Please show all work and answer to recieve full points The average surface tempe

Question

Please show all work and answer to recieve full points

The average surface temperature of the Earth in November 2012 was 61.61 degree F. The Earth's inner core is estimated to be 5700 K, surprisingly similar to the surface temperature of the sun (5778 K). Following the derivation presented in class for composite slabs and cylinders, derive an expression for the thermal resistance of a spherical shell. Which layer(s) is/are most responsible for insulating us from the Earth's core? Assuming steady state, calculate the overall heat transfer coefficient between the Earth's core and lithosphere, as well as the rate of heat transfer within the Earth. Will convection in the lithosphere significantly change your answer to part (c)? Assuming that the heating of the Earth is entirely due to radiation from the sun (a good assumption), and that the radiative heat from the sun is distributed evenly over the Earth's surface (a not-so-good assumption), estimate F12 for the sun and Earth.

Explanation / Answer

1. the equation for the rate of heat transfet

dQ = -kA dT/dx;

let us take the value of heat flow rate at a distance r from the center and a thickness dr;

dQ = - kA dT/dr;

A = 4 *pi *r2 ;

on integrating the expression

Q = k*A dT* ln r2/r1;

Thermal resistance = ln (r2/r1)/kA;

2. Layer most responsible for insulating us from earth's core is the one with maximun thermal resistence ;

for this the layer with maximum temperature difference and least temperature difference.

Ans : Mantle

3. Overall heat transfer co efficient :

h = k1 A1/ ln (r2/r0) + k2 A2 /ln(r2/r1) + ..................... + kn An ln (rn /r n-1);

4.

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