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.

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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.28P: For flow over a slightly curved isothermal surface, the temperature distribution inside the boundary...

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