The temperature controller for a clothes dryer consists of a

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 degree 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 degree C (T_set) when the air temperature T is less than T_set. If the convection heat transfer coefficient between the air and the exposed switch surface of 50 mm^2 is25 W/m^2 K, how much heater power is required when the desired dryer air temperature is T_a = 50 degree C? Please write the energy balance equation first.

Solution

Switch opens when temperature reaches 70⁰ C

When ambient temperature is less than 70⁰ C, it is heated so that it reaches 70⁰ and opens the switch.

Amount of heat required to increase the temperature to 70⁰ = hA(T_set - T_a)

Q = 25 x (50 / 10⁶) x (70 -50) = 0.025 W