Heat transfer Fourier’s Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F = -k∇T, which means that heat energy flows from hot regions to cold regions. The constant k > 0 is called the conductivity, which has metric units of J/(m-s-K). A temperature function for a region D is given. Find the net outward heat flux ∫∫S F ⋅ n dS = -k∫∫S ∇T ⋅ n dS across the boundary S of D. In some cases, it may be easier to use the Divergence Theorem and evaluate a triple integral. Assume k = 1. T(x, y, z) = 100 + e-z;D = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1}

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Q: Heat transfer Fourier’s Law of heat transfer (or heat conduction) states that the heat flow vector F…

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