(Heat flow in 3-space) The internal energy, E, of a volume e
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(Heat flow in 3-space) The internal energy, E, of a volume element dV within a homogeneous solid is cT dV; where and c a
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(Heat flow in 3-space) The internal energy, E, of a volume element dV within a homogeneous solid is cT dV; where and c are constants (the density and specific heat of the solid material), and T D T .x; y; z; t / is the temperature at time t at position .x; y; z/ in the solid. Heat always flows in the direction of the negative temperature gradient and at a rate proportional to the size of that gradient. Thus, the rate of flow of heat energy across a surface element dS with normal NO is ?krT NO dS, where k is also a constant depending on the material of the solid (the coefficient of thermal conductivity). Use
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