Mathematical modeling for the convection boundary layer flow in a viscous fluid with newtonian heating and convective boundary conditions

摘要

Problems of convection boundary layer flow are important in engineering and industrialudactivities. Such flows are applied to manage the thermal effects in many industrialudoutputs for example in electronic devices, computer power supply and also in engineudcooling system such as cooling fins in a car radiator. In modeling the convectiveudboundary layer flow problems, there are four common boundary conditions consideredudnamely as the constant or prescribe wall temperature, constant or prescribe surface heatudflux, Newtonian heating and conjugate or convective boundary conditions. Generally,udthe boundary conditions that are usually applied are the constant/prescribe walludtemperature or constant/prescribe surface heat flux. In this study, the boundaryudcondition considered are the Newtonian heating and convective boundary conditions.udThe Newtonian heating is the heat transfer from the surface is taken to be proportionaludto the local surface temperature and which is usually termed conjugate convective flowudand convective boundary conditions is where heat is supplied through a boundingudsurface of finite thickness and finite heat capacity. The interface temperature is notudknown a priori but depends on the intrinsic properties of the system, namely the thermaludconductivity of the fluid or solid. The mathematical modeling for the convectionudboundary layer flow in a viscous fluid is investigated. Three problem have been studied,udthere are forced convection on a stagnation point flow over a stretching sheet, theudextended from the first problem by considering the effects of magnetohydrodynamic inuda presence of thermal radiation and the mixed convection on a stagnation point flowudpast a stretching vertical surface. All of the governing equations which is in the form ofudnon linear partial differential equation from each problem are reduced to ordinaryuddifferential equations by using similarity transformation before being solvedudnumerically by using the implicit finite difference scheme known as the Keller-boxudmethod. The numerical codes in the form of computer programmes are developed byudusing the MATLAB software. Six parameter which is the Prandtl number, stretchingudparameter, conjugate parameter, magnetic parameter, thermal radiation parameter andudbuoyancy parameter are considered. The features of the flow and heat transferudcharacteristics for various values of these parameter are analyzed and discussed. It isudfound that, the increase of Prandtl number, stretching parameter, thermal radiationudparameter and buoyancy parameter in an assisting buoyant flow results a decrease inudsurface temperature. Meanwhile, the trend goes opposite with magnetic parameter,udconjugate parameter and buoyancy parameter in an opposite buoyant flow. Futhermore,udit is found that the trends for skin friction coefficient, temperature and velocity profilesudfor convective boundary conditions is quite similar to the Newtonian heating case. Onudthe other hand for heat transfer profiles, it is found that the trends is contrary for alludparameters considered except the conjugate parameter.