Estimation of the Transient Surface Temperature and Heat Transfer Coefficient of Convective Cooling for Large Slab and Long Cylinder by Using an Inverse Heat Conduction Method

Inverse heat conduction method is a technique to determine heat flux and surface temperature on an inaccessible surface of wall by measuring the temperature on an accessible boundary. The objective of this paper is to develop a method by which stable prediction of heat transfer on an inaccessible boundary could be obtained without altering the thermal boundary condition that would have existed were sensor not present. In this work, three points backward finite difference applied to the 1-D heat equation for large slab and long cylinder with constant thermophysical properties and uniform initial temperature. The numerical solutions of the heat equations are performed with symbolic Maple software. It is demonstrated that approximate temperature distributions for the three bodies are equivalent to analytical solution using first term series solution. It is also shown that the series solution converge rapidly for long times, and for Fo > 0.2, ony the first term of the series nned to be retained for 2% accuracy.