3. Steady state heat loss from a furnace can be simplified as a 1-D heat transfe

Question

3. Steady state heat loss from a furnace can be simplified as a 1-D heat

transfer model as shown in the figure on the right.

The bottom surface temperature of the brick layer

is maintained at 500%uF0B0C. The surface area is 4 m2.

(A) Apply energy balance on the control

surface shown by the dash lines and

derive an expression for determining the

temperature of the top surface of the

brick.

(B) Calculate the top surface temperature.

(C) Safety concern requires that the top

surface temperature should be lower than

60%uF0B0C. Two options can be used to achieve the goal. One is to increase the

thickness of the brick layer. Calculate how thick the brick layer should be. The

other option is to change the material. Since thermal conductivity is a material

property, calculate the thermal conductivity of this potential material. Look at the

Appendix and point out which materials may be suitable. Among those suitable

materials, does the material have sufficient strength and is it not flammable?

Explanation / Answer

Q/(4 m^2) = k (500 C - T)/d
The value for Q in units of energy per unit time is probably given in the figure.
The value of "d", the thickness of the brick, is probably given in the figure.
The value of "k", the conductivity of brick, you must look up somewhere,
T = 500 C - Qd/[k (4 m^2)]


(C) Go back to my first equation:
d = k (440 K) (4 m^2) / Q "option one"

k = dQ/[(440 K)(4 m^2)]

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