Mathematical modeling for the convection boundary layer flow in a viscous fluid with newtonian heating and convective boundary conditions - Muhammad Khairul Anuar , Mohamed (2013)
Problems of convection boundary layer flow are important in engineering and industrial activities. Such flows are applied to manage the thermal effects in many industrial outputs for example in electronic devices, computer power supply and also in engine cooling system such as cooling fins in a car radiator. In modeling the convective boundary layer flow problems, there are four common boundary conditions considered namely as the constant or prescribe wall temperature, constant or prescribe surface heat flux, Newtonian heating and conjugate or convective boundary conditions. Generally, the boundary conditions that are usually applied are the constant/prescribe wall temperature or constant/prescribe surface heat flux. In this study, the boundary condition considered are the Newtonian heating and convective boundary conditions. The Newtonian heating is the heat transfer from the surface is taken to be proportional to the local surface temperature and which is usually termed conjugate convective flow and convective boundary conditions is where heat is supplied through a bounding surface of finite thickness and finite heat capacity. The interface temperature is not known a priori but depends on the intrinsic properties of the system, namely the thermal conductivity of the fluid or solid. The mathematical modeling for the convection boundary layer flow in a viscous fluid is investigated. Three problem have been studied, there are forced convection on a stagnation point flow over a stretching sheet, the extended from the first problem by considering the effects of magnetohydrodynamic in a presence of thermal radiation and the mixed convection on a stagnation point flow past a stretching vertical surface. All of the governing equations which is in the form of non linear partial differential equation from each problem are reduced to ordinary differential equations by using similarity transformation before being solved numerically by using the implicit finite difference scheme known as the Keller-box method. The numerical codes in the form of computer programmes are developed by using the MATLAB software. Six parameter which is the Prandtl number, stretching parameter, conjugate parameter, magnetic parameter, thermal radiation parameter and buoyancy parameter are considered. The features of the flow and heat transfer characteristics for various values of these parameter are analyzed and discussed. It is found that, the increase of Prandtl number, stretching parameter, thermal radiation parameter and buoyancy parameter in an assisting buoyant flow results a decrease in surface temperature. Meanwhile, the trend goes opposite with magnetic parameter, conjugate parameter and buoyancy parameter in an opposite buoyant flow. Futhermore, it is found that the trends for skin friction coefficient, temperature and velocity profiles for convective boundary conditions is quite similar to the Newtonian heating case. On the other hand for heat transfer profiles, it is found that the trends is contrary for all parameters considered except the conjugate parameter.