Meshless Radial Basis Function Simulation of Natural Convection in a Trapezoidal Cavity Heated from Below.

Natural convection heat transfer within trapezoidal cavity has been studied numerically. The present study is attended to reviewed heat and fluid flow patterns for natural convection in a trapezoidal cavity with uniformly heated bottom wall. The left and right walls are maintained at uniform cold temperature and the top wall is assumed to be thermally insulated. The mathematical model is conducted by the mass, momentum and energy equations and solved by applying multiquadrics radial basis function (MQRBF) method. The MQRBF method is extended using an improved primitive variable formulation to solve the governing equations. The method was based on implicit Euler scheme for temporal discretization and MQRBF method for spatial discretization. The effects of Rayleigh number on the flow and heat transfer process in the trapezoidal cavity are investigated. Stream function, isothermal patterns and the Nusselt number are presented for the Rayleigh numbers varied as 10³, 104 and 105. Comparing the numerical results of a test case obtained using the present method with those obtained using finite element and finite volume method shows very good agreement. [ABSTRACT FROM AUTHOR]