Question

The outside dimensions of a small cubical furnace constructed of fire clay bricks (K=2 W/mK) are 0.5 m x 0.5 m x 0.5 m, the walls are being 0.1 m thick. The temperatures at the inside and outside surface temperatures are ${500}^{o}C$ and ${50}^{o}C$ respectively. Also the heat transfer coefficient for top surface is $12W/m^{2}K,$ bottom surface is $8W/m^2$K and side surface is $15W/m^{2}K$ with surrounding temperature taken as ${35}^{o}C$. The heat transfer from the cube to the surrounding is

• A. 0.6 KW
• B. 9 KW
• C. 0.3 KW
• D. 12 KW

Answer 1

The correct option is C 0.3 KW

The heat transfer from the cube to the surroundings = The total heat covected out from all the sides of the cube to the surroundings
$Q_{total}=Q_{convectionfromtop}+Q_{convectionfrombottom}+Q_{convectionfromsides}$

$=h_{top}A\Delta T+h_{bottom}A\Delta T+h_{sides}\left(4A\right)\left(\Delta T\right)$

$=(h_{top}+h_{bottom}+4h_{side})\times A\Delta T$

$=(12+8+4\times 15)0.5\times 0.5(50-35)$

= 300 W = 0.3 kW