Suppose a solid object in R has a temperature distribution given by T(x,y,z). The heat flow...

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Suppose a solid object in R° has a temperature distribution given by T(x,y,z). The heat flow vector field in the object is F = - kVT, where the conductivity k is a property of the material. Note that the heat flow vector points in the direction opposite to that of the gradient, which is the direction of greatest temperature decrease. The divergence of the heat flow vector is V•F= - kV• VT = - kV?T (the Laplacian of T). Compute the heat flow vector field and its divergence for the following temperature distribution. T(x,y,z) = 100 (1+x² +y² +z² Compute the heat flow vector field. F = OOD Compute the divergence. V•F = Suppose a solid object in R° has a temperature distribution given by T(x,y,z). The heat flow vector field in the object is F = - kVT, where the conductivity k is a property of the material. Note that the heat flow vector points in the direction opposite to that of the gradient, which is the direction of greatest temperature decrease. The divergence of the heat flow vector is V•F= - kV• VT = - kV?T (the Laplacian of T). Compute the heat flow vector field and its divergence for the following temperature distribution. T(x,y,z) = 100 (1+x² +y² +z² Compute the heat flow vector field. F = OOD Compute the divergence. V•F =