Question

A thin electrical heating element provides a uniform heat flux qo" to the outer surface of a duct through which air flows. The duct wall has a thickness of 10 mm and a thermal conductivity of 20 W/m·K. (a) At a particular location, the air temperature is 30°C and the convection heat transfer coefficient between the air and inner surface of the duct is 100 W/m2·K. What heat flux is required to maintain the inner surface of the duct at Ti = 58°C? (b) For the conditions of part (a), what is the temperature To of the duct surface next to the heater?

Answer 1

Answer:

a)q= 2800 W/m²

b)To=59.4°C

Explanation:

Given that

L = 10 mm

K= 20 W/m·K

T=30°C

h= 100 W/m²K

Ti=58°C

a)

Heat flux q

q= h ΔT

q= 100 x (58 - 30 )

q= 2800 W/m²

b)

As we know that heat transfer by Fourier law given as

Q= K A ΔT/L

Lets take outer temperature is To

So by  Fourier law

To= Ti + qL/K

Now by putting the values

To= Ti + qL/K

$To= 58 + 2800 \times \dfrac{ 0.01}{20}$

To=59.4°C