Chapter 1, Problem 1.78P

A thin electrical heating element provides a uniformheat flux ${q^{″}}_0$ to the outer surface of a duct through whichairflows. The duct wall has a thickness of 10 mm and athermal conductivity of $\text{20}\text{W/m}\cdot \text{K}$ .

(a) At a particular location, the air temperature is 30°Cand the convection heat transfer coefficientbetween the air and inner surface of the duct is $100{\text{W/m}}^{\text{2}}\cdot \text{K}$ . What heat flux ${q^{″}}_0$ is required tomaintain the inner surface of the duct at $T_i=\text{ 85}°\text{C}$ ?
(b) For the conditions of part (a), what is the temperature $\left(T_o\right)$ of the duct surface next to the heater?
(c)With $T_i=\text{ 85}°\text{C}$ , compute and plot ${q^{″}}_0$ and $T_o$ as afunction of the air-side convection coefficient h forthe range $10\le h\le 200{\text{W/m}}^{\text{2}}\cdot \text{K}$ . Briefly discussyour results.