Numerical solution of convection-diffusion problems in irregular domains mapped onto a circle

A coordinate transformation methodology has been developed for convection-diffusion problems with an arbitrary solution domain. An algebraic coordinate transformation is used that maps the solution domain onto a circle. The transformed conservation equations are discretized by a control-volume finite difference technique. Sample computations are performed for fully developed flow and heat transfer in a polygonal duct, and for natural convection in a square cavity, to validate the present methodology. The numerical results obtained compared reasonably well, even in the extreme case of a rectangular domain mapped onto a circle.