Consider a thin cylindrical one-dimensional cable with constant thermal properties and constant cross-section radius R, which has no internal sources of thermal energy. Assume that the lateral surface of the cable is not completely insulated, and that the heat energy flowing out of the lateral sides per unit surface area is proportional to the difference between the cable temperature and the outside temperature, Uoconst. Repeat the derivation of the heat equation for this case, and show that this leads to the following PDE: d'u [u(x.()-] where y = const

Consider a thin cylindrical one-dimensional cable with constant thermal properties and constant cross-section radius R, which has no internal sources of thermal energy. Assume that the lateral surface of the cable is not completely insulated, and that the heat energy flowing out of the lateral sides per unit surface area is proportional to the difference between the cable temperature and the outside temperature, Uoconst. Repeat the derivation of the heat equation for this case, and show that this leads to the following PDE: d'u [u(x.()-] where y = const

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Consider a thin cylindrical one-dimensional cable with constant thermal properties and constant cross-section
radius R, which has no internal sources of thermal energy. Assume that the lateral surface of the cable is not
completely insulated, and that the heat energy flowing out of the lateral sides per unit surface area is
proportional to the difference between the cable temperature and the outside temperature, Uou=Const.
Repeat the derivation of the heat equation for this case, and show that this leads to the following PDE:
a'u
= K
[u(x,1)-] where y = const
cp

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