GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.