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.

Question

Chemistry

Leonidas Molina

16 February, 16:00

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.

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Answers (1)

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Angela Rasmussen · Answer 1

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