Pipe Heat Transfer and Insulation

Method & assumptions

1. Steady one-dimensional radial heat flow, constant properties and bulk temperatures along the length; perfect layer contact, no internal heat generation. Actual diameters are required, not nominal pipe sizes.
2. For length L: inner-film resistance = 1/(hi π Di L); pipe resistance = ln(Do/Di)/(2π kp L); insulation resistance = ln((Do + 2t)/Do)/(2π ki L); outer-film resistance = 1/(ho π (Do + 2t) L).
3. Add the four resistances. Q = (Tfluid − Tambient)/Rtotal; heat per length = Q/L. Each surface temperature follows from the preceding temperature minus Q times that layer resistance. Negative Q means heat enters the pipe.
4. Bare comparison removes insulation and uses the bare outer surface area with the same film coefficients. Magnitude reduction = |Qbare| − |Q|; a negative result means increased heat transfer. Added insulation need not reduce heat transfer for every radius and fixed coefficient.
5. Defaults are a constructed teaching case, not certified copper or insulation properties. Supply conductivities at the relevant temperatures and convection coefficients for the actual flow conditions. The comparison assumes these coefficients remain unchanged.
6. Radiation, axial fluid cooling, fittings/supports, thermal bridges, fouling/contact resistance, moisture, condensation and transient effects are excluded. This is not an insulation product selection, minimum thickness requirement or economic optimum.

Sources

• US DOE Fundamentals Handbook, Heat Transfer: cylindrical conduction pp. 11–17 and combined convection pp. 20–23 ↗