Question

A block made of a certain material has a thickness of 20 cm and a thermal conductivity of 0.04 m C. At a particular instant in time the temperature distribution with x, the distance from the left surface of the block, is T =-100 x2 + 20 x, where x is in meter. Calculate the heat flux at the left (x = 0) and right face of the block.

Answer 1

Answer:

heat flux ( Q ) = 8 W/m³ uniform heat flux throughout the block

Explanation:

flat plate ecuation with uniform source:

• d2T / dx² = - Q / k...........from general balance
• if x = 0 ⇒ dT / dx = 0 ; Q = 0
• if x = L ⇒ T = T1

∴ k = 0.04 W/mC;   L = 0.2 m

If T = - 100x² + 20x

⇒ dT / dx = - 200x + 20

⇒ d2T / dx² = - 200 = - Q / k

⇒ Q / k = 200

⇒ Q = 200 * 0.04 W/mC

⇒ Q = 8 W/m³