.Modelica.Thermal.HeatTransfer.Components.Convection

Information

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 the convective 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 is nearly never constant in practice. For example, Gc may be a function of 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 calculated from properties of the fluid flowing over the solid. Examples:

Machines cooled by air (empirical, very rough approximation according to [Fischer2017, p. 452]:

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 plate to the fluid (= solid.Q_flow) is kept constant (according to [Holman2010, p.265]):

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/mu  (Reynolds number)
   Pr : = cp*mu/k     (Prandtl number)
   v  : Absolute velocity of fluid
   x  : distance from leading edge of flat plate
   rho: density of fluid (material constant
   mu : 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