Laminar and Turbulent Flow and Heat Transfer between Parallel Surfaces

Brief description of the caseThis case involves forced convection flow between two smooth, parallel, heated surfaces over a range of Reynolds number(Re) covering both laminar and turbulent flows. This study focused on the calculation of heat transfer and friction at solid sur-faces. The geometry and resulting flow pattern for a fully turbulent flow are shown in Figure 1. A range of values of inletvelocity were considered resulting in a Re range of 100 (laminar) to 105 (turbulent). Domain length in the flow direction wasmade long enough to allow the flow and the temperature field to develop fully. The computational results shown are for thefully developed region.

NomenclatureTw Wall temperature

Uin Inlet velocity Tin Inlet temperature � Density � Viscosity f Fanning friction factorNu Nusselt numberRe Reynolds number = [ ]Pr Prandtl number

Figure 1 (a): Geometry of the case (b): Velocity profile for fully turbulent flow

ResultsFLOTHERM, experimental and analytical results are compared fora) Fanning friction factor (f) b) Nusselt number (Nu) and c) veloc-ity profile in Figure 2.

NotesFanning Friction Factor: The Fanning friction factor is a non-dimensionalmeasure of the friction effect of the wall surface. For laminar flow, f is given by the analytical expression:

f=

For turbulent flow, empirical correlations are available for various rangesof Re:

f= for 5000<Re<3x104

and,f= for 1.2x104<Re<1.2x106

Nusselt Number: The Nusselt number, Nu, is calculated as:for laminar flow:Nu= 7.54For Turbulent flow:Nu = 0.023 Re0.8Pr0.3 for Re>104

Velocity Profile: For laminar flow the fully developed profile can be derived ana-lytically; it is given by:

= 1- ( )2 , y=0 at the symmetry axis

for turbulent flow:

= 1+((f/2).05/K2)( +log(1- (y/b).05)+(y/b).05)where y is the distance from the symmetry plane and K2 is Von-Karman’s universal

constant of 0.36.

ReferenceSadik Kakac, Ramesh K. Shah and Win Aung. Handbook of Single-PhaseConvective Heat Transfer. John Wiley and Sons, Inc, ISBN 0-471-81702-3

�Uin (4b)�

24Re

0.1268Re0.3

0.0868Re0.25

U 3Uin 2 ( )y

b

UUin

56 Figure 2: Comparison of FLOTHERM, Experimental and Analytical Results