Heat Transfer
Heat Transfer
Questions cover conduction resistance networks, convection correlations, radiation exchange, and heat-exchanger sizing. The exam favors combined-mode and LMTD problems.
Core rules
- Fourier law: q = −kA dT/dx. Plane-wall resistance R = L/(kA); cylindrical resistance R = ln(r₂/r₁)/(2πkL). Add series resistances; contact resistance is an extra interface term.
- Convection: q = hA(T_s − T_∞); Nu = hL/k. For turbulent flow in a smooth tube, Dittus–Boelter: Nu = 0.023 Re^0.8 Pr^n, with n = 0.4 for heating and 0.3 for cooling.
- Radiation: q = εσA(T_s⁴ − T_sur⁴), σ = 5.67 × 10⁻⁸ W/m²·K⁴. Temperatures must be absolute. For a small body in a large enclosure, use the enclosure temperature.
- Heat exchangers: Q = UAΔT_lm; counterflow gives the highest LMTD for the same terminal temperatures. NTU–effectiveness is convenient when outlet temperatures are unknown.
Worked example
A plane wall of area 2 m², thickness 0.1 m, and k = 50 W/m·K has a 100 K temperature difference. q = kAΔT/L = 50 × 2 × 100 / 0.1 = 100,000 W = 100 kW. The thermal resistance is R = L/(kA) = 0.1/(50 × 2) = 0.001 K/W, and q = ΔT/R = 100/0.001 = 100 kW, which confirms the result.
Traps
Using Celsius in Stefan–Boltzmann; using the arithmetic mean temperature difference instead of LMTD; forgetting the area of a cylindrical surface; omitting fouling resistance; and applying a Nusselt correlation outside its Re/Pr range.