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.

Respuesta :

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

[tex]W = \dot{m}c_p \Delta T[/tex]

Where

[tex]C_p =[/tex] Specific heat

[tex]\dot{m}[/tex]= Mass flow rate

[tex]\Delta T[/tex] = Change in Temperature

Our values are given as

[tex]C_p = 1.005kJ/kgK \rightarrow[/tex] Specific heat of air

[tex]T_1 = 50\°C[/tex]

[tex]\dot{m} = 2kg/s[/tex]

[tex]W = 8kW[/tex]

From our equation we have that

[tex]W = \dot{m}c_p \Delta T[/tex]

[tex]W = \dot{m}c_p (T_2-T_1)[/tex]

Rearrange to find [tex]T_2[/tex]

[tex]T_2 = \frac{W}{\dot{m}c_p}+T_1[/tex]

Replacing

[tex]T_2 = \frac{8}{2*1.005}+(50+273)[/tex]

[tex]T_2 = 326.98K \approx 53.98\°C[/tex]

Therefore the exit temperature of air is 53.98°C