In the process of evaluation of U, we need to calculate various parameters. Below paragraph mentions few of them.

1. **Reynolds number** (**Re**) Reynolds number, which relates inertial forces to viscous forces and thereby characterizes the type of flow regime

2. **Prandtl number (Pr)**, which relates the thermal properties of the fluid to the conductivity of the pipe.

3. **Nusselt number (Nu) **, a dimensionless group defining the relative significance of the film heat transfer coefficient to the conductivity of the pipe wall

All above three parameters are linked as shown below

Calculation of Reynold’s Number

where:

Dh is the hydraulic diameter of the pipe; its characteristic travelled length, , (m).

Q is the volumetric flow rate (m3/s).

A is the pipe cross-sectional area (m²).

v is the mean velocity of the object relative to the fluid (SI units: m/s).

mu is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s)).

nue is the kinematic viscosity ( (m²/s).

rho is the density of the fluid (kg/m³).

Calculation of Prandtle number :

Where

Based on these parameter, we can now calculated Heat transfer co-efficient on either side.

Where kw is thermal conductivity of the bulk fluid.

With this you are now equipped to calculate over all heat transfer.