Chapter 1, Problem 1.27P

The temperature controller for a clothes dryer consists of a bimetallic switch mounted on an electrical heater attached to a wall-mounted insulation pad.

The switch is set to on at 70°C, the maximum dryer air temperature. To operate the dryer at a lower air temperature, sufficient power is supplied to the heater such that the switch reaches 70°C $\left(T_{set}\right)$ when the air temperature Tis less than $T_{set}$ . If the convection heat transfer coefficient between the air and the exposed switch surface of $\text{3}0{\text{ mm}}^{\text{2}}$ is $\text{25}{\text{W/m}}^{\text{2}}\cdot \text{K}$ , how much heater power $P_e$ is required when the desired dryer air temperature is $T_{\infty }=50°\text{C}$ ?