What is the form of the overall heat transfer equation?

• A. Q = UAΔT_lm
• B. Q = UAΔT
• C. Q = hAΔT
• D. Q = kAΔT

Answer: (A)

The main idea is that the rate of heat transfer through a surface or exchanger is described by the overall heat transfer form Q = U A ΔT_lm. Here, U is the overall heat transfer coefficient that bundles together conduction through walls and convection on both sides, A is the heat transfer area, and ΔT_lm is the log-mean temperature difference between the two fluids or sides. The temperature difference typically isn’t constant along the length of an exchanger, especially in counterflow or parallel-flow configurations, so using a single ΔT would misrepresent the driving force. The log-mean temperature difference correctly averages that varying driving force to give the true heat transfer rate.

The other expressions represent different situations. Q = U A ΔT would be valid only if the temperature difference were effectively constant along the length, which is not generally the case. Q = h A ΔT is the local form for convection at a single surface with a heat transfer coefficient h. Q = k A ΔT / L comes from Fourier’s law for conduction through a solid slab of thickness L with thermal conductivity k.