State Newton's law of cooling.

• A. dQ/dt = h A (T∞ - T_s)
• B. dQ/dt = h A (T_s - T∞)
• C. dQ/dt = -h A (T_s - T∞)
• D. dQ/dt = k A ΔT / L

Answer: (B)

Newton's law of cooling says the rate of convective heat transfer is proportional to the temperature difference between the surface and the surrounding fluid. The standard form is dQ/dt = h A (T_s - T∞), where h is the convective heat transfer coefficient, A is the surface area, T_s is the surface temperature, and T∞ is the ambient fluid temperature. This form makes sense: when the surface is hotter than the surroundings (Ts > T∞), heat flows out of the surface, giving a positive dQ/dt in this convention.

The other options either reverse the temperature difference or mix in a conduction-style expression. For example, using (T∞ - Ts) would flip the sign and imply heat flow in the opposite direction under the same conditions, while -h A (T_s - T∞) enforces the opposite sign again. The last option, k A ΔT / L, is the conduction through a solid (Fourier’s law) rather than convection at a surface.

So the best choice, reflecting the convection form of Newton’s law of cooling, is dQ/dt = h A (T_s - T∞), with the understanding that the sign convention defines dQ/dt as the rate of heat transfer to the surroundings.