Finite-Analytic Numerical Solution of Heat Transfer in Two-Dimensional Cavity Flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (103) for Prandtl numbers of 0.1, 1, and 10. The cavity wall is considered to be isothermal at Tw, while the moving wall is held at a different isothermal temperature Tm. Details of temperature, vorticity, and stream functions in the cavity are investigated.