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 displayed on the 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 at the inner boundary to a specified tolerance. All boundaries are set to the analytical thermal boundary layer solution, and the initial condition is set to 1. Note that the plot The thermal boundary layer around the semicircle is shown on the right disregards . Note that the solution at the singularity where (θ=0) is disregarded. | 