A Greenhouse Is in the Shape of the Graph $z = 36 - x ^ { 2 } - y ^ { 2 }$

Essay

A greenhouse is in the shape of the graph $z = 36 - x ^ { 2 } - y ^ { 2 }$ with the floor at z = 0.Suppose the temperature around the greenhouse is given by $T = 3 x ^ { 2 } + 3 y ^ { 2 } + ( z - 6 ) ^ { 2 }$ .Let ${ \vec { H } } = - \nabla T$ be the heat flux density field.
Calculate the total heat flux outward across the boundary wall of the greenhouse.