**PipeFlow_Laminar**

Procedure PipeFlow_laminar (Re, Pr, LoverD: Nusselt_T, Nusselt_H, f) returns the average Nusselt number and friction factor for a circular tube characterized by Reynolds and Prandtl numbers, length/diameter, and relative roughness. The Reynold's number is expected to be < 2300.

**Inputs:**

Re - Reynolds number based on properties evaluated at the bulk average temperature [-]

Pr - Prandtl number of the fluid evaluated at the bulk average temperature [-]

LoverD - ratio of tube length to diameter.

**Outputs:**

Nusselt_T - average Nusselt number assuming a constant wall temperature

Nusselt_H - average Nusselt number assuming a constant wall heat flux

f - apparent Darcy friction factor [-]

**Notes**

The Darcy friction factor is calculated using a correlation recommended in Eqn 192, p98 of Shah and London (1978). The correlation is applicable in the developing and fully-developed region and limits to 64/Re.

The average Nusselt number correlations are obtained from the correlation provided by Bennett (2020a). The correlation is valid for laminar flow with inverse Graetz number, L/(D Re Pr), > 1e-6 and Pr>0.5 for errors of less than 2.5%. It can be used down to Pr>0.1 with errors rising to 10%. The derivative of the average values is taken numerically to provide the local values. The average Nusselt numbers assume simultaneously developing flow; however, it is possible to obtain values consistent with thermally developing/hydrodynamically developed flow by calling the procedure with a large Prandtl number.