According to Newton’s law of cooling for convection, the heat transfer rate from a hotter body to a colder fluid is proportional to which factors?

Introduction / Context:
Newton’s law of cooling provides a linearized model for convective heat transfer near a surface. It is central to HVAC, electronics cooling, and thermal design, simplifying complex boundary-layer physics into an engineering correlation using a heat transfer coefficient.

Given Data / Assumptions:

• A solid surface at temperature T_s interacts with a fluid at T_∞.
• Heat transfer coefficient h captures flow, properties, and geometry effects.
• Area A is the effective heat-exchange surface.

Concept / Approach:
Newton’s law states q = h * A * (T_s − T_∞). Thus, for a given h, heat transfer is directly proportional to both area A and the temperature difference ΔT. Therefore, the correct interpretation is that both factors simultaneously influence the rate, not one or the other exclusively.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional reasoning confirms that doubling area or doubling temperature difference doubles q; doing both quadruples q if h is unchanged.

Why Other Options Are Wrong:

• Area only or ΔT only ignores the other factor.
• “Either/or exclusively” misunderstands the multiplicative dependence.
• Fluid density alone does not appear explicitly; its effect is embedded in h.

Common Pitfalls:
Treating h as constant across large ΔT or different flow regimes; in reality, h may change, but the basic proportionality form remains valid.

Final Answer:
The product of surface area and temperature difference (both apply)