Chapter 8, Problem 8.44P

The products of combustion from a burner are routed to an industrial application through a thin-walled metallic duct of diameter $D_i=1$ m and length $L=\text{ 1}00\text{ m}$ . The gas enters the duct at atmospheric pressure and a mean temperature and velocity of $T_{m,i}=1600$ K and $u_{m,i}=10$ m/s. respectively. It must exit the duct at a temperature that is no less than $T_{m,o}=1400$ K. What is the minimum thickness of an alumina—silica insulation $\left(k_{\text{ins}}=0.125\text{W/m}\cdot \text{K}\right)$ needed to meet the outlet requirement under worst case conditions for which the duct is exposed o ambient air at $T_{\infty }=250$ K and a cross-flow velocity of $\text{V }=\text{ 15 m}/\text{s}$ ? The properties of the gas may be approximated as those of air, and as a first estimate, the effect of the insulation thickness on tile convection coefficient and thermal resistance associated with the cross flow may be neglected.