**AnnularFlow_Laminar**

Procedure AnnularFlow_Laminar(Re, Pr, LoverD, r|star : Nusselt_T, Nusselt_H, f) returns lower and upper bounds on the Nusselt number and friction factor for fully-developed flow in an annular space assuming laminar flow. The flow is characterized by Reynolds and Prandtl numbers and the ratio of the inner to outer annular radius. 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 - length to diameter ratio

r|star - ratio of inner to outer radius

**Outputs:**

Nusselt_T - lower bound on the average Nusselt number (based on the annular wall surface area)

Nusselt_H - upper bound on the average Nusselt number (based on the annular wall surface area)

f - apparent Darcy friction factor [-] .

**Notes:**

The Darcy friction factor is calculated using a correlation recommended in Eqn 431 of Shah and London (1978). The correlation is corrected for the developing region using the form provided by Shah and London.

The Nusselt numbers returned from this procedure apply to the wall separating the annulus from the pipe. The outer wall of the annulus is assumed to be adiabatic. Two values are provided to provide upper and lower bounds. The values are based on Bennett (2020b).