Chapter 2, Problem 159P

A solar heat flux $q_s$ is incident on a sidewalk whose thermal conductivity is k, solar absorptivity is $\alpha {.}_s,$ and convective heat transfer coefficient is h. Taking the positive $x$-direction to be toward the sky and disregarding radiation exchange with the surrounding surfaces, the correct boundary condition for this sidewalk surface is

1. $-k\frac{dT}{dx}={\alpha }_s{q}_s$
2. $-k\frac{dT}{dx}=h(T-T_{\infty })$
3. $-k\frac{dT}{dx}=h(T-T_{\infty })-{\alpha }_s{q}_s$
4. $h(T-T_{\infty })-{\alpha }_s{q}_s$
5. None of them