Which equation determines the required heat transfer surface area to achieve a given heat transfer rate, accounting for losses with U and the inlet/outlet temperatures?

Which equation determines the required heat transfer surface area to achieve a given heat transfer rate, accounting for losses with U and the inlet/outlet temperatures?

• A. Overall Heat Transfer Equation
• B. Fourier’s Law
• C. Newton’s Law of Cooling
• D. Continuity Equation

Answer: (A)

Sizing a heat transfer surface uses a single relationship that ties the heat rate to the area, the overall transfer capability, and the driving temperature difference between the streams. The appropriate equation is Q = U A ΔT_lm, where U is the overall heat transfer coefficient, A is the surface area, and ΔT_lm is the log-mean temperature difference based on the inlet and outlet temperatures of the two fluids. This form directly shows how to pick the required area to achieve a specified heat transfer rate, since you can rearrange it to A = Q / (U ΔT_lm). The other ideas focus on different heat transfer ideas. Fourier’s law deals with conduction through a solid (q = kA dT/dx) and isn’t the sizing relation for a surface exchanging heat between fluids. Newton’s law of cooling describes convective exchange at a surface with a single fluid (q = h A (T_s - T∞)) and doesn’t incorporate the two-fluid driving force via a log-mean temperature difference. The continuity equation is about mass conservation, not heat transfer.

Sizing a heat transfer surface uses a single relationship that ties the heat rate to the area, the overall transfer capability, and the driving temperature difference between the streams. The appropriate equation is Q = U A ΔT_lm, where U is the overall heat transfer coefficient, A is the surface area, and ΔT_lm is the log-mean temperature difference based on the inlet and outlet temperatures of the two fluids. This form directly shows how to pick the required area to achieve a specified heat transfer rate, since you can rearrange it to A = Q / (U ΔT_lm).

The other ideas focus on different heat transfer ideas. Fourier’s law deals with conduction through a solid (q = kA dT/dx) and isn’t the sizing relation for a surface exchanging heat between fluids. Newton’s law of cooling describes convective exchange at a surface with a single fluid (q = h A (T_s - T∞)) and doesn’t incorporate the two-fluid driving force via a log-mean temperature difference. The continuity equation is about mass conservation, not heat transfer.