This circle boundary layer case demonstrates the method of manufactured solutions in which an analytical heat source is derived from an analytical expression of the thermal boundary layer (shown on right). This derived heat source is applied to a vortex flow around a circular annulus of radius r = [ 1 , 2 ], and the numerical heat flux at the inner boundary is checked with the analytical heat flux to a specified tolerance. All boundary temperatures are set to the analytical thermal boundary layer solution, and the initial condition is set to 1. The thermal boundary layer around the semicircle is shown on the right. Note that the singularity at (θ=0) in the figure on the right is disregarded. | 