Temperature distribution in a laminar circular jet

The effect of heat generated by friction on the temperature distribution in a circular laminar jet is calculated. Boundary layer equations for an incompressible fluid passing through a circular orifice are presented and a similar solution of the energy equation is employed. The resulting nonhomogeneous linear partial differential equation is reduced to Gauss' hypergeometric equation by a proper transformation of the similarity variable and solved for various values of the Prandtl number. It is found that as the Prandtl number decreases from unity, the overall temperature difference due to frictional heat increases near the jet axis and decreases further away from the axis, with the reverse phenomenon occurring in the case of an increasing Prandtl number.