Show that, if purely Neumann conditions are imposed along the boundary, then the integral of the temperature

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Show that, if purely Neumann conditions are imposed along the boundary, then the integral of the temperature gradient over the perimeter, $\Gamma$,

\[\int_{\Gamma} \frac{\partial T}{\partial n} d \Gamma=0\]

has to be equal to zero in order to maintain a steady-state temperature profile inside the medium. This is called the consistency condition. Explain the physical meaning of this condition.

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Advanced Transport Phenomena Analysis Modeling And Computations

ISBN: 9780521762618

1st Edition

Authors: P. A. Ramachandran

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Question Posted: Apr 19, 2024 07:01 AM

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Show that, if purely Neumann conditions are imposed along the boundary, then the integral of the temperature

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Advanced Transport Phenomena Analysis Modeling And Computations

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