HEAT TRANSFER (CONDUCTION, CONVECTION, RADIATION)

Three modes carry heat. Conduction: q = -k·A·dT/dx, governed by thermal conductivity k. Multi-layer walls add resistances in series: R = L/(k·A). Convection: q = h·A·ΔT, with h from Nusselt-number correlations (Dittus-Boelter for turbulent pipe flow, Churchill-Chu for natural convection). Radiation: q = ε·σ·A·(Ts⁴ - T∞⁴). Fins extend surface area; efficiency η = tanh(mL)/mL where m = sqrt(hP/kA).

• q = -k·A·dT/dx (conduction)
• q = h·A·(Ts - T∞) (convection)
• q = εσA(Ts⁴ - T∞⁴) (radiation)
• η_fin = tanh(mL)/mL, m = sqrt(hP/(kA))
• τ = ρ·V·cp / (h·A) (lumped)

References & StandardsIncropera "Fundamentals of Heat Transfer", ASHRAE Fundamentals

Use for any temperature-driven heat-flow problem: building walls, pipe insulation, electronic-component cooling, furnace walls, heat-sink design. Identify dominant mode(s) and build a thermal resistance network. For transient problems with Bi < 0.1, use lumped-capacitance: T(t) = T∞ + (T0 - T∞)·exp(-t/τ). For higher Biot number, use the Heisler charts or finite-difference solution.