External_Flow_Plate_L_ND
Procedure External_Flow_Plate_L_ND(Re, Pr, Re_l: Nusselt,C_f) returns the average Nusselt number and friction coefficient for flow parallel to a flat plate using the correlation provided by Lienhard (2020) which consider the transition region.
Inputs:
Re - Reynold's number [-], where
where
r is the density of the fluid
m is the viscosity of the fluid
L is the length of the plate
u_infinity is the velocity of the flow
Pr - Prandtl number [-], where
where
c_p is the specific heat capacity of the fluid
k is the conductivity
Re_l - local Reynolds number [-] where transition region starts (3x103 < Re_l < 5x105)
Note that if the value of Re_l is < 0 then it is interpreted as the turbulence intensity (u`/u, as a percentage)
In this case, the empirical equation from Mayle (1991) is used.
Outputs:
Nusselt - average Nusselt number assuming a constant wall temperature[-]. The Nusselt number is defined:
where
h is the average heat transfer coefficient
C_f - average friction coefficient [-]. The friction coefficient is defined:
where
t is the average shear stress
Notes
This procedure integrates the local values provided by External_Flow_L_ND_local which uses the methodology presented by Lienhard (2020) to determine the local Nusselt number and friction factor.
Note that the procedure External_Flow_Plate_ND provides the same functionality but uses the less accurate but more computationally efficient correlations described by Nellis and Klein (2018).
Example:
Re=1e6
Pr=0.7
Re_l = 5e4
Call external_flow_plate_l_nd(Re, Pr, Re_l: Nusselt_bar,C_f_bar)
{Solution:
C_f_bar=0.004492
Nusselt_bar=1782
}