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.
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AJ/m^2·K
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BW/m^2·K
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CW/m·K
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DJ/m·K
Answer
Correct Answer: W/m^2·K
Explanation
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:
Start with qʺ = h (T_s - T_∞).Assign units: qʺ → W/m^2; ΔT → K.Compute h units: (W/m^2)/K = W/m^2·K.Confirm dimensional consistency in exchanger formulas: Q = U A ΔT_lm ⇒ U must be W/m^2·K.Select W/m^2·K.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