Consider a solid bar of length L with variable cross-sectional area given by A(x) , where x ∈ [0, L] is distance along the bar. If the sides of the bar are insulated and if A(x) varies slowly, it is reasonable to make an approximation in which the heat flows only in the x direction. Consider the rate of change of the total thermal energy between arbitrary positions x = a and b to derive a heat equation for the bar in terms of the temperature u(x, t) . You may assume the density, heat capacity and thermal conductivity are constant (i.e. constant thermal properties) and that there is no heat source.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Fast pls i will give u like for sure solve this question correctly in 5 min pls Consider a solid bar of length L with variable cross-sectional area given by A(x) , where x ∈ [0, L] is distance along the bar. If the sides of the bar are insulated and if A(x) varies slowly, it is reasonable to make an approximation in which the heat flows only in the x direction. Consider the rate of change of the total thermal energy between arbitrary positions x = a and b to derive a heat equation for the bar in terms of the temperature u(x, t) . You may assume the density, heat capacity and thermal conductivity are constant (i.e. constant thermal properties) and that there is no heat source.
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