Convection - MapleSim Help

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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

 See Also The components described in this topic are from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.

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