Mixed Convection Boundary Layer Flow Research Articles

Mixed Convective Flow of a Powell-Eyring Fluid over a Non-linear Stretching Surface with Thermal Diffusion and Diffusion Thermo

The effect of thermal diffusion (Soret) and diffusion thermo (Dufour) on the heat and mass transfer characteristic in the mixed convective boundary layer flow of Powell-Erying fluid over a nonlinear stretching surface is investigated. Homotopy Analysis Method is applied to obtain an approximate analytic solution for the velocity, temperature and concentration distribution. The effects of non-Newtonian fluid parameters E and δ on the flow, heat and mass transfer are investigated and discussed. It has been found that due to nonlinear stretching of surface and the presence of buoyancy, the Soret number and Dufour number enhance the concentration and temperature in the boundary layer respectively.

Influence of Magnetic Field, Viscous Dissipation and Thermophoresis on Darcy-Forcheimer Mixed Convection Flow in Fluid Saturated Porous Media

This paper presents an application of the spectral homotopy analysis method (SHAM) to solve a problem of darcy-forcheimer mixed convection flow in a porous medium in the presence of magnetic field, viscous dissipation and thermopherisis. A mathematical model governed the flow is analyzed in order to study the effects of chemical reaction, magnetic field, viscous dissipation and thermophoresis on mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. The similarity variable is used to transform the governing equations into a boundary valued problem of coupled ordinary differential equations which are then solved using spectral homotopy Analysis Method. The spatial domains are discretized using Chebyshev-Gauss-Lobatto points and numerical computations are carried out for the non-dimensional physical parameters. A parametric study of selected parameters is conducted and the results for the velocity, temperature and concentration are illustrated graphically and physical aspects of the problem are discussed.

Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder

This article deals with the study of the steady axisymmetric mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder with prescribed external flow and surface temperature. By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique namely homotopy analysis method (HAM). Expressions for velocity and temperature fields are developed in series form. In this study, three different types of nanoparticles are considered, namely alumina (), titania (), and copper () with water as the base fluid. For copper-water nanofluid, graphical results are presented to describe the influence of the nanoparticle volume fraction on the velocity and temperature fields for the forced and mixed convection flows. Moreover, the features of the flow and heat transfer characteristics are analyzed and discussed for foregoing nanofluids. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids.

Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing

In this paper, the numerical solution of mixed convective laminar boundary layer flow around a vertical slender body with suction or blowing has been investigated. Firstly, the governing boundary layer partial differential equations have been made dimensionless and then simplified by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are solved numerically by using computer software. Finally, the flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number, body-radius parameter and other driving parameters. Finally the effects of involved parameters on the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.

Unsteady coupled heat and mass transfer by mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface in the presence of radiation and chemical reaction

The effects of radiation and chemical reaction on coupled heat and mass transfer by unsteady mixed convection boundary-layer flow of a micropolar fluid near the region of the stagnation point on a double-infinite vertical flat plate are studied. The free stream velocity and the surface temperature and concentration are assumed to vary linearly with the distance along the surface. The flow is impulsively set into motion and both of the temperature and concentration at the surface are also suddenly changed from that of the ambient fluid. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, angular velocity, temperature and concentration profiles as well as the skin-friction coefficient, wall couple stress, Nusselt number and the Sherwood number is presented graphically for various parametric conditions and discussed.

Mixed convection–radiation on stagnation-point flow of nanofluids over a stretching/shrinking sheet in a porous medium with heat generation and viscous dissipation

Abstract This paper is concerned with the effects of thermal radiation of mixed convection boundary layer flow towards a stagnation-point flow over a stretching/shrinking embedded in porous medium in nanofluids with heat generation and viscous dissipation. Dual solutions are obtained for shrinking sheet case. The basic equations are solved numerically by using Runge–Kutta–Fehlberg method with shooting technique. This method is more suitable to the present boundary value problem as it has advantages like automatic grid generation and convergence test in order to get very accurate results compared to Runge–Kutta-fourth order method which lacks these features. Results are compared with the previously published results and excellent agreement has been obtained. It is found that suction parameter decreases the velocity and temperature profiles for stretching sheet, whereas reverse trend is obtained for shrinking sheet. It is also found that the boundary layer thickness for second solution is higher than first solution for the three types of nanofluids for shrinking sheet. It is important to note that addition of nanoparticles into the base fluid produced an increase in the skin-friction.

Magnetohydrodynamic (MHD) mixed convection slip flow and heat transfer over a vertical porous plate

The effects of velocity slip and thermal slip on MHD boundary layer mixed convection flow and heat transfer of an incompressible fluid past a plate in presence of suction/blowing are presented. Using similarity transformations the governing partial differential equations are reduced to ordinary differential equations and the nonlinear equations are then solved numerically with the help of shooting method. The present analysis reveals that by reducing the boundary layer thickness, the increasing velocity slip parameter makes the fluid velocity to increase whereas non-dimensional temperature decreases for increasing values of velocity slip parameter. The rate of heat transfer decreases with the increasing values of thermal slip. With increasing values of suction (blowing) parameter the surface temperature decreases (increases).

G-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

Mixed Convection Boundary-layer Flow Past a Vertical Surface Embedded in a Porous Medium: Exponential Case

The steady, mixed convection boundary-layer flow on a vertical surface is considered when there is either an exponentially increasing/decreasing surface temperature with a constant outer flow or an exponentially increasing/decreasing outer flow with a constant surface temperature, characterized by the mixed convection parameter \(\lambda \). A different behaviour is observed in aiding flow or in opposing flow, and whether the boundary condition is increasing or decreasing. An exponentially decreasing surface temperature sets up a flow at large distances driven by the outer flow with the temperature field decreasing at a rate proportional to \(x^{-3/2}\). An exponentially increasing surface temperature gives rise to a different behaviour for aiding and opposing flow. For aiding flow and temperature field increases as \(\mathrm{e}^x\). For opposing flow the solution breaks down at a finite distance from the leading edge effectively where the wall velocity goes to zero at \(-\log \lambda \). With an exponentially decreasing surface temperature for aiding flow the solution evolves to the free convection limit For opposing flow the solution breaks down at a finite distance from the leading edge, effectively where the wall velocity goes to zero. For an exponentially increasing outer flow the solution evolves to the forced convection limit.

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable surface in the presence of magnetic field. To achieve this, one parameter linear group transformation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non-Newtonian fluid (Powell-Eyring model) parameters ɛ and δ on the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ɛ whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.

Mixed convection flow along an inclined permeable plate: effect of magnetic field, nanolayer conductivity and nanoparticle diameter

Steady, two-dimensional mixed convection boundary layer flow of an incompressible $${\rm Al}_2{\rm O}_3$$ –water nanofluid along an inclined permeable plate in the presence of transverse magnetic field has been examined numerically. The governing equations (Boussinesq approximation) with associated boundary condition are solved using FEM for nanofluid containing spherical-shaped nanoparticles having volume fraction ranging from 1 to 4 %. Static-based model for calculating the effective thermal conductivity at 300 K, proposed by Leong et al. (J Nanopart Res 8:245–254, 2006) and Murshed et al. (Int J Therm Sci 47:560–568, 2008) has been implemented. Effect of various pertinent parameters with different classical and experimental models for effective dynamic viscosity is discussed.

Mixed convection flow of a micropolar fluid over a continuously moving vertical surface immersed in a thermally and solutally stratified medium with chemical reaction

The coupled heat and mass transfer by mixed convection boundary layer flow of a micropolar fluid over a continuously moving isothermal vertical surface immersed in a thermally and solutally stratified medium have been investigated in the presence of chemical reaction effect. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by the Keller box method. Comparison with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the skin-friction coefficient as well as the Nusselt number and the Sherwood number is presented graphically for various parametric conditions and discussed.

Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis

Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis

Mixed Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate in a Doubly Stratified Porous Medium

Mixed Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate in a Doubly Stratified Porous Medium

Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection

The purpose of this work is to study the effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a vertical wedge with heat generation/absorption in the presence of uniform suction or injection. The fluid is assumed to be viscous and incompressible. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Both accelerating and decelerating free stream flows are considered. Non-similar solutions are obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are carried out for different values of dimensionless parameters on velocity, temperature and concentration profiles graphically reported in the present study. Also, numerical results are presented for the local skin friction coefficient, the local Nusselt number and the local Sherwood number. Results indicate that the time effect is crucial on velocity, temperature and concentration profiles, and on the local skin friction coefficient, the local Nusselt and Sherwood numbers. The buoyancy assisting force causes overshoot in the velocity profile for lower Prandtl number fluids. Results are compared with previously published work and are found to be in an excellent agreement.

Marangoni Mixed Convection Boundary Layer Flow in a Nanofluid

The problem of Marangoni mixed convection boundary layer flow and heat transfer that can be formed along the interface of two immiscible fluids in a nanofluid is studied using different types of nanoparticles. Numerical solutions of the similarity equations are obtained using the shooting method. Three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (23AlO) and titania (2TiO) are consideredby using a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter ϕ of the nanofluid. The influences of the interest parameters on the reduced velocity along the interface, velocity profiles as well as the reduced heat transfer at the interface and temperature profiles were presented in tables and figures.

G-Jitter mixed convective slip flow of nanofluid past a permeable stretching sheet embedded in a Darcian porous media with variable viscosity.

The unsteady two-dimensional laminar g-Jitter mixed convective boundary layer flow of Cu-water and Al2O3-water nanofluids past a permeable stretching sheet in a Darcian porous is studied by using an implicit finite difference numerical method with quasi-linearization technique. It is assumed that the plate is subjected to velocity and thermal slip boundary conditions. We have considered temperature dependent viscosity. The governing boundary layer equations are converted into non-similar equations using suitable transformations, before being solved numerically. The transport equations have been shown to be controlled by a number of parameters including viscosity parameter, Darcy number, nanoparticle volume fraction, Prandtl number, velocity slip, thermal slip, suction/injection and mixed convection parameters. The dimensionless velocity and temperature profiles as well as friction factor and heat transfer rates are presented graphically and discussed. It is found that the velocity reduces with velocity slip parameter for both nanofluids for fluid with both constant and variable properties. It is further found that the skin friction decreases with both Darcy number and momentum slip parameter while it increases with viscosity variation parameter. The surface temperature increases as the dimensionless time increases for both nanofluids. Nusselt numbers increase with mixed convection parameter and Darcy numbers and decreases with the momentum slip. Excellent agreement is found between the numerical results of the present paper with published results.

Solar Radiation Assisted Mixed Convection Flow Along a Vertical Plate

ABSTRACTSolar radiation assisted mixed convection boundary layer flow of Newtonian fluid along a non- reflecting, non-absorbing and ideally transparent semi-infinite vertical plate is studied here. Beer's law is used to express the solar radiation term. It is convenient to transform the non-linear dimensionless parabolic partial differential equations into (i) primitive variable formulation (PVF) and (ii) stream function formulation (SFF) before applying the numerical schemes. Coupled equations thus obtained from PVF are integrated numerically through implicit finite difference method together with the Gaussian elimination technique whereas block tridiagonal Keller-box technique is adopted to simulate the system of equations obtained from SFF. Numerical results from these two methods are also compared graphically in order to test the validation of the two schemes. However, due to less computation time and accuracy numeric results of shear stress, local Nusselt number coefficient, velocity and temperature profiles are obtained via SFF. It is found that velocity as well as temperature of the non-absorbing fluid enhances owing to the increase in solar radiation parameter.

The effect of unsteadiness on mixed convection boundary-layer stagnation-point flow over a vertical flat surface embedded in a porous medium

The unsteady mixed convection boundary-layer flow towards a stagnation point on a heated vertical surface embedded in a porous medium is considered. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using a similarity transformation. These are then solved numerically using the Keller-box method. These numerical results are complemented by asymptotic solutions for large values of A. The influence of dimensionless parameters λ (mixed convection), A (time variation), n (wall temperature variation) on the flow field and heat transfer is analyzed and discussed, dual solutions being found for both assisting and opposing buoyant flows.

Non-Newtonian Mixed Convection Flow along an Isothermal Horizontal Circular Cylinder

The mixed convective laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is studied along an isothermal horizontal circular cylinder using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively. Here, it is found that heating the cylinder delays separation and if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a very cold cylinder there will not be boundary-layer on the cylinder.