This circle boundary layer case involves a heat source being demonstrates the method of manufactured solutions in which an analytical heat source is derived from an analytical expression of the thermal boundary layer. This derived heat source is applied to a vortex flow around a circular annulus of radius r = [ 1 , 2 ]. The , 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 boundary temperatures are set to a thermal condition which is a function of r and θ. The applied heat source is also a function of r and θthe analytical thermal boundary layer solution, and the initial condition is set to 1. | 
