Natural convective conjugate cooling mechanism in vertical fins

An analysis is presented of the conjugate free convective heat transfer from a vertical, thermally thin fin heated from above to the surrounding fluid. An estimate is presented of the thermal penetration length over which the temperature of a very long fin would decrease from its maximum value at the top to the ambient temperature of the fluid. The solution of the problem is shown to depend on two nondimensional parameters: the Prandtl number of the fluid and the ratio s of the thermal penetration length to the actual length of the fin. The overall heat transfer rate for thermally short fins (large s) is practically independent of the fin material, whereas it depends on the thermal conductivity of the fin when s is small. Numerical and asymptotic results are given covering the whole range of s