WOLFRAM SYSTEM MODELER
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Calculation of mean convective heat transfer coefficient kc of a straight pipe for a hydrodynamically developed turbulent fluid flow at uniform wall temperature or uniform heat flux with neglecting or considering of pressure loss influence.
There are basically three differences:
Neglect pressure loss influence (roughness == 1):
The mean convective heat transfer coefficient kc for smooth straight pipes is calculated through its corresponding Nusselt number Nu according to [Dittus and Boelter in Bejan 2003, p. 424, eq. 5.76]
Nu = 0.023 * Re^(4/5) * Pr^(1/3).
Consider pressure loss influence (roughness == 2):
The mean convective heat transfer coefficient kc for rough straight pipes is calculated through its corresponding Nusselt number Nu according to [Gnielinski in VDI 2002, p. Ga 5, eq. 26]
Nu = (zeta/8)*Re*Pr/(1 + 12.7*(zeta/8)^0.5*(Pr^(2/3)-1))*(1+(d_hyd/L)^(2/3)),
where the influence of the pressure loss on the heat transfer calculation is considered through
zeta = (1.8*log10(Re)-1.5)^-2.
The mean convective heat transfer coefficient kc in dependence of the chosen calculation (neglecting or considering of pressure loss influence) results into:
kc = Nu * lambda / d_hyd
|d_hyd||as hydraulic diameter of straight pipe [m],|
|kc||as mean convective heat transfer coefficient [W/(m2K)],|
|lambda||as heat conductivity of fluid [W/(mK)],|
|L||as length of straight pipe [m],|
|Nu = kc*d_hyd/lambda||as mean Nusselt number [-],|
|Pr = eta*cp/lambda||as Prandtl number [-],|
|Re = rho*v*d_hyd/eta||as Reynolds number [-],|
|v||as mean velocity [m/s],|
|zeta||as pressure loss coefficient [-].|
Note that there is no significant difference for the calculation of the mean Nusselt number Nu at a uniform wall temperature (UWT) or a uniform heat flux (UHF) as heat transfer boundary in the turbulent regime (Bejan 2003, p.303).
The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figures below.
Note that the higher the Prandtl number Pr there is a higher difference in Nusselt numbers Nu comparing the neglect and consideration of pressure loss.