Question

Consider a single heat source located at the originwithtemperature

T(x,y,z)= 25/√(x²+y²+z²)

a)Calculate the heat flux across the surface

S={(x,y,x): z= √(1-x²-y²), x²+y² <=1}

b) Repeat the calculation in part (a) usingtheparametrization

x= sinu cosv, y=sinusinv, z=cosu, 0<=u <= π/2, 0<=v<=2π