Chapter 5, Problem 5.11P

The base plate of an iron has a thickness of $L=7\text{mm}$ and is made from an aluminum alloy $\left(\rho =2800{\text{kg/m}}^{\text{3}},c=900\text{J/kg}\cdot \text{K,}k=180\text{W/m}\cdot \text{K,}\epsilon =0.80\right).$ An electric resistance heater is attached to the inner surface of the plate, while the outer surface is exposed to ambient air and large surroundings at $T_{\infty }=T_{\text{sur}}=25°\text{C}\text{.}$ The areas of both the inner and outer surfaces are $A_s=0.040{\text{m}}^{\text{2}}\text{.}$

If an approximately uniform heat flux of $q_h^n=1.25\times {10}^4{\text{W/m}}^{\text{2}}$ is applied to the inner surface of the base plate and the convection coefficient at the outer surface is $h=10{\text{W/m}}^{\text{2}}\cdot \text{K,}$ estimate the time required for the plate to reach a temperature of $135°\text{C}\text{.}$ Hint: Numerical integration is suggested in order to solve the problem.