Magnetohydrodynamic Natural Convection Flow in an Enclosure with a Finite Length Heater Using the Differential Quadrature (DQ) Method

An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems

“…The heat transfer (convection and diffusion) problems attract many researchers interest and they have wide applications, for example, in energy system, which includes the solar collector, nuclear reactor, heat transfer, natural convective motion of fluid flow…etc. Most numerical simulations for these problems can be currently carried out by using finite differences method(FDM) and finite elements method(FEM) [1,3,6,7,10,11,14,16,17,18,22]. These techniques for solving numerically these problems may be very complex and require a large number of grid points to obtain accurate solutions.…”

“…In [13] Meral was used DQM to discretize one-and two-dimensional nonlinear heatand mass-transfer equations and using the Runge-Kutta method to solved the resulting nonlinear system of ordinary differential equations numerically. Öğüt [17 ], investigate the effects of the direction of magnetic force, heater length, and heater location on heat and fluid flow in the enclosure, and he showed that isotherms and streamlines are employed generally to depict the mechanism of heat and fluid flow, and the solution of the governing equations by using the Solving Two-dimensional Heat Transfer Problems differential quadrature method is an effective technique. Verma et al [25] have used DQM to obtain the numerical solutions for nonlinear diffusion equations.…”

“…where U , is interpreted as column vector of unknown functions, F is the column vector of the velocity of flow, 0 α > is the column vector of the variable diffusivity of diffusion terms, and g is the column vector of potential functions, with appropriate initial and boundary conditions. In recent years, many models have been used to describe flow problems that involve two mechanism of the flow (convection and diffusion) [8,17,20]. In this paper, we will develop the differential quadrature method to solve heat transfer problems.…”