Chapter 2, Problem 167P

A plane wall of thickness L is subjected to convection at both surfaces with ambient temperature $T_{\infty 1}$ and and heat transfer coefficient h₁ at the inner surface and corresponding $T_{\infty 2}$ and and h₂ values at the outer surface. Taking the positive direction of $x$ to be from the inner surface to the outer surface, the correct expression for the convection boundary condition is

1. $k\frac{dT(0)}{dx}=h_1[T(0)-T_{\infty 1}]$
2. $k\frac{dT(L)}{dx}=h_2[T(L)-T_{\infty 2}]$
3. $-k\frac{dT(0)}{dx}=h_1(T_{\infty 1}-T_{\infty 2})$
4. $-k\frac{dT(L)}{dx}=h_2(T_{\infty 1}-T_{\infty 2})$
5. None of them