A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m K, r

Question

A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m K, rho = 7850 kg/m3, c = 430 J/kg.K) and is of thickness L = 10 mm. One side of it is exposed to furnace gases and the opposite surface is well insulated from the surroundings. At the furnace start-up the wall is at an initial temperature of Ti = 300 K, and combustion gases at T infinity = 1300 K enter the furnace, providing a convective coefficient of h = 25 W/m2 K at the exposed wall. Calculate the Biot number and comment on applicability of Lumped Capacitance Method for this problem. How long will it take for the inner surface of the steel to achieve a temperature of T s,i= 1200 K ?

Explanation / Answer

a) biot no. = hl/k = 4.17 * 10 ^-3 << 1

so lumped capacitance method can be applied

b) for lumped capacitance method

Ts,i- T / (Ti - T) = exp ( -ht/cl)

so t = 3108.95 sec

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