WOLFRAM SYSTEM MODELER
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Calculation of the mean convective heat transfer coefficient kc for a laminar fluid flow through an even gap at different fluid flow and heat transfer situations.
There are basically three differences:
The mean convective heat transfer coefficient kc for an even gap is calculated through the corresponding Nusselt number Nu_lam according to [VDI 2002, p. Gb 7, eq. 43] :
Nu_lam = [(Nu_1)^3 + (Nu_2)^3 + (Nu_3)^3]^(1/3)
with the corresponding mean convective heat transfer coefficient kc :
kc = Nu_lam * lambda / d_hyd
|cp||as specific heat capacity at constant pressure [J/(kg.K)],|
|d_hyd = 2*s||as hydraulic diameter of gap [m],|
|eta||as dynamic viscosity of fluid [Pa.s],|
|h||as height of cross sectional area in gap [m],|
|kc||as mean convective heat transfer coefficient [W/(m2.K)],|
|lambda||as heat conductivity of fluid [W/(m.K)],|
|L||as overflowed length of gap (normal to cross sectional area) [m] ,|
|Nu_lam||as mean Nusselt number [-],|
|Pr = eta*cp/lambda||as Prandtl number [-],|
|rho||as fluid density [kg/m3],|
|s||as distance between parallel plates of cross sectional area [m],|
|Re = rho*v*d_hyd/eta||as Reynolds number [-],|
|v||as mean velocity in gap [m/s].|
The summands for the mean Nusselt number Nu_lam at a chosen fluid flow and heat transfer situation are calculated as follows:
Note that the fluid properties shall be calculated with an arithmetic mean temperature out of the fluid flow temperatures at the entrance and the exit of the gap.
The mean Nusselt number Nu_lam representing the mean convective heat transfer coefficient kc in dependence of the chosen fluid flow and heat transfer situations (targets) is shown in the figure below.