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

$T_2 = \frac{8}{2*1.005}+(50+273)$

$T_2 = 326.98K \approx 53.98\°C$

Therefore the exit temperature of air is 53.98°C