Grashof Number for a Specified Density

 

For the free convection problems encountered in Bird, Stewart, and Lightfoot that cannot be modeled using the ideal gas law the densities are specified for the fluids used.  The Grashof Number is calculated using the following equation.

The density is assumed to be a linear function of the temperature.

 

 

MATLAB Code

 function Grashoff = grlcalc (Th,Tc,P,B,rho_high,rho_low,index)
 % Calculates the Grashoff number using a specified density for the
 % low and high temperatures. Note: For Bird, Stewart and Lightfoot
 % parameter 'B' should be the radius of the tube or half the
 % distance between two parallel plates
 % Argument List:
 %   Th       [=] temperature of the hot plate in units of Tdeg
 %   Tc       [=] temperature of the cold plate in units of Tdeg
 %   P        [=] pressure in units of Pa
 %   B        [=] the representative length of the system in units of m
 %   rho_high [=] Density at the higher temperature
 %   rho_low  [=] Density at the lower temperature
 %   index    [=] index of compounds whose Grashoff numbers are calculated
 % Returns:
 %   Gr       [=] Grashoff number in dimensionless units
 % Example:
 % for a single component system of water (Tdeg=Kelvin)
 %           >> grlcalc(500,350,101325,.01,.92,.95)
 %           ans =
 %                     1.2743e+003
 rhobar=(rho_high+rho_low)/2;
 if nargin<6
        fprintf('Too few arguments')
 elseif nargin==6
        Grashoff=rhobar.*9.8.*abs(rho_low-rho_high).*B.^3./(mucalc((Th+Tc)./2)).^2;
 else
        Grashoff=rhobar.*9.8.*abs(rho_low-rho_high).*B.^3./(mucalc((Th+Tc)./2,index)).^2;
 end

 

 

Prashant Setty, 2005