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dEdt
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Fourier's law of thermal conduction states that [tex]\mathbf{j}=-k\nabla T,[/tex] where [itex]\mathbf{j}[/itex] is the heat flux. Integrating both sides of this equation over a closed surface gives the equation [tex]\frac{dQ}{dt}=-k\int \nabla T \cdot d\mathbf A.[/tex]
If there is a temperature discontinuity across this surface, then [itex]\frac{dQ}{dt}[/itex] diverges, in contradiction with Newton's law of cooling. Are Fourier's law of conduction and Newton's law of cooling mutually incompatible?
If there is a temperature discontinuity across this surface, then [itex]\frac{dQ}{dt}[/itex] diverges, in contradiction with Newton's law of cooling. Are Fourier's law of conduction and Newton's law of cooling mutually incompatible?