Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling

Abstract

General solution for thermal spreading and system resistances of a circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable for a general axisymmetric heat flux distribution which reduces to three important distributions including isoflux and equivalent isothermal flux distributions. The dimensionless system resistance depends on four dimensionless system parameters. It is shown that several special cases presented by many researchers arise directly from the general solution. Tabulated values and correlation equations are presented for several cases where the system resistance depends on one system parameter only. When the cylinder sides are adiabatic, the system resistance is equal to the one-dimensional resistance plus the spreading resistance. When the cylinder is very long and side cooling is small, the general relationship reduces to the case of an extended surface (pin fin) with end cooling and spreading resistance at the base. The special case of an equivalent isothermal circular source on a very thin infinite circular disk is presented.