External_Flow_Sphere
Procedure External_Flow_Sphere(Fluid$, T_inf, T_s, P, u_inf, D: F_d, h, C_d, Nusselt, Re) calculates the average heat transfer coefficient and drag force and coefficient for external flow past a sphere as detailed in White (1991) and Nellis and Klein. Propeties are evaluated at the film temperature. The units of the inputs and outputs of the procedure depend on the units setting in EES.
Inputs
Fluid$ is a string or string variable that can be any fluid in the EES data base. The fluid can be an ideal gas, a real fluid, a brine, or an incompressible fluid in the Solid-Liquid_Props fluids library.
T_inf - the free stream fluid temperature in [C], [K], [F], or [R].
T_s - the surface temperature of the sphere in [C], [K], [F], or [R].
P - pressure can be in [Pa], [kPa], [bar], [MPa], [atm] or [psia]. (Note that for brines, this parameter provides the concentration in % instead of pressure.)
u_inf - free stream velocity of the flow in [m/s] or [ft/min]
D - diameter of the sphere in [m] or [ft]
Outputs
F_d - drag force [N] or [lbf]
h - average heat transfer coefficient in [W/m^2-K] or [Btu/hr-ft^2-R]
C_d - drag coefficient [-], where
,
where r is the density of the fluid and Afr is the frontal area.
Nusselt - average Nusselt number [-], where
where k is the conductivity of the fluid
Re - Reynolds number [-], where
where m is the viscosity of the fluid
Notes:
This procedure is responsible for determining the property data of the fluid specified and calculating the Reynold and Prandtl numbers. This procedure then passes the Reynold and Prandtl numbers to the non-dimensional procedure External_Flow_Sphere_ND. The non-dimensional procedure returns the values for C_d and Nusselt. External_Flow_Sphere calculates the drag force and the heat transfer coefficient for convection from the drag coefficient and the Nusselt number,
Example:
$unitSystem SI K kPa J
$VarInfo F_D units=N
$VarInfo h units=W/m^2-K
T_s=328 [K]
Fluid$='air'
T_inf=297 [K]
P=101.3 [kPa]
u_inf=10 [m/s]
D=0.01 [m]
Call external_flow_sphere(Fluid$, T_inf, T_s, P, u_inf, D: F_d, h, C_d, Nusselt, Re)
{Solution:
F_d=0.002134 [N]
h=122.8 [W/m^2-K]
C_d=0.4812 [-]
Nusselt=46.22 [-]
Re=5,897 [-]}