Identify the law — heat transfer proportional to area and temperature difference The statement “heat flow rate between two bodies is directly proportional to the exposed surface area and the temperature difference between them” refers to which law?

Introduction / Context:
Engineers often linearize convective heat transfer using an overall heat transfer coefficient. This linear form is rooted in a classical empirical law relating heat flow to temperature difference.

Given Data / Assumptions:

• Surface temperature T_s and fluid bulk temperature T_∞.
• Convective heat transfer area A and coefficient h.

Concept / Approach:
Newton’s law of cooling states q = h * A * (T_s − T_∞). It treats the convective boundary layer as a lumped resistance, proportional to area and linearly dependent on temperature difference, with proportionality constant h capturing fluid properties and flow regime.

Step-by-Step Solution:

Verification / Alternative check:
Contrast: Fourier’s law is q = −k * A * dT/dx (conduction); Stefan–Boltzmann gives q = ε * σ * A * (T_s^4 − T_sur^4) (radiation), not linear in ΔT for large differences.

Why Other Options Are Wrong:
First law asserts energy conservation, not a transfer rate relation. “Newton’s law of heating” is not a standard term; heating or cooling both follow the same convection relation. Stefan’s law has T^4 dependence, not linear.

Common Pitfalls:
Applying Newton’s law outside its valid range (very large temperature differences with strong radiation or rapidly varying h).

Final Answer:

Newton's law of cooling