Select the correct SI unit for the overall heat transfer coefficient U in convection–conduction composite analysis.

Introduction / Context:
The overall heat transfer coefficient U aggregates conduction and convection resistances into a single parameter for heat exchanger and wall calculations. Using correct units ensures dimensional consistency when computing heat duties from temperature differences.

Given Data / Assumptions:

• General heat-transfer relation: q = U * A * ΔT_lm (or q = U * A * ΔT for simple cases).
• q measured in watts (W), area A in m^2, temperature difference in kelvin (K).

Concept / Approach:
Rearranging q = U * A * ΔT shows U must carry units that convert A * ΔT to power: U = q / (A * ΔT). Therefore, U has SI units W / (m^2 * K) = W/m^2·K.

Step-by-Step Solution:

Verification / Alternative check:
For conduction only, the analogous coefficient k uses W/m·K; including area-normalized convection terms on both sides yields U in W/m^2·K.

Why Other Options Are Wrong:

• (b) Missing temperature dimension.
• (c) Units of thermal conductivity k, not overall U.
• (d) Incomplete units.
• (e) K/W is overall thermal resistance per unit area inverted, not U.

Common Pitfalls:
Confusing U with k or h; h and U both use W/m^2·K, while k uses W/m·K.

Final Answer:
W/m^2·K