External_Flow_Sphere_ND
Procedure External_Flow_Sphere_ND(Re,Pr: Nusselt, C_d) returns the average Nusselt number and the drag coefficient for an isothermal sphere of diameter D in crossflow. The propeties are evaluated at the film temperature.
Inputs:
Re - Reynold's number based on properties evaluated at the film temperature [-], defined as
where
r is the density of the fluid
m is the viscosity of the fluid
D is the diameter of the sphere
u_infinity is the velocity of the flow
Pr - Prandtl number of the fluid evaluated at the film temperature [-], defined as
where
cp is the specific heat capacity of the fluid
k is the conductivity
Outputs:
Nusselt - average Nusselt number assuming a constant wall temperature[-]
where
h is the average heat transfer coefficient
C_d - drag coefficient [-]
where
F_D is the drag force
A_fr is the frontal area
Notes
This procedure is called by External_Flow_Sphere to calculate the Nusselt number and drag coefficient. The procedure uses the Whitaker correlation (Whitaker, S., AICHE J., Vol. 18, 361, 1972) as reported in Mills, A.F. Basic Heat and Mass Transfer, Irwin, 1995 and presented in Nellis and Klein. The correlation is valid for Re<7.6E4. The coefficient of drag uses the correlation presented by White (1991). Data for the coefficient of drag are available for Reynolds numbers up to 2E5.
Example
call External_Flow_Sphere_ND(Re,Pr: Nusselt, C_d)
Re=10000 [-]
Pr=2 [-]
{Solution: Nusselt=101.1 [-] C_d=0.4618 [-]}