# .Buildings.Fluid.HeatExchangers.PlateHeatExchangerEffectivenessNTU

## Information

Model of a plate heat exchanger without humidity condensation. This model transfers heat in the amount of

Q̇ = Q̇max ε
ε = f(NTU, Z, flowRegime),

where max is the maximum heat that can be transferred, ε is the heat transfer effectiveness, NTU is the Number of Transfer Units, Z is the ratio of minimum to maximum capacity flow rate and flowRegime is the heat exchanger flow regime. such as parallel flow, cross flow or counter flow.

The flow regimes depend on the heat exchanger configuration. All configurations defined in Buildings.Fluid.Types.HeatExchangerConfiguration are supported.

#### Convective heat transfer coefficients

The convective heat transfer coefficients scale proportional to (ṁ/ṁ0)n, where is the mass flow rate and 0 is the nominal mass flow rate. By default, the exponents are n=0.8 for both streams. The convective heat transfer coefficients are computed based on the UA-value, neglecting the thermal conductance of the heat exchanger material. The ratio of the convection coefficients at design conditions can be adjusted using the parameter r0=(hA)0,1 ⁄ (hA)0,2 where (hA)0,1 and (hA)0,2 are the respective products of the heat transfer coefficient times surface area. By default, the ratio r0 is computed based on the similarity law for turbulent flow, which states that the convective heat transfer coefficient h follows the proportionality law

h ∝ k (ρ v x / η)n1 Pr1/3,

where k is the heat conductivity of the fluid, ρ is the density, v is the flow velocity, x is the characteristic length, η is the dynamic viscosity and Pr is the Prandtl number. Under the assumption that both sides of the heat exchanger are identical, and considering that the velocity is proportional to the mass flow rate divided by the density, the ratio r0 is

r0 = (k1 (ṁ0,1 / η0,1)n1 Pr0,11/3) ⁄ (k2 (ṁ0,2 / η0,2)n2 Pr0,21/3).

This is the default setting for the parameter `r_nominal`. Thus, if both sides of the heat exchanger have the same temperature difference, and the same medium, then r0=1. However, if medium 1 is air and medium 2 is water, and the heat exchanger is designed to have the same temperature drop for both media, then r0=0.5.

#### Related model

For a heat and moisture exchanger, use Buildings.Fluid.MassExchangers.ConstantEffectiveness.

## Revisions

• March 15, 2022, by Michael Wetter:
Introduced parameter `r_nominal` and exposed exponents of convective heat transfer coefficients.
This is for issue 2918.
• September 25, 2018, by Michael Wetter:
First implementation.

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