AEE 331 Heat Transfer

Homework VIIDue 9 December 2014, Tuesday, 17.00 (submit to room 010)

1. A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m ·K, ρ = 7850 kg/m3, c =430 J/kg · K) and is of thickness L = 10 mm. To protect it from the corrosive effects of the furnacecombustion gases, one surface of the wall is coated with a thin ceramic film that, for a unit surface area, hasa thermal resistance of R

′′

t,f = 0.01 m2 ·K/W . The opposite surface is well insulated from the surroundings.At furnace start-up the wall is at an initial temperature of Ti = 300 K, and combustion gases at

T∞ = 1300 K enter the furnace, providing a convection coefficient of h = 25 W/m2 ·K at the ceramic film.Assuming the film to have negligible thermal capacitance, how long will it take for the inner surface of thesteel to achieve a temperature of Ts,i = 1200 K? What is the temperature Ts,o of the exposed surface of theceramic film at this time?

2. Consider the one-dimensional wall shown in the sketch, which is initially at a uniform temperature Tiand is suddenly subjected to the convection boundary condition with a fluid at T∞.

For a particular wall, case 1, the temperature at x = L1 after t1 = 100 s is T1(L1, t1) = 315oC. Anotherwall, case 2, has different thickness and thermal conditions as shown below.

How long will it take for the second wall to reach 28.5oC at the position x = L2? Use as the basis foranalysis, the dimensionless functional dependence for the transient temperature distribution expressed inEquation 5.38*.

* Incropera, Frank P. Fundamentals of heat and mass transfer (6th edition), John Wiley & Sons

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