Approximate solution of a class of radiative heat transfer problems

An approximate solution is presented for a class of radiative heat transfer problems within enclosures having black or diffuse-gray surfaces based on a modified Taylor series expansion method: such radiative transfer problems are generally represented by integral equations. The approach avoids use o f any boundary/initial conditions associated with the original Taylor serie s expansion method and leads to an approximate solution in a simple closed form to the radiant integral equations, which can be computed straightforwa rdly on a modern personal computer using symbolic computing codes such as M aple. The method can be effectively and efficiently applied to deal with en closures involving more than one or two surfaces, for which direct numerica l integration may be subject to instability, or require and excessive amoun t of computation. The computed numerical results for representative thermal problems are in excellent agreement with those obtained by other numerical approaches.