Heat transfer: absolute temperatures and resistance accounting

Absolute temperatures are K; differences are K. Conductivity is W/(m K), convection coefficient W/(m^2 K), heat rate W, and resistance K/W. Radiation uses absolute fourth powers; passing Celsius silently changes the physics. Geometry and properties are constant, and the equations are ideal baselines.

Conduction and convection

Full wall resistances include area: L/(k*A), ln(r2/r1)/(2*pi*k*L), and (1/r1-1/r2)/(4*pi*k). Cylinder/sphere radii require r2>r1>0. composite_wall returns each temperature drop from Q*R and includes supplied film resistances. A missing film is represented by None, not zero; zero h is rejected. At least one physical layer is required.

The legacy overall_u name returns conductance 1/sum(R) [W/K] for full resistances. It does not return area-normalized U [W/(m^2 K)]. To obtain U, divide the conductance by area. The documentation now makes this distinction explicit without changing existing numeric behavior.

Lumped cooling requires Bi=h*Lc/k typically below 0.1, where Lc=V/A. The function cannot check Bi without conductivity; that assessment remains the caller’s responsibility. Semi-infinite conduction requires alpha>0 and t>0; t=0 is excluded rather than resolving the discontinuous boundary condition.

Exchangers and limits

NTU is nonnegative and Cr=Cmin/Cmax lies in [0,1]. Counterflow at Cr=1 uses NTU/(1+NTU). Stable expm1 expressions preserve tiny NTU, and log1p preserves near-equal terminal temperature differences in LMTD. Temperature crossing is excluded by requiring both terminal differences positive.

from engineeringkit.heat_transfer import composite_wall
result = composite_wall(400, 300, [(.1, 1), (.2, 2)], A=2)
# Q=1000 W, interfaces [400, 350, 300] K.
fig, ax = result.plot()

Tests check interface energy balance, cylindrical thin-wall limit, equal- temperature radiation, cooling endpoints and exchanger limiting cases. Fin formulas assume a straight constant-section fin with an adiabatic tip.