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Convection

Lumped thermal element for heat convection

Description

The Convection component models a linear heat convection between solid geometries and fluid flow over the solid by determining the convective thermal conductance, ${G}_{c}$, by measurements. The basic constitutive equation for convection is

 ${Q}_{\mathrm{flow}}={G}_{c}\cdot \left({T}_{\mathrm{solid}}-{T}_{\mathrm{fluid}}\right)$

If ${G}_{c}$ is an input value, it may be calculated according to

 ${G}_{c}=h\cdot A$

where the heat transfer coefficient, h, is calculated from properties of the fluid flowing over the solid.

Example: Machines cooled by air

$\frac{W}{{m}^{2}\cdot K}$ (forced convection)

$\frac{W}{{m}^{2}\cdot K}$ (free convection)

where

$v$: Air velocity in m/s

Laminar flow with constant velocity of a fluid along a flat plate where the heat flow rate from the plate to the fluid (= solid.$Q$) is kept constant:

 $h=\frac{\mathrm{Ν}k}{x}$

Connections

 Symbol Units Description ${G}_{c}$ $\frac{W}{K}$ Constant thermal convection between the two materials $\mathrm{solid}$ - Thermal input port $\mathrm{fluid}$ - Thermal output port

Variables

 Symbol Units Description $h$ $\frac{W}{{m}^{2}\cdot K}$ Heat transfer coefficient $\mathrm{Ν}$ - $\frac{hx}{k}$  (Nusselt number) $\mathrm{ℜ}$ - $\frac{vx\mathrm{ρ}}{\mathrm{μ}}$ (Reynolds number) $\mathrm{Pr}$ - $\frac{{c}_{p}\mathrm{μ}}{k}$  (Prandtl number) $v$ - Absolute velocity of fluid $x$ - Distance from leading edge of flat plate $\mathrm{ρ}$ - Density of fluid (material constant) $\mathrm{μ}$ - Dynamic viscosity of fluid (material constant) ${c}_{p}$ - Specific heat capacity of fluid (material constant) $k$ - Thermal conductivity of fluid (material constant) and the equation for h holds, provided that $\mathrm{ℜ}<5\cdot {10}^{5}$ and $0..6<\mathrm{Pr}<50$ $W$ - Watts $T$ - Temperature

Initial Conditions

 Symbol Units Description Modelica ID ${Q}_{\mathrm{flow0}}$ W Heat flow rate from to ${\mathrm{port}}_{b}$ Q_flow ${\mathrm{ΔT}}_{\mathit{0}}$ $K$ Initial temperature difference dT