Plane duct, laminar flow

FULLY DEVELOPED LAMINAR FLOW IN A PLANE DUCT... 

This equation describes the temperature distribution in fully developed laminar plane duct flow when the wall heat flux is a constant. It can be written in terms of the specified wall heat flux. qw, by noting that when Eq. (4.77) is used to give the value of dT dy y = w in Eq. (4.71), the following is obtained ... 

Because the area of the duct per unit width is 2w and because, by definition, the mass flow rate is equal to the (density x area X mean velocity), this shows that the mean velocity in fully developed laminar plane duct flow is 6/4 (= 1.5) times the center line velocity. 

Next consider fully developed laminar flow through a plane duct whose wall temperature is kept constant As with pipe flow, for this boundary condition, Eq. (4.69) gives ... 

Consider constant-property, fully developed laminar flow between two large parallel plates, i.e., in a wide plane duct. One plate is adiabatic and the other is isothermal and the velocity is high enough for viscous dissipation effects to be significant. Determine the temperature distribution in the flow. 

The laminar pulsatile flow in a plane duct can be treated as the simplest unsteady problem in basic fluid mechanics with applications, for instance, to engineering vibrators [199, 507], In biological and medical fluid mechanics, one meets the pulsating blood flow in arteries and the air flow in lungs. The generalization of such flows was suggested in literature [598, 601], and is of interest for this chapter. 

Like in Section 3.1.1, let us put an infinite droplet EPR into the plane duct and consider the pressure-driven laminar flow, Fig. 3.1. One obtains a generalization of problem... 

Two types of corrugations (triangular and rectangular) in parallel plate ducts are displayed in the insets of Figs. 5.60 and 5.61, respectively. Sparrow and Charmchi [290] have obtained the solutions for fully developed laminar flow in these ducts. The flow in the duct is considered to be perpendicular to the plane of the paper. Both ducts are assumed to be infinite in the span-... 

A number of analytical results are available for fully developed Nusselt values for the laminar flow of power law fluids in rectangular channels having aspect ratios ranging from 0 (i.e., plane parallel plates) to 1.0 (i.e., a square duct). Newtonian results (n = 1) are available for the T, HI, and H2 boundary conditions for the complete range of aspect ratios. Another limiting case for which many results are available is the slug or plug flow condition, which corresponds to n = 0. At other values of n, results are available for plane parallel plates and for the square duct. 

Where H is the charmel height (the smaller dimension in a rectangular channel), tw,av the average wall shear stress, V the kinematic viscosity, and p the density of the fluid. In internal flows, the laminar to turbulent transition in abrupt entrance rectangular ducts was found to occur at a transition Reynolds number Ret = 2200 for an aspect ratio ac = I (square ducts), to Ret = 2500 for flow between parallel planes with = 0 [4]. For intermediate channel aspect ratios, a linear interpolation is recommended. For circular tubes. Ret = 2300 is suggested. These transition Reynolds number values are obtained from experimental observations in smooth channels in macroscale applications of 3 mm or larger hydraulic diameters. Their applicability to microchannel flows is still an open question. 

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