A spherical shell of thermal conductivity k?has inside radius r 1 and outside radius r 2 (figure).
Question:
A spherical shell of thermal conductivity k?has inside radius r1 and outside radius r2 (figure). The inside of the shell is held at a temperature T1, and the outside at temperature T2. In this problem, you are to show that the thermal current through the shell is given by Consider a spherical element of the shell of radius r?and thickness dr.
(a) Why must the thermal current through each such element be the same?
(b) Write the thermal current I?through such a shell element in terms of the area A = 4pr2, the thickness dr, and the temperature difference dT?across the element.
(c) Solve for dT?in terms of dr?and integrate from r?= r1 to r?= r2.
(d) Show that when r1?and r2 are much larger than r2- r1, Equation 21-22 is the same as Equation 21-7.
Step by Step Answer:
a From conservation of energy the thermal current through each shell m...View the full answer
Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
Authors: Edmund G. Seebauer, Robert L. Barry
