Answered

The temperature at a point in a ball with conductivity is inversely proportional to the distance from the center of the ball. find the rate of heat flow across a sphere of radius with center at the center of the ball.



Answer :

bharathparasad577

The heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

Consider the diagram below, the heat flow will be

Fourier's law in radial coordinates

qr = -k.AdT/dr

Substituting the values of the area of sphere,

qr = -k (4πr²) dT/dr

Integrating we get

qr/4π∫dr/r^2 = ∫kdt

qr/4π ∫dr/r^2 = ∫kdt

qr/4π (1/r1 - 1/r2) = k(t2-t1)

qr = 4πkr1r2(t1-t2) / (r2 - r1)

The thermal resistance is expressed as

R = (r2 - r1) / 4πkr1r2)

Therefore, the heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

To know more about heat flow, refer: https://brainly.com/question/13791231

#SPJ4

Other Questions