Multiple solutions of convection boundary layer flow for different types of fluids with various boundary conditions (original) (raw)
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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid and in the presence of thermal radiation. The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. By means of similarity transformation, the governing partial differential equations are reduced into ordinary differential equations. The similarity equations were solved for three types of nanoparticles, namely copper, alumina and titania with water as the base fluid, to investigate the effect of the nanoparticle volume fraction parameter phi, the constant magnetic/porous medium parameter I >, the mixed convection parameter lambda, the Prandtl number Pr and the radiation parameter R (d) on the flow and heat transfer characteristics. The skin-friction coefficient and Nusselt number as well as the velocity an...
The problems of flow and heat transfer in the boundary layers of a continuous stretching/shrinking surface have attracted considerable attention of researchers due to their numerous applications in industrial manufacturing processes. Some of the applications are extraction of polymer sheets, paper production, hot rolling and glass-fiber production. Eringen [1] formulated the micropolar fluid theory as an extension of the Navier-Stokes model of classical hydrodynamics to facilitate the description of the fluids with complex molecules .The micropolar fluids are generally defined as isotropic, polar fluids in which deformation of molecules is neglected. Physically, a micropolar model can represent fluids whose molecules can rotate independently of the fluid stream flow and its local vortices. Micro polar fluids have important applications in colloidal fluids flow, blood flows, liquid crystals, lubricants and flow in capillaries, heat and mass exchangers etc.
2011
The boundary-layer flow of a nanofluid on a linearly moving permeable vertical surface in the presence of magnetic field, heat generation or absorption, thermopherosis, Brownian motion and suction or injection effects is studied. Similarity solutions are obtained for the boundary-layer equations subject to power-law wall temperature, nanoparticles volume fraction and velocity variations. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. A detailed parametric study is performed to access the influence of the various physical parameters on the longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and the results are presented in both graphical and tabular forms.
The boundary-layer flow of a nanofluid on a linearly moving permeable vertical surface in the presence of magnetic field, heat generation or absorption, thermopherosis, Brownian motion and suction or injection effects is studied. Similarity solutions are obtained for the boundary-layer equations subject to power-law wall temperature, nanoparticles volume fraction and velocity variations. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. A detailed parametric study is performed to access the influence of the various physical parameters on the longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and the results are presented in both graphical and tabular forms.
IEEE Transactions on Nanotechnology, 2015
This study examines the effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer due to nanofluid over a stretching sheet. It takes into account the effect of Brownian motion and thermophoresis parameters. The non-linear governing equations and their associated boundary conditions are reduced into dimensionless form by similarity variables. The resulting systems of equations are then solved numerically using fourth order Runge-Kutta method along with shooting technique. The solution for the problem depends on parameters: magnetic M, velocity ratio B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, thermophoresis Nt, and reciprocal of magnetic Prandtl number A. Numerical results of the study are obtained for velocity, temperature, induced magnetic field and concentration profiles as well as skin friction coefficient, the local Nusselt number and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number and Sherwood number decrease with an increase in B and M parameters. However, the local Nusselt number-θ ′ (0) increases with an increase in Bi and local Sherwood number-ϕ ′ (0) decreases with an increase in convective parameter Bi. The study indicated that the flow velocity and the skin friction coefficient on stretching sheet are strongly influenced by velocity ratio (B < 1) and magnetic parameters. It is also observed that the skin friction coefficient-f ′′ (0) is an increasing function of magnetic parameter and a decreasing function of velocity ratio parameter B. The study also shows that the local heat transfer rate-θ ′ (0) is an increasing function of the convective parameter Bi, but it is a decreasing function of magnetic parameter M, velocity ratio parameter B and thermophoresis parameter Nt.
2014
In this paper the effects of variable viscosity and variable thermal conductivity of unsteady laminar incompressible mixed convection flow of an electrically conducting fluid at the stagnation of a two-dimensional body and an axi-symmetric body in the presence of applied magnetic field is investigated. Both prescribed wall temperature and prescribed heat flux condition have been considered. The problem was studied under the effects of variable viscosity, and variable thermal conductivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically using Runge-Kutta shooting method with guessed initial conditions. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. The results presented, demons...
Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid in the presence of magnetic field is investigated. The partial differential equations governing the problem have been transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically by using the shooting method with sixth-order of Runge-Kutta technique which are compared with Homotopy Adomian's Decomposition Method (HAM) for special case when magnetic field parameter is zero For fluids of medium molecular weight (H2, air), profiles of the dimensionless velocity, temperature and concentration distributions are shown graphically for various values of parameters embedded in the flow model. Finally, numerical values of physical quantities, such as the local skin friction coefficient, the local Nusselt number and the local Sherwood number are presented in tabular form.
Journal of Applied Research and Technology, 2017
The problem of unsteady mixed convection electrical magnetohydrodynamic (MHD) flow and heat transfer induced due to nanofluid over a permeable stretching sheet using Buongiorno model is investigated. The transverse electric and magnetic fields are considered in the flow field, while in the heat convection is associated with the thermal radiation, heat generation/absorption, viscous and Ohmic dissipations, and chemical reaction is incorporated in the mass diffusion. A similarity transformation is used to reduce the boundary layer governing equations which are partial differential equations to nonlinear differential equations and then solved numerically using implicit finite difference scheme. The nanofluid velocity and temperature are sensitive to an increase in the electric field, which resolved the problem of sticky effects due to the magnetic field. Destructive chemical reaction increases the level nanoparticles concentration while reversed behave happened in the case of the generative chemical reaction. Heat source boosts the fluid temperature while as opposite occurred with the heat sink. Thermal and concentration stratifications decreased the fluid temperature and the nanoparticles concentration profiles. Buoyancy ratio parameter reduced the Nusselt and Sherwood numbers whereas mixed convection parameter increases for higher values. A comparison with the previous study available in literature has been done and found an excellent agreement with the published data.
Procedia Engineering, 2017
The present work is focused on the unsteady MHD boundary layer flow and heat transfer over a wedge stretching surface moving in a nanofluid with the effects of various dimensionless parameters by using the Boungiorno model. The solution for the velocity, temperature and nanoparticle concentration depends on parameters like Prandtl number Pr, Brownian motion Nb, thermophoresis Nt, unsteadiness parameter A, velocity ratio parameter λ, pressure gradient parameter β and magnetic parameter M. The local similarity transformation is used to convert the governing partial differential equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved by using fourth order RungeKutta method along with shooting technique. Numerical results are obtained for distributions of velocity, temperature and nanoparticle concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The results are shown in graphically and as well as in a tabular form. From the graph the results indicate that the velocity increases for increasing values of magnetic parameter, unsteadiness parameter and pressure gradient parameter but decreases for velocity ratio parameter. The temperature profile increases for thermophoresis and Brownian motion parameter but reverse results arises for Prandtl number and velocity ratio parameter. On the other hand, nanoparticle concentration decreases for thermophoresis parameter, Lewis number and velocity ratio parameter. But in case of Brownian motion parameter the concentration decreases up to η < 1 and then increases. Besides, the present results are compared with previously published work and found to be in good agreement.
Thermal Science, 2014
Forced convection boundary layer magneto-hydrodynamic (MHD) flow of a nanofluid over a permeable stretching plate is studied in this paper. The effects of suction-injection and viscous dissi1pation are taken into account. The nanofluid model includes Brownian motion and thermophoresis effects. The governing momentum, energy and nanofluid solid volume fraction equations are solved numerically using an implicit finite difference scheme known as Keller-box method and the results are compared with available numerical data. The results for the dimensionless velocity, dimensionless temperature, dimensionless nanofluid solid volume fraction, reduced Nusselt and reduced Sherwood numbers are presented illustrating the effects of magnetic parameter, suction-injection parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, Eckert number and Lewis number.