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A thin electrical heating element provides a uniform heat flux q” to the outer s

ID: 1717810 • Letter: A

Question

A thin electrical heating element provides a uniform heat flux q” 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. At a particular location, the air temperature is 30° C and the convective heat transfer coefficient between the air and inner surface of the duct is 100 W/m2 K. What heat flux q” is required to maintain the inner surface of the duct at Ti at 85° C? For those conditions, what is the temperature To of the duct surface next to the heater?

Explanation / Answer

>> As, heat flux = Q'

>> Given,  

Ta = Air Temperature = 30° C

Ti = Inlet Temperature = 85° C

To = Outlet Temperature = ?

h = 100 W/m2-K

k = Thermal Conductivity = 20 W/m-K

dx = thickness = 10 mm = 0.01 m

>> Now, as heat loss due to conduction between inner and outer surface = Heat loss to surroundings by convection

=> Q = Heat transfer = kA(Ti - To) = hA(Ti - Ta)

=> Heat flux, Q" = Q/A = k(Ti - To) = h(Ti - Ta)      ........(1)...

=> Q" = 100*(55) = 5.5 kW/m2 ....HEAT FLUX...ANSWER...

Also. from (1)...

=> 5500 = 20*(To - 85)

=> To = 360 ° C   ....OUTER SURFACE TEMPERATURE ........................ANSWER.....

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