Question

A furnace wall consists of 200 mm layer of refractory bricks, 6 mm layer of steel plate and a 100 mm layer of insulation bricks. The maximum temperature of the wall is 1150°C on the furnace side and the minimum temperature is 40°C on the outermost side of the wall. An accurate energy balance over the furnace shows that the heat loss from the wall is 400 W/m². It is known that there is a thin layer of air between the layers of refractory bricks and steel plate. Thermal conductivities for the three layers are 1.52, 45 and 0.138 W/m°C respectively. Find : 

(i) To how many millimetres of insulation brick is the air layer equivalent ? 

(ii) What is the temperature of the outer surface of the steel plate ?

Answer 1

Thickness of refractory bricks, L_A = 200 mm = 0.2 m 

Thickness of steel plate, L_C = 6 mm = 0.006 m 

Thickness of insulation bricks, L_D = 100 mm = 0.1 m 

Difference of temperature between the innermost and outermost side of the wall, 

∆t = 1150 – 40 = 1110°C

Thermal conductivities : 

k_A = 1.52 W/m°C ; k_B = k_D = 0.138 W/m°C ; k_C = 45 W/m°C 

Heat loss from the wall, q = 400 W/m² 

(i) The value of x = (L_C) :

Q = \(\cfrac{A.∆t}{\sum\cfrac LK}\) or \(\cfrac QA\) = q = \(\cfrac{∆t}{\sum\cfrac LK}\)

0.8563 + 0.0072 x = \(\cfrac{1110}{400}\) = 2.775

x = \(\cfrac{2.775-0.8563}{0.0072}\) = 266.5 mm.

(ii) Temperature of the outer surface of the steel plate t_so :

Answer 2

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