A thin stainless steel disk of thickness \(b\) and outer radius \(r_{o}\) has been heat treated to a high, uniform initial temperature of \(T_{i}\). The disk is then placed upon a small stand and allowed to cool. The ambient air and surroundings are at \(T_{\infty}\) and \(T_{\text {sur }}\), respectively. The convection coefficients on the top and bottom disk surfaces, \(h_{t}\) and \(h_{b}\), are known, as is the plate emissivity, \(\varepsilon\). Derive a differential equation that could be solved to determine the transient thermal response of the disk, \(T(r, t)\). List the appropriate initial and boundary conditions.

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h. T Top view Side view To Tsur