Forced convection correlations

The thermal solver uses different forced convection correlations to model thermal exchange between a fluid in motion and a solid surface in different geometrical configurations using forced convection thermal couplings.

Fully developed duct flow

The convection correlations for the fully developed duct flow are obtained from the following equations [4]:

For laminar flow in a circular pipe, and , the Nusselt number is:

For laminar flow in a rectangular duct, and , the Nusselt number is:

For turbulent flow in a circular pipe and rectangular pipe, when

For transition flow, for 2000 < Reduct < 2300,

where:

  • NuD is the duct Nusselt number for the fully developed duct flow.

  • Dduct is the duct hydraulic diameter, evaluated at the narrower end of the nozzle or diffuser.
  • Aductis the duct cross-sectional area, evaluated at the narrower end of the nozzle or diffuser.

Developing duct flow

To compute the developing duct flow, the thermal solver multiplies a length correction factor, hm, with the Nusselt number for the fully developed duct flow hm = 1.

hm is defined as a function of X/Dduct, where X is the distance from the entrance.

For laminar flow, Reduct < 2300, the solver computes the length correction factor as follows:

  • For X+<0.02
  • For X+>0.02

where

For turbulent flow, , the following table [4] lists hm used by the thermal solver:

X/Dduct 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 >10.0
hm (turb) 2.2 2.4 1.85 1.45 1.4 1.32 1.23 1.2 1.15 1.12 1.1

Flat plate in free stream

The convection correlations for the flat plate in a free stream are obtained from the following equations:

For laminar flow, Re < 2·105, the local Nusselt number is:

For transient flow, 2·105 < Re < 3·105

For turbulent flow, Re > 3·105

where:

  • Nuxis the plate local Nusselt number.
  • is the local plate Reynolds number, where ρ is the fluid density, x is the distance from the leading edge of the plate in the direction of the flow, V is the fluid velocity, μ is the viscosity of the fluid.

Plate aligned with free stream correlation

The convection correlations for the plate in the flow direction are obtained from the following equations [5]:

For laminar flow, Re < 4·105, the local Nusselt number:

For transient flow, 4·105 < Re < 6·105

For turbulent flow, Re > 6·105

Sphere in flow correlation

The convection correlation for the sphere in flow is obtained from the following equation [5]:

Cylinder across flow correlation

The correlations for a cylinder in the cross flow are obtained from the following equations [5]:

For Re < 100, the Nusselt number is:

For Re > 100, the Nusselt number is: