Finite element simulation of natural convection from an open rectangular cavity containing adiabatic circular cylinder

Abstract

A numerical simulation of two-dimensional laminar steady-state natural convection in a rectangular open cavity has been investigated. An adiabatic circular cylinder is placed at the center of the cavity and the opposite wall to the aperture is heated by a constant heal flux. 'fhe top and bOllom wall> are kept at the constant temperature, The fluid is concerned wilh Prnndtl numbers 0.72, 1.0 and 7.0. The properties of the fluid were assumed to be constant"] he physical problems are rcprcscmcd mathematically by different ,els of goveming equations along with the corresponding boundary conditions. In this the,i" a finite element method for sleady-sMe il1C<Jmpres<iblenatural convection tlows has been developed. The non-dimensional governing equatio", are discreti7ed by using Ga1crkin weighted residual method of finite element formulatiol1. The obtained results are presented in terms of streamline~ and isotherm" heat transfer characteristics Nusseit numbers for Orashof numbers from 10' to 10' and for an inclination angles of the cavity ranges for OO,15°,30"al1d45". The obtained results arc also presented" ith the variation of diftcrcnt diameter ratio, of the cylil1der.The re,uits ,how that tile Nusselt numbers increase with the increasing of Grashof numbers. Also the Nusselt number chilllgessubstantially with the inclination angle of the ca, ity while better thelmal performilllce is also scnsilivc to the boundary condition of the heated wall. Mesh ret,nement led to solutions for Omshofnumber, from 10' to 10".