Athin 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?

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=59.4°C

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