In this study, the numerical investigation of boundary layer flow over a moving plate in a nanofluid with viscous dissipation and constant wall temperature is considered. The governing non-linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation. The transformed equations are then solved numerically using the Keller-box method. Numerical solutions are obtained for the Nusselt number, Sherwood number and the skin friction coefficient as well as the concentration and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number, plate velocity parameter, Brownian motion and thermopherosis parameters, Eckert number and Lewis number are analyzed and discussed. It is found that the presence of viscous dissipation reduces the range of the plate velocity parameter for which the solution exists. The increase of both Brownian motion and thermophoresis parameters results to the decrease of the Nusselt number, while the Sherwood number increases with the increase of the thermophoresis parameter.
Present study consider the mathematical modeling for mixed convection boundary layer flow and heat transfer on a horizontal circular cylinder with viscous dissipation. The transformed partial differential equations are solved numerically by using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the reduced Nusselt number, the local skin friction coefficient, the velocity and temperature profiles. The features of the flow for various values of the Prandtl number, Eckert number and mixed convection parameter are discussed. The results in this paper is original and important for the researchers working in the area of boundary layer flow and this can be used as reference and also as complement comparison purpose in future
a b s t r a c tThis paper considers steep wave impact on seawalls of various geometries. A simple analytical model for the pressure impulse due to a wave of idealized geometry and dynamics is developed and applied to the following geometries: (a) vertical seawall with a berm, (b) vertical seawall with a ditch at its base and (c) vertical seawall with a block missing (damaged condition).The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the rigid surface conditions and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, rigid wall conditions and by matching the values and the horizontal derivatives of the solutions in each rectangular region at their mutual boundary. The method yields the pressure impulse throughout the entire region. The overall impulse and moment impulse on the seawall and a simple model for the uprush of the spray jet after the impact are also presented. The effects of different impact regions and different geometries can therefore be quickly estimated and used to show trends in the results. It is shown that berms generally have a beneficial effect on reducing the impulse, moment impulse and uprush, but not the maximum pressure impulse on the seawall, whereas ditches are generally and sometimes strongly detrimental for all effects except uprush. A missing block in the seawall gives an almost constant or linearly decreasing value inside the gap (depending on the boundary condition applied at the rear of the gap being hard or soft respectively); the soft case can affect the pressure impulse on the front face of the seawall, thereby affecting the impulse and moment impulse.
Abstract. In this study, the numerical investigations of the mixed convection on a stagnation point flow past a stretching vertical surface with Newtonian heating is considered. The non linear partial differential equations that governed the model are transformed by similarity variables before being solved numerically using the Keller-box method. The numerical solutions are obtained for the surface temperature, the heat transfer coefficient, the reduced skin friction coefficient and the reduced Nusselt number as well as the velocity and the temperature profiles. The features of the flow and heat transfer characteristics for pertinent parameters which are Prandtl number, stretching parameter, buoyancy parameter and conjugate parameter are analyzed and discussed.
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