Numerical investigation of the unsteady convective flow along a wedge with thermophoresis

Abstract

In this thesis titled “Numerical Investigation of the Unsteady Convective Flow along a Wedge with Thermophoresis” characteristic of an unsteady twodimensional laminar forced convective hydrodynamic heat and mass transfer flow of a viscous incompressible fluid along a heated wedge in the presence of thermophoresis have been studied. The potential flow velocity has been taken as a function of the distance x and time t. The governing time dependent non-linear partial differential equations are reduced to a set of non-linear ordinary differential equations by introducing a new class of similarity transformations. Comparisons with published works are done, and the results are found to be in excellent agreement. The resulting local similarity equations for unsteady flow have been solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Depending on various flow conditions the work can be summarized as follows: Local similarity solutions for unsteady two-dimensional forced convective heat and mass transfer flow along a wedge with thermophoresis are investigated at the outset. Numerical results for the velocity, temperature and concentration profiles as well as local skin-friction coefficient, rate of heat and mass transfer, thermophoretic velocity and thermophoretic particle deposition velocity for different values of unsteadiness parameter, wedge angle parameter, Prandtl number, Schmidt number, thermophoretic coefficient, thermophoresis parameter and concentration ratio are displayed graphically in addition to tabular form. The results show that the thermophoretic particle deposition velocity decreases as the thermophoretic coefficient increases but it increased a bit with the increase of unsteadiness parameter. Secondly, the effects of thermophoresis particle deposition on an unsteady two dimensional forced convective heat and mass transfer flow past a wedge with respect to variable fluid viscosity due to changes in temperature and Prandtl number has been studied. Results for the non-dimensional velocity, temperature, concentration, variable Prandtl number and thermophoretic velocity are presented graphically whereas thermophoretic particle deposition velocity is shown in the tabular form for various values of the pertinent parameters. The obtained numerical results indicate that in modeling the thermal boundary-layer flow with a temperature-dependent viscosity, the Prandtl number shall be treated as a variable rather than a constant within the boundary layer to obtain realistic results. Thirdly, unsteady two dimensional magnetohydrodynamic (MHD) forced convective heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid along a porous wedge in the presence of the temperature-dependent thermal conductivity and variable Prandtl number have been carried out numerically. The velocity, temperature, concentration, thermophoretic velocity and thermophoretic particle deposition velocity are computed and discussed in details for various parametric conditions. The numerical results show that the heat transfer rate decreases by 45% when the thermal conductivity variation parameter varies from 0 to 9 for variable Prandtl number, but decreases by 77% for constant Prandtl number in case of suction. Finally, thermophoretic particle deposition on unsteady two dimensional convective slip flow over a wedge with temperature dependent fluid properties such as fluid viscosity and thermal conductivity have been studied numerically. The nondimensional velocity, temperature and concentration as well as thermophoretic velocity and thermophoretic particle deposition velocity for different values of the related parameters are displayed graphically and tabular form. The obtained numerical results show that both the fluid velocity and thermophoretic particle deposition velocity increase with the increasing values of the variable viscosity parameter as well as wedge angle parameter.