Influence of Soret-Dufour and thermophoresis on hydromagnetic mixed convection heat and mass transfer over an inclined flat plate with non-uniform heat source/sink and chemical reaction

The paper is devoted to the study of thermophoresis and Soret-Dufour effects on magnetohydrodynamic mixed convective heat and mass transfer over an inclined flat plate with non-uniform heat source/sink. Governing non-linear coupled ordinary differential equations are solved numerically using Runge-Kutta Fehlberg technique with shooting scheme. The effects of various physical parameters on the velocity, temperature, and concentration profiles are depicted graphically. The values of skin-friction coefficient, Nusselt number and Sherwood number are presented in a tabular form. It is found that increase in thermophoretic and chemical reaction parameters retard the velocity and concentration distributions in the boundary layer.     

On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species

Finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with constant heat flux and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The concentration profiles are compared with the exact solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction, the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Numerical study for the effects of thermophoresis and variable thermal conductivity on heat and mass transfer over an accelerating surface with heat source

A modified numerical solution scheme, for local similarity boundary layer analysis, is used to study the effects of thermophoresis and variable thermal conductivity on heat and mass transfer over an accelerating surface with heat source in the presence of suction and blowing. This numerical scheme is efficient and accurate and it can be programmed and applied easily and its application is illustrated, step by step, by studying the above mentioned problem. The resulting boundary layer equations are solved numerically by Chebyshev finite difference method. Numerical results for the velocity, temperature and concentration as well as for the skin friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Heat and mass transfer on a stretching sheet with a magnetic field in a visco-elastic fluid flow through a porous medium with heat source or sink

A mathematical model will be analyzed in order to study the role of an applied magnetic field on heat and mass transfer in a visco-elastic fluid flow through a porous medium with a stretching sheet in the presence of such effect as heat generation or absorption. A similarity transformation is used to reduce the governing partial differential equations into ordinary ones, which are solved numerically by shooting method. Numerical results for the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Mass transfer effects on impulsively with variable surface heat flux

Numerical Solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with variable surface heat flux and mass transfer is presented here. The governing equations are solved using implicit finite-difference scheme of Crank-Nicolson type. The velocity profiles are compared with exact Solution and are found to be in good agreement. The transient and steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that there is a rise in the velocity due to the presence of a mass diffusion. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate

Summary The forced convective heat and mass transfer along a semi-infinite vertical flat plate is investigated for non–Newtonian power law fluids in the presence of a strong nonuniform magnetic field, and the Hall currents are taken into account. The similarity solutions are obtained using transformations group theory. These are the only symmetry transformations admitted by the field equations. The application of one-parameter groups reduces the number of independent variables by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. Furthermore the similarity equations are solved numerically by using a fourth-order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the power-law viscosity index n, generalized Schmidt number Sc, generalized Prandtl number Pr, the magnetic parameter M and the Hall parameter m.     

Homotopy analysis method for chemical reaction and thermophoresis effects on heat and mass transfer for mhd hiemenz flow over a porous wedge in the presence of heat radiation

An analytical technique, namely, the homotopy analysis method, is applied to analyze the effect of chemical reaction and thermophoresis particle deposition on the MHD mixed convective heat and mass transfer for a Hiemenz flow over a porous wedge in the presence of heat radiation. The fluid is assumed to be viscous and incompressible. Analytical and numerical calculations are carried out for different values of dimensionless parameters, and an analysis of the results obtained shows that the flow field is influenced appreciably by the buoyancy ratio as well as by the thermal diffusion and suction/injection parameters. The effects of these parameters on the process characteristics are investigated methodically, and typical results are illustrated. An explicit, totally analytical, and uniformly valid solution is derived which agrees well with numerical results.     

MHD flow and heat transfer in a channel bounded by a shrinking sheet and a plate with a porous substrate

This research is concerned with heat transfer and an MHD flow of a viscous incompressible electrically conducting fluid in a channel bounded by a shrinking sheet and an impermeable plate. A fluid-saturated porous substrate of a very low permeability is attached to the impermeable plate. The flow in the channel is induced by the upper shrinking sheet, where a constant suction is imposed. By introducing the similarity transformations, the governing partial differential equations for the flow and heat transfer are transformed to ordinary differential equations which are solved analytically by using the perturbation series method for a small shrinking parameter. Expressions for the velocity distribution, temperature field, skin friction, and heat transfer rate are obtained, and numerical computations are carried out for various parameters. The results are displayed graphically and discussed.     

Radiative flow of Casson fluid over a moving wedge filled with gyrotactic microorganisms

The present study investigates the effects of thermophoresis and Brownian motion on two-dimensional magnetohydrodynamics (MHD) radiative Casson fluid past a moving wedge filled with gyrotactic microorganisms. Numerical results are presented graphically as well as in tabular form with the aid of Runge-Kutta and Newton’s methods. Effects of pertinent parameters on velocity, temperature, concentration and density of motile organism distributions are presented and discussed for two flow cases namely suction and injection. The obtained results are validated by comparing with the available previous studies and found good agreement. The thermal and concentration boundary layer are significantly modulated with the rise of thermophoresis and Brownian motion parameters for both suction and injection flow cases. The increasing values of thermophoresis parameter boost up the temperature and concentration field while thermal boundary layer decreased for increasing the Brownian motion parameter. With the rise of Casson fluid parameter, the velocity increases but the temperature, concentration and density of motile organism is found to decrease in both suction and injection flow cases. The influence of the pertinent parameters on the local shear stress coefficient, local Nusselt and local Sherwood numbers are discussed with the assistance of the table for two flow cases separately (suction and injection). The thermal radiation parameter boost up the local Sherwood number, gyrotactic microorganisms mass transfer rate and depreciates the local Nusselt number for the suction and injection flow cases. An important finding of the present investigation is that the gyrotactic microorganisms can enhance the heat and mass transfer rate.     

Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy

An analysis is performed to study the combined effects of nonlinear thermal radiation, Arrhenius activation energy, chemical reaction and heat generation/absorption on the steady three-dimensional magnetohydrodynamic flow of Eyring-Powell nanofluid flow over a slendering stretchable sheet with velocity, thermal and solutal slips. The prevailing partial differential equations are transmuted into coupled non-linear ordinary differential equations via with the suitable similarity transformations. The resultant non-linear coupled differential equations are solved numerically by using the R-K 4^th order method along with shooting scheme. The results are calculated to measure the influence of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient are presented graphically and in tabular form. It is noticed that the temperature is more impactable for higher values of radiative heat transport. The local Sherwood number decays exponentially for all the values of the chemical reaction parameter. We compared the present results for the limiting cases with previously published results, which has shown reliability and efficiency.     

Thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders

The thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders was studied numerically. The objective of this research was to study the effect of free convection and the distance between cylinders, on deposition of particles. Continuity, momentum and energy equations were solved to determine the velocity and temperature profiles in the channel. The particle trajectories were evaluated by solving the Lagrangian equation of motion that included the drag, Brownian diffusion and thermophoresis forces. It was found that the temperature gradient near the channel wall, in mixed flow regime, is higher than the temperature gradient in forced convection regime. Increasing the temperature gradient increased the effect of thermophoresis on deposition of particles. It was observed that the deposition was increased with the Richardson number. The distance between cylinders is a parameter that influences the deposition of particles. Temperature gradient decreases with increasing the cylinders’ distance; on the other hand, the length of the high temperature gradient zone, which is located in the region between the cylinders where the most deposition occurs, will be increased. These two opposite phenomena cause the fact that at a distance which is four times longer than the cylinders’ length, a maximum cumulative deposition fraction occurs. It was eventually concluded that the thermophoresis and the inertial impaction are dominant deposition mechanisms of particles on the channel wall.     

Hall effect on MHD flow and heat transfer over a stretching sheet with variable thickness

We investigate the MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness. The wall temperature and the wall velocity are assumed to vary. The effects of external magnetic field along the sheet and the Hall currents are considered. The governing equations are solved numerically using an implicit finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in very good agreement. The effects of the physical parameters on the velocity and temperature fields are presented graphically and analyzed. The effect of the Hall current gives rise to a cross flow. Moreover, the Hall current and the magnetic field have strong effect on the flow and heat transfer characteristics, i.e., shear stress and the Nusselt number.     

Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation

Summary Magnetohydrodynamic natural convection boundary layer flow on a sphere with uniform heat flux in presence of heat generation has been investigated in this paper. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is then solved numerically by two distinct efficient methods, namely (i) implicit finite difference method together with the Keller box scheme and (ii) perturbation or series solution technique. The results of the surface shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution as well as temperature distribution are shown graphically for a selection of parameter sets consisting of the heat generation parameter and the magnetic parameter.     

Heat Transfer in a Micropolar Fluid along a Non-linear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature

In this paper, heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of a micropolar fluid passed a non-linear stretching sheet taking into account the effects of a temperature-dependent viscosity and variable wall temperature are studied numerically for local similarity solutions by applying the Nachtsheim-Swigert iteration method. The results corresponding to the dimensionless temperature profiles and the local rate of heat transfer are displayed graphically for important material parameters. The results show that in modeling the thermal boundary layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results and therefore it must be treated as a variable rather than a constant within the boundary layer. The results also show that the local rate of heat transfer strongly depends on the non-linear stretching index and temperature index.     

Numerical modeling of the aerodynamics, heat exchange, and combustion of a polydisperse ensemble of coke-ash particles in ascending axisymmetric two-phase flow

A two-dimensional stationary model of motion, heat and mass exchange, and chemical reaction of polydisperse coke and ash particles in ascending gas-suspension flow has been constructed with allowance for the turbulent and pseudoturbulent mechanisms of transfer in the dispersed phase. The system of equations that describes motion and heat transfer in the solid phase has been closed at the level of the equations for the second moments of velocity and temperature pulsations, whereas the momentum equations of the carrying medium have been closed using the equation for turbulent gas energy, which allows for the influence of the particles and heterogeneous reactions.     

Unsteady three-dimensional combined heat and mass free convective flow over a stretching surface with time-dependent chemical reaction

Summary This paper investigates the combined effects of the free convective heat and mass transfer on the unsteady three-dimensional laminar boundary layer flow over a stretching surface. The stretching rates of the surface are assumed to vary as a reciprocal of a linear function of time. Generation or consumption of the diffusing species due to a homogeneous chemical reaction is considered. The chemical reaction rate is assumed to vary with time according to a power law. With appropriate similarity transformation, the boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying a fifth-order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Prandtl number Pr, Schmidt number Sc, the unsteadiness parameter λ, the chemical reaction parameter γ₀ and the reaction order n are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various values of the parameters. A comparison is made between the present work and previous results.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that is mixed convection parameter λ_t, modified mixed convection parameter λ_c, Prandtl number Pr, heat generation/absorption parameter δ, Schmidt number Sc, thermophoresis parameter N_t, and thermophoretic coefficient k are sketched in graphical form. Numerical results for skin friction, heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters. It is reported that in enhancement in heat, generation boosts up the fluid temperature at some positions of the surface of the sphere. As heat absorption parameter is decreased temperature field increases at position X = π/4 on the other hand, no alteration at other considered circumferential positions is noticed.     

Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with variable heat fluxes embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The buoyancy induced boundary layer adjacent to a vertical surface is analyzed using a non-Darcy flow model. The parameters for inertia, buoyancy ratio, exponent of heat flux, position and diffusion have been examined. The governing differential equations of continuity, momentum, energy and concentration are transformed into a set of coupled equations and solved using similarity analysis with numerical technique. Results show the velocity, temperature and concentration profiles related to local Nusselt and Sherwood numbers at different magnitude of Soret and Dufour numbers.     

Impacts of nonuniform heat source or sink on MHD mixed convection along an exponentially stretching surface

This paper investigates steady MHD mixed convection flow over an exponentially stretching surface in presence of nonuniform heat source or sink. The dimensional nonlinear partial differential equations governing the flow and temperature fields are expressed in nondimensional form using suitable nonsimilar transformations. Then, numerical solutions are obtained by solving these nondimensional equations using implicit finite difference scheme in combination with Quasilinearization technique. Effects of various physical parameters on velocity and temperature profiles are analyzed numerically. Further, numerical results in terms of the skin-friction coefficient and local Nusselt number are presented graphically and also in tabular form.