MHD 3D free convective flow of nanofluid over an exponentially stretching sheet with chemical reaction

This paper deals with a problem where the effect of variable magnetic field and chemical reaction on free convective flow of an electrically conducting incompressible water based nanofluid over an exponentially stretching sheet has been investigated. In the present study, Buongiorno model associated with Brownian motion and thermophoretic diffusion is employed to describe the heat transfer enhancement of nanofluids. Some suitable similarity transformations reduced the governing boundary layer non-linear partial differential equations into a set of ordinary non-linear differential equations. The transformed equations are then solved numerically using fourth order Runga-Kutta method along with Shooting technique. The major outcomes of the present study is that the magnetic field impedes the fluid motion while thermal as well as mass buoyancy forces accelerate it, the thermophoretic diffusion enhances dimensionless fluid temperature as well as concentration leading to thicker thermal and concentration boundary layers. On the other hand, concentration exponent, Brownian motion parameter and chemical reaction parameter exhibit reverse trend on temperature and concentration. In addition, the presence of magnetic field under the influence of thermal as well as mass buoyancies supports to reduce the rate of heat transfer as well as wall shear stress while the first order chemical reaction develops a thinner concentration boundary layer.     

Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface

Summary The development of velocity and temperature fields of an incompressible viscous electrically conducting fluid, caused by an impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid, is studied. The partial differential equations governing the unsteady laminar boundary-layer flow are solved numerically using an implicit finite difference scheme. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stresses inx-andy-directions and the surface heat transfer increase with the magnetic field and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.     

Unsteady free convective flow through a porous medium

Unsteady 2-dimensional free-convective flow through a porous medium bounded by an infinite vertical plate is considered, when the temperature of the plate is oscillating with the time about a constant non-zero mean value. An analytical solution for the velocity field is derived and the effects of K (permeability parameter) and ω (parameter of frequency) on the velocity field are discussed.     

Unsteady free convection flow over a continuous moving vertical surface

Summary The problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated. Both constant surface temperature and constant surface heat flux conditions have been considered. The nonlinear coupled partial differential equations governing the flow have been solved numerically using the Keller box method and the Nakamura method which both give closely similar solutions. The results indicate that the cooling rate of the sheet can be enhanced by increasing the buoancy parameter or the velocity of the sheet. It is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas. The overshoot in the velocity occurs near the surface when the buoyancy parameter exceeds a certain critical value.     

Unsteady MHD heat and mass transfer of a non-Newtonian nanofluid flow of a two-phase model over a permeable stretching wall with heat generation/absorption

The combined effects of magnetic field and heat generation or absorption on unsteady boundary-layer convective heat and mass transfer of a non-Newtonian nanofluid over a permeable stretching wall have been addressed. A power-law model includes Brownian motion and thermophoresis influences are utilized for non-Newtonian nanofluids with a convective boundary condition. The non-linear governing equations are reduced into ODEs by similarity transformations and solved numerically by using Runge-Kutta-Fehlberg 4th–5th order numerical method (RKF45) with shooting technique. The different physical parameters effects such as the magnetic parameter $(M)$, the heat source/sink parameters $(\lambda )$, the unsteadiness parameter $(A)$, the generalized Prandtl and Lewis numbers on the dimensionless velocity, temperature and nanoparticles volume fraction, in addition to the skin friction, local Nusselt and Sherwood numbers are analyzed. It is reached that the thermal and concentration boundary-layer thickness has higher values with the increasing of magnetic field and heat generation in the case of a pseudo-plastic nanofluid than others.     

Unsteady mass transfer with a heterogeneous chemical reaction during laminar flow past a sphere

Unsteady mass transfer toward a solid sphere is investigated in the region of Peclet numbers 1Pe1000. Diffusion flow in the presence of a first-order chemical reaction is calculated and the relaxation time of the steady regime as a function of the Peclet number is determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 1, pp. 73–79, January, 1976.     

Unsteady laminar flow over a rough surface

A model is developed for the unsteady laminar flow of athin fluid film over a substrate with roughness of the same order as the film height. The limits of large and small surface resistance and small surface-roughness are investigated and it is shown that at leading order the classical parabolic form for the velocity profile is retrieved in all cases. Empirical expressions for the depth-averaged velocity and the ratio of the average to maximum velocities are investigated and shown to agree with the present theory under certain conditions. The method is verified by comparison with experiments for steady uni-directional flow over a surface of known roughness.     

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

The present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.     

Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.     

Structure of free convective flow in a closed three-dimensional cavity

Results are presented which were obtained from visual studies of free convective motion in a closed three-dimensional cavity formed by a rectangular housing and a heater located centrally inside the housing.     

Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface

Summary The effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The velocity profiles are compared with previously published works and are found to be in good agreement. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite element method. 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 concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

On a three-dimensional heat transfer problem for a forced convective flow

We consider the hydrodynamic and thermal boundary layers for the flow represented by Fig. 2. Assuming that WU₀, we obtain approximate formulas for the friction and the heat transfer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 1, pp. 25–30, January, 1972.     

An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream

An analytic technique, namely the homotopy analysis method, is applied to study the flow and heat transfer characteristics in an electrically conducting fluid near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity and temperature. The effects of free convection and internal heat generation or absorption are also considered. Within the framework of boundary layer approximations, the explicit, totally analytic and uniformly valid solutions governed by a set of three fully coupled, highly non-linear equations are obtained, which agree well with numerical results.     

Unsteady free convective boundary-layer flow near a stagnation point in a heat-generating porous medium

The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T ? T _∞) ^p , (p ≥ 1), where T is the fluid temperature and T _∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h _s from the boundary. If h _s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t ^?1) for t large. When h _s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h _s . For p > 2 there is a critical value h _s,crit (dependent on the exponent p) of h _s such that the solution still approaches a nontrivial steady state if h _s < h _s,crit. For h _s > h _s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.     

Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

Finite element analysis of combined heat and mass transfer in hydromagnetic micropolar flow along a stretching sheet

This paper presents a finite element solution of the problem of heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching sheet. The transformed equations for the flow regime are solved numerically by using finite element method. The effect of important parameters namely magnetic field parameter, material parameter, Eckert number and Schmidt number over velocity, microrotation, temperature and concentration functions has been studied. It has been observed that the magnetic field parameter has the effect of reducing the velocity and increasing the microrotation, temperature and concentration while the micropolar parameter has the opposite effect on these functions except temperature function. Temperature increases with the increase in Eckert number and concentration decreases with the increase in Schmidt number.     

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.