Convection

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*hA: 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 [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 aflat plate where the heat flow rate from the plateto 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