# 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 aflat 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

NameLabelDescriptionData TypeValid Values

mo__nmodifiers

Number of Modifiers

Specifies the number of modifiers

Number

mo__modifiers

Modifiers

Structure

mo__modifiers/varname

Variable name

Cell of strings

'Q_flow'
'dT'

mo__modifiers/attribute

Attribute

Cell of strings

'start'
'fixed'

mo__modifiers/value

Value

## Ports

NameTypeDescriptionIO TypeNumber

Gc

implicit

Signal representing the convective thermal conductance in [W/K]

input

1

solid

implicit

input

2

fluid

implicit

output

1