Boundary layer flow of a second grade fluid with variable heat flux at the wall (original) (raw)
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020
This study theoretically investigates the effects of viscous dissipation and boundary plate thickness on an incompressible heat generating/absorbing fluid with nonuniform internal temperature unlike lumped heat capacitance assumption. The flow, which is laminar is induced by free convection caused by asymmetric heating of the channel boundaries and internally generated energy caused by viscous dissipation. In addition, convection through the boundary plates is also considered in the flow formation. One of the plates channel moves along the flow direction while the other is stationary. Due to the non-linear and coupling nature of the governing flow equations, homotopy perturbation method (HPM) has been adopted to analytically find the approximate solution to the problem. The effects of thermodynamic and hydrodynamic parameters are depicted in graphs and tables. It is discovered from the investigation that, both the velocity and temperature profiles increase with increase in viscous dissipation. Velocity distribution decreases with increase in Biot number while the temperature distribution near the heated plate increases with increase in Biot number. The increase in boundary plate thickness causes a boost in the fluid flow across the medium and reduces the temperature of the fluid near the heated plate. It is further discovered that the rate of heat transfer on both plates increase with increase in Biot number while they drastically dropped when the boundary plate thickness is increased. The shear stresses on the surface of both plates increase with increase in heat generation < 0 while reverse cases were observed with increase in heat absorption > 0. It is further observed that the volume flow rate within the channel increases with increase in viscous dissipation .
2015
This paper studied the steady laminar two – dimensional stagnation point flow of an incompressible viscous electrically conducting fluid at stagnation point with heat transfer. Uniform magnetic field is applied externally normal to the plane of the wall. Employing similarity transformations, the governing partial differential equations are transformed into ordinary differential equations. This were solved in non – dimensional state numerically using central differences for the derivatives and Thomas algorithm for the solution of the set of discretized equations in the infinite domain ∞ < <η 0 . A finite domain in the η-direction was used instead with η chosen large enough to ensure that the solutions are not affected by imposing the asymptotic conditions at a finite distance. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These results are pre...
Unsteady Solutions of Thermal Boundary Layer Equations by using Finite Difference Method
We studied the equation of continuity and derived the Navier-Stockes (N-S) equations of motion for viscous compressible and incompressible fluid flow, Boundary layer and thermal boundary layer equations are then derived. Then we studied unsteady solutions of thermal boundary layer equations. Thermal Boundary layer equations have been non-dimensionalised by using non-dimensional variable and the equations have been derived from Navier-Stokes equation and concentration equation by boundary layer technique. The non-dimensional boundary layer equations are non-linear partial differential equations. These equations are solved by using finite difference method. The solution of heat and mass transfer flow is studied to examine the velocity, temperature and concentration distribution. The effect on the velocity, temperature and concentration profiles for various parameters entering into the problems are separately discussed and shown graphically.
Journal of Molecular Liquids, 2016
In this article, heat transfer analysis of an unsteady oblique stagnation point flow of elastico-viscous Walter's B fluid over an oscillating-stretching surface, heated due to sinusoidal wall temperature is presented. The governing partial differential equations are transformed into dimensionless form. The solution of obtained partial differential equations is computed numerically using Chebyshev Spectral Newton Iterative Scheme (CSNIS). The computed results are highly accurate and compared with previous studies in limiting sense. The effects of involving parameters on the fluid flow and heat transfer are shown through tables and graphs. It is importantly noted that the amplitude of the local Nusselt number and skin friction coefficient enhances due to increase in the values of unsteady parameter. The heat transfer rate increases, with increase in the values of Prandtl number. In non-Newtonian fluid, the heat transfer rate decreases as compare to Newtonian fluid case. The variation of skin friction coefficient and local Nusselt number are discussed for the wide range of time and various pertinent parameters.
Laminar boundary layer in low Prandtl number flows with variable thermal properties on a flat plate
Journal of Engineering Mathematics, 1974
The laminar boundary layer flow of a low Prandtl number fluid with arbitrary thermal properties past a flat plate is studied by the method of matched asymptotic expansions. By assuming power law relations for the viscosity, density and Prandtl number, the first order results for the skin friction, the recovery factor and the heat transfer rate at the wall are obtained. It turns out that the outer flow in the thermal boundary layer is governed by a simple nonlinear differential equation of second order, which is correct to all orders in Prandtl number. Exact and approximate solutions to this outer equation are obtained. Further, it is shown that the first order terms for the recovery factor are independent of the thermal properties, while the heat transfer terms have a complicated dependence. The skin friction result shows the dependence on thermal properties, Mach number and heat transfer rate.
Boundary Layer Flow of Second Grade Fluid in a Cylinder with Heat Transfer
Mathematical Problems in Engineering, 2012
An analysis is carried out to obtain the similarity solution of the steady boundary layer flow and heat transfer of a second grade through a horizontal cylinder. The governing partial differential equations along with the boundary conditions are reduced to dimensionless form by using the boundary layer approximation and applying suitable similarity transformation. The resulting nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved by homotopy analysis method (HAM). The effects of the physical parameters on the flow and heat transfer characteristics of the model are presented. The behavior of skin friction coefficient and Nusselt numbers is studied for different parameters.
Mathematical Problems in Engineering, 2013
Mixed convection boundary layer caused by time-dependent velocity and the surface temperature in the two-dimensional unsteady stagnation point flow of an in-compressible viscous fluid over a stretching vertical sheet is studied. The transformed nonlinear boundary layer equations are solved numerically using the shooting technique in cooperation with Runge-Kutta-Fehlberg (RKF) method. Different step sizes are used ranging from 0.0001 to 1. Numerical results for the skin friction coefficient and local Nusselt number are presented for both assisting and opposing flows. It is found that the dual solutions exist for the opposing flow, whereas the solution is unique for the assisting flow. Important features of the flow characteristics are displayed graphically. Comparison with the existing results for the steady case show an excellent agreement.
Archives of Mechanics, 2008
A theoretical analysis is made for the steady two-dimensional post-stagnationpoint flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity, the free stream velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a coupled system of ordinary differential equations, which is then solved numerically by a finite-difference method. Results are presented in terms of ...
Effects of variable fluid properties and boundary conditions on thermal convection
International Communications in Heat and Mass Transfer, 1983
The onset of convection in a fluid layer heated from below is considered. The fluid properties are allowed to vary with temperature according to a linear relation. The fluid layer is bounded by two horizontal rigid plates, and the lower boundary is considered a perfect thermal conductor whereas the upper one is taken with a finite thermal conductivity. With these asymmetric boundary conditions linear variations in density, thermal conductivity and specific heat yield first-order corrections to the critical value of the Rayleigh number whereas linear variations in viscosity and thermal expansion coefficient give rise to second-order corrections to the critical Rayleigh number. The greatest effect is due to thermal conductivity variation. When the boundary conditions are symmetric the corrections are second-order.
Steady Free Convection Boundary Layer Flows at a Vertical Plate with Variable Fluid Properties
journal of modern mechanical engineering and technology, 2017
This paper investigates the similarity solutions of the steady two-dimensional flow of a stream of viscous fluid with far field viscosity past a vertical plate. The variable viscosity, thermal conductivity and heat sink in momentum and energy equations are incorporated. The governing system of equations are transformed into dimensionless equations and solved numerically by using Maple-13 software for different boundary conditions and for various values of parameters. The effects of different values of physical parameters on the velocity and temperature profiles as well as on the skin-friction coefficient and Nusselt number are discussed.