Analytical and Numerical Accurate Solutions of the Steady Convection-Diffusion in Potential Flow Around a Circular Cylinder Heated with Uniform Heat Flux

The fundamental problem of the steady convection-diffusion in potential flow around a heated circular cylinder with uniform heat flux is solved both analytically and numerically. The analytical solution is derived in closed form by using the method of Green’s function and presented as an integral. This solution is useful to validate the numerical codes of several others more complex problems considering Neumann boundary condition. It is thereby used to check the present numerical solution with potential flow. The asymptotic solution, at a great distance in the thermal wake region behind the cylinder is also obtained. It divulges the existence of singularities which lead to a deterioration of the accuracy of the numerical solution. An accurate numerical solution is then obtained by solving efficiently theses singularities. Its validity and its accuracy are supported by a comparison with the results derived from the exact analytical solution with relative error less than 0.1%, notably for the thermal characteristics. A useful correlation formula giving the overall Nusselt number as function of Péclet number is also proposed.