Page 56 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 37

z T
( m> ( "C>
0 30
0.1 46
0.2 59
0.3 70
0.4 79
0.5 85
0.6 89
0.7 90
0.8 89
0.9 86
1 .o 80

where z is the distance measured from one side of the wall. Determine the uniform
rate of energy generation per unit volume within the wall.
(Answer: 1920 W/ m3)

2.7 The geothermal gradient is the rate of increase of temperature with depth in
the earth's crust.

a) If the average geothermal gradient of the earth is about 25 "C/ km, estimate the
steady rate of heat loss from the surface of the earth.
b) One of your friends claims that the amount of heat escaping from 1 m2 in 4 days
is enough to heat a cup of coffee. Do you agree? Justify your answer.
Take the diameter and the thermal conductivity of the earth as 1.27 x lo4 km and
3 W/ m. K, respectively.
(Answer: a) 38 x 109kW)

2.8 Estimate the earth's age by making use of the following assumptions:
(i) Neglecting the curvature, the earth may be assumed to be semi-infinite plane
that began to cool from an initial molten state of To = 1200°C. Taking the
interface temperature at z = 0 to be equal to zero, the corresponding temperature
distribution takes the form

T=Toerf(') 2@

where erf (x) is the error function defined by