functionflowWork_equalHeatFlowRate

Function that returns the flow work ratio for equal heat flow rate

Extends from Modelica.Icons.Function (Icon for functions).

Information

Function that returns the ratio of flow work for equal heat flow rate.

If we want to operate the device such that the same amount of heat is transferred with the same inlet temperature, resulting in the same outlet temperatures, we can use for the same heat flow rate

Q̇ = ṁ cp ΔT,

adjust the mass flow rate according to

ṁ ⁄ ṁ0 = cp,0 ⁄ cp,

and use for the flow work the equation W = V̇ Δp / rho.

This function uses these equations to compute the ratio of the the flow work that results from a change in medium properties for the same heat flow rate.

The flow coefficient is n=1 for laminar and n=1.688 for turbulent flow. Note that typical textbook equations use n=2. The value n=1.688 is based on a friction coefficient for a Reynolds number of Re=2,300...10,000, in which case the friction coefficient can be approximated as f1 = 0.2767 Re-0.312 with a maximum error or 0.8% (Melinder, 2010), and hence the pressure drop is proportional to v1.688, where v is the flow velocity.

The function assumes that the flow geometry and the flow regime (laminar or turbulent) do not change when the medium changes.

References

Melinder, Åke (2010a). Handbook on Indirect Refrigeration and Heat Pump Systems. Kullavik, Sverige: Svenska Kyltekniska Föreningen. https://varmtochkallt.se/wp-content/uploads/Projekt/Effsys2/P02/ke-Melinder-engelsk-handbok.pdf

Inputs

TypeNameDefaultDescription
RealnFlow coefficient n, n=1 for laminar, n=2 for fully turbulent

Outputs

TypeNameDefaultDescription
Realratio_WFloRatio of flow work

Revisions

  • May 11, 2026, by Michael Wetter:
    First implementation.