Units and dimensions – Heat transfer coefficient in SI units Select the correct SI unit for the (overall) heat transfer coefficient h used in convection and overall heat transfer calculations.

Introduction / Context:The heat transfer coefficient h relates heat flux to a temperature difference at a surface. Using correct SI units avoids dimensional mistakes in design equations such as qʺ = h * (T_s - T_∞) and in overall heat transfer calculations for exchangers (Q = U * A * ΔT_lm).

Given Data / Assumptions:

• Heat flux qʺ has units W/m^2.
• Temperature difference ΔT has units K.
• h is defined by qʺ = h * ΔT.

Concept / Approach:From qʺ = h * ΔT, rearrange to h = qʺ / ΔT. Since qʺ is W/m^2 and ΔT is K, h must be W/m^2·K. This unit is also used for overall heat transfer coefficient U in exchanger analysis.

Step-by-Step Solution:

Verification / Alternative check:Textbooks and standards uniformly list h and U in W·m^-2·K^-1.

Why Other Options Are Wrong:

• J/m^2·K or J/m·K: Energy units, not power; would imply time integration.
• W/m·K: Unit for thermal conductivity k, not h.

Common Pitfalls:Confusing h with k; k appears in Fourier’s law (q = -k A dT/dx) with units W/m·K, whereas h multiplies a temperature difference per unit area.

Final Answer:W/m^2·K