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

`0.015\ \text{W}`

Step-by-step 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* 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* 30* 10^(-6)(70-50)\\\Rightarrow P_e=0.015\ \text{W}`

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