# Convection

Lumped thermal element for heat convection (Q_flow = Gc*dT)

## Library

Modelica/Thermal/HeatTransfer/Components

## Description

This is a model of linear heat convection, e.g., the heat transfer between a plate and the surrounding air; see also:ConvectiveResistor.It may be used for complicated solid geometries and fluid flow over the solid by determining theconvective thermal conductance Gc by measurements. The basic constitutive equation for convection is

Q_flow = Gc*(solid.T - fluid.T); Q_flow: Heat flow rate from connector 'solid' (e.g., a plate) to connector 'fluid' (e.g., the surrounding air)

Gc = G.signal[1] is an input signal to the component, since Gc isnearly never constant in practice. For example, Gc may be a functionof the speed of a cooling fan. For simple situations,Gc may be *calculated* according to

Gc = A*h A: Convection area (e.g., perimeter*length of a box) h: Heat transfer coefficient

where the heat transfer coefficient h is calculatedfrom properties of the fluid flowing over the solid. Examples:

**Machines cooled by air** (empirical, very rough approximation accordingto R. Fischer: Elektrische Maschinen, 10th edition, Hanser-Verlag 1999,p. 378):

h = 7.8*v^0.78 [W/(m2.K)] (forced convection) = 12 [W/(m2.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 plateto the fluid (= solid.Q_flow) is kept constant(according to J.P.Holman: Heat Transfer, 8th edition,McGraw-Hill, 1997, p.270):

h = Nu*k/x; Nu = 0.453*Re^(1/2)*Pr^(1/3); where h : Heat transfer coefficient Nu : = h*x/k (Nusselt number) Re : = v*x*rho/mue (Reynolds number) Pr : = cp*mue/k (Prandtl number) v : Absolute velocity of fluid x : distance from leading edge of flat plate rho: density of fluid (material constant mue: dynamic viscosity of fluid (material constant) cp : specific heat capacity of fluid (material constant) k : thermal conductivity of fluid (material constant) and the equation for h holds, provided Re < 5e5 and 0.6 < Pr < 50

## Parameters

Name | Label | Description | Data Type | Valid Values |
---|---|---|---|---|

| Number of Modifiers | Specifies the number of modifiers | Number | |

| Modifiers | Add new modifier | Structure | |

| Variable name | Cell of strings | 'Q_flow' | |

| Attribute | Cell of strings | 'start' | |

| Value |

## Ports

Name | Type | Description | IO Type | Number |
---|---|---|---|---|

| implicit | Signal representing the convective thermal conductance in [W/K] | input | 1 |

| implicit | input | 2 | |

| implicit | output | 1 |