Mathematical model of Heat Transfer Coefficient between inner surface of the pipe and moving fluid:

U = \frac{\lambda}{d} \, {\rm Nu}

where

thermal conductivity of flowing fluid

inner pipe diameter

dimensionless Nusselt number (Nu)


The Nusselt number (Nu) correlations are:

Stagnant fluidNatural ConvectionForced Convection
OEIS sequence A282581

McAdams 

McAdams, W.H. (1954) Heat Transmission. McGraw-Hill, New York.



{\rm Nu}=3.6568



\mbox{Nu}_D= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}_D^{1/6}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2



{\rm Nu}=0.023 \cdot \mbox{Re}_D^{0.8} \cdot \mbox{Pr}^{0.4}\cdot \left( \frac{\mu}{\mu_w} \right)^{0.14}



See also

Physics / Thermodynamics / Heat Transfer /  Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model

[ Thermal conductivity ] [ Nusselt number (Nu) ]


References