Question

Air is to be heated steadily by an 8-kW electric resistance heater as it flows through an insulated duct. If the air enters at 55°C at a rate of 2 kg/s, determine the exit temperature of air. Solve using appropriate software.

Answer 1

To solve this problem it is necessary to apply the concepts related to the heat exchange of a body.

By definition heat exchange in terms of mass flow can be expressed as

`W = \dot{m}c_p \Delta T`

Where

`C_p =` Specific heat

`\dot{m}`= Mass flow rate

`\Delta T` = Change in Temperature

Our values are given as

`C_p = 1.005kJ/kgK \rightarrow` Specific heat of air

`T_1 = 50\°C`

`\dot{m} = 2kg/s`

`W = 8kW`

From our equation we have that

`W = \dot{m}c_p \Delta T`

`W = \dot{m}c_p (T_2-T_1)`

Rearrange to find
`T_2`

`T_2 = \frac{W}{\dot{m}c_p}+T_1`

Replacing

`T_2 = (8)/(2*1.005)+(50+273)`

`T_2 = 326.98K \approx 53.98\°C`

Therefore the exit temperature of air is 53.98°C