Question

The heat flow vector field for conducting objects is **F**=−k∇T, where T(x,y,z) is the temperature in the object and k is a constant that depends on the material. Compute the outward flux of **F **across the given surface S for the given temperature distribution. Assume k=1.

T(x,y,z,)=−7ln( x^{2} +y^{2} + z^{2})

S is the sphere xStep 1

Assume *k = *1.

Then the vector field becomes, **F **= −∇T.

Find ∇T as follows.

Step 2

The parametric description of the sphere of radius *a*, centered at the origin is given by,

Step 3

Take the partial derivative of the parameterization with...

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