Heat Transfer
Scope
Conduction, convection, radiation, exchanger design, and transient cooling.
Concepts to own
- Resistance networks: R = L/(kA) for a slab, ln(r2/r1)/(2πkL) for a cylinder, 1/(hA) for a film; fouling resistances add in series.
- Overall coefficient: 1/U = 1/hi + Rf,i + t/k + Rf,o + 1/ho, referred to a stated area.
- Dimensionless groups: Nu = hD/k = f(Re, Pr); Dittus-Boelter Nu = 0.023 Re^0.8 Pr^n with n = 0.4 for heating and 0.3 for cooling.
- LMTD: ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2), with correction factor F < 1 for multipass; effectiveness-NTU when outlet temperatures are unknown.
- Radiation: q = σ ε A (T1⁴ − T2⁴), with absolute temperatures.
- Boiling and condensing coefficients are orders of magnitude above gas convection, so the limiting film sets U.
- Lumped capacitance is valid only for Biot number below about 0.1.
Traps
- Using an arithmetic mean temperature difference instead of the LMTD.
- Ignoring the F factor for shell-and-tube units with a temperature cross.
- Fouling resistance given in ft²·h·°F/Btu and used with SI coefficients.
- Radiation computed with degrees Celsius.
Worked example
Hot oil cools from 150 °C to 90 °C against water heated from 20 °C to 60 °C in countercurrent flow. ΔT1 = 150 − 60 = 90, ΔT2 = 90 − 20 = 70, so ΔTlm = 20/ln(90/70) = 79.6 °C. Then A = Q/(U F ΔTlm).
Rule of thumb: if the two terminal differences are within 20% of each other, the arithmetic mean is within about 1% and makes a good check.