Question

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 open at 70 °C, the maximum dryer air temperature. In order to operate the dryer at a lower air temperature, sufficient power is supplied to the heater such that the switch reaches 70 °C (Tset) when the air temperature T is less than Tset. If the convection heat transfer coefficient between the air and the exposed switch surface of 30 mm2 is 25 W/m2 ꞏ K.
Required:

How much heater power Pe is required when the desired dryer air temperature is T[infinity]=50°C?

Answer 1

Answer:

$0.015\ \text{W}$

Explanation:

$T_{set}$ = Set temperature = $70^{\circ}\text{C}$

$T_\infty$ = Air temperature = $50^{\circ}\text{C}$

A = Surface area = $30\ \text{mm}^2=30\times 10^{-6}\ \text{m}^2$

h = Convection heat transfer coefficient = $25\ \text{W/m}^2\text{K}$

Heater power is given by

$P_e=hA(T_{set}-T_\infty)\\\Rightarrow P_e=25\times 30\times 10^{-6}(70-50)\\\Rightarrow P_e=0.015\ \text{W}$

The required heater power is $0.015\ \text{W}$