formula: see text], thermal heat source parameter [Formula: see text], exponential heat source parameter [Formula: see text], Prandtl number (Pr) and Lewis number (Le) are presented with the help of graphs. It is observed that the heat transfer effects increase by increasing thermal and exponential heat sources, and mass transfer effects enhance by increasing the activation energy. Entropy generation for this flow system is also analyzed. Entropy decreases with an increase in the electric field parameter. In contrast, the Bejan number initially increases with an increase in the electric field parameter. After some particular value of electric field parameter, it changes its behavior in the boundary layer and decreases with an increase in the electric field parameter. Entropy and Bejan number increase with an increment in the concentration difference parameter. The accuracy of the results is validated by those of published literature and found in reasonable justification. The present results may be helpful in many engineering and industrial applications like manufacturing lubrication, natural gas networks, cooling nuclear reactors and spray processes.

Tangent-hyperbolic nanoliquid flow in a microchannel, thermal and irreversibility rate analysis

ABSTRACT The objective of the current investigation is to examine the influence of buoyancy force, heat source, Brownian motion, thermophoresis, chemical reaction, transverse magnetic field and convective boundary condition on flow of tangent-hyperbolic nanofluid through an upright microchannel. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations. The RKF45 method along with the shooting technique is used to solve the fluidic system numerically. The Buongiorno model is considered to observe the influence of thermophoresis, Brownian motion and chemical reaction with mixed convection. Graphical and numerical illustrations are presented to visualize the behavior of different parameters of interest on velocity, temperature, concentration and entropy generation of the flow system. The substantial findings of this study have been recorded as the amplification in the thermal and solutal Grashof number causes an increment in the flow rate in a channel, the thermal energy builds up with Brinkman number and heat source parameter, another significant outcome of the present analysis is that there is a downfall in the concentration field with the strengthening of thermophoresis parameter.

Effect of Stenotic Height on Lipid Concentrated Blood Flow through a Microchannel in The Presence of Magnetic Field

In this article, we develop mathematical models for blood momentum, energy equation with lipid concentration, and lipid concentration equation, all of which are subjected to an oscillatory boundary at the channel's upper wall. Using the oscillatory conditions, the governing models were scaled to a set of dimensionless models and reduced to an ordinary differential equation. The reduced perturbed equations were directly solved, yielding blood velocity, temperature, and lipid concentration profiles. Using Wolfram Mathematica, version 10, the obtained flow profiles were coded by varying some of the important biophysical parameters. Conclusively, it is noticed that the thermal Grashof number and solutal Grashof number increase caused the blood velocity to increase; the concentration source parameter increase also increased the blood velocity. Furthermore, the velocity decreases with the increase in the Hartman and Schmidt numbers, respectively. Further investigation revealed that increasing the height of stenosis and lipid source parameter increases the temperature profile, but increasing radiation absorption, Prandtl number, oscillatory frequency, and womersley number decreases the temperature of the fluid. These findings are of great interest to mathematicians, physicists, and other researchers working on blood flow issues and the development of medical prosthetic devices.

Planar Couette flow of power law nanofluid with chemical reaction, nanoparticle injection and variable thermal conductivity

This article presents the transport of thermal energy and mass in the mixed convection steady planar Couette flow of power-law nanofluid with variable thermal conductivity through a permeable microchannel. The entropy production deliberation here is to investigate the irreversibility aspects. The momentum equation has been made by the permeability of the porous medium, Hall current effect, thermal, and solutal bouncy force. The mathematical model for the thermal energy has been formulated by Ohmic dissipation, Brownian motion, temperature-dependent thermal conductivity, and thermophoresis. The microchannel boundaries retain the no-slip boundary conditions. The concentration formulation has been made by nanoparticle injection rate and chemical reaction. The momentum, energy, and solutal formulations have been numerically cracked by means of Runge–Kutta–Fehlberg fourth fifth-order numerical procedure. The applied Hall current effect generates the fluid flow in the transverse direction. The flow along both axial and transverse direction enhances with thermal and solutal Grashof number and diminutions with permeability of the porous medium. Optimum magnitude of thermophoresis and Brownian motion amplifies the thermal energy of the shear thinning fluid. Concentration field exhibits the opposite nature with the nanoparticle injection rate parameter and chemical reaction parameter. Hall current parameter enhances the irreversibility of the Newtonian nanofluid.

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

AbstractThe purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.

Unsteady Double Diffusive Mixed Convective Flow Over a Vertical Permeable Plate in a Porous Medium

In this article, we analytically investigated the effects of fluctuating free stream and suction velocities on unsteady mixed convective flow over a vertical permeable plate in the occurrence of an unvarying porous medium with a thin environment, time-dependent suction, and viscous dissipation. The governing equations of the physical phenomena give rise to a bunch of extremely non-linear coupled PDE's involving various non-dimensional parameters. An analytical solution has been obtained through the plots for distinct chief physical parameters like Grashof number, the amplitude of the fluctuating suction velocity parameter, amplitude of fluctuating free stream velocity parameter, Prandtl number, permeability parameter, solutal Grashof number, and Eckert number, which are involved in the solution. Also, a comparison has been made with published results in the absence of some non-dimensional parameters for a particular case and found in good agreement. The study results that the fluctuating free stream velocity increases the velocity, temperature increases, and a reverse tendency is observed in the Eckert number.

Free Convection Flow From an Inclined Porous Plate Embedded in a Porous Medium in the Presence of Diffusion Thermo Effect, Heat Source, and Chemical Reaction

An analytical solution to the problem of magnetohydrodynamics free convection flow past an inclined porous plate considering the heat source, diffusion thermo effect, and chemical reaction is obtained. The governing equations for velocity, temperature, and concentration are evaluated using the perturbation method. The effect of relevant physical parameters like porosity parameter, heat source, magnetic parameter, radiation parameter, solutal Grashof number, thermal Grashof number, Dufour effect, chemical reaction on the velocity, temperature, concentration profiles, skin friction, mass flux, and heat flux are demonstrated and discussed graphically. It is noticed that velocity and concentration decrease under the effect of the chemical reaction.

An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity

Since mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivity and mass diffusivity and solved its dimensionless form by applying the finite element method which is the main novelty of this work. Nonlinear governing equations are created because of changing thermal conductivity and mass diffusivity. Nonlinear solutions can be achieved by employing the Galerkin finite element approach. Temperature and concentration‐based thermal conductivity and mass diffusivity are considered. The model is expressed as a set of partial differential equations, and furthermore, it is reduced to a system of dimensionless ordinary differential equations. These obtained equations are solved with the finite element method with linear interpolating polynomials and numerical integration. In addition, a Matlab solver bvp4c is also considered for comparison purposes or validation of the computed results. The graphs depict the effect of various parameters on the velocity, temperature, and concentration curves. The results show that thermal and diffusive wave propagation is significantly affected by thermal conductivity and mass diffusivity changes. Results show that flow velocity escalates by rising values of thermal and solutal Grashof numbers.