Bejan number

Thermal diffusivity Temperature sensitivity Temperature difference Thickness of tube Aspect ratio, relation of Cp/Cy Fluid dielectric constant Wall zeta potential Dimensionless temperature Friction factor, Debye length Mean free path Dynamic viscosity Kinematic viscosity Bejan number Density... 

Figure 4.6. The Bejan number Be for the circular Couette flow for 7 = 300 K, r0 = 0.02 m, and r = 0.019 m. Reprinted with permission...

The Bejan number Be peaks appear in the middle part of a Couette device due to the development of maximum temperature in that region. An increase in Be indicates a competition between the irreversibilities caused by heat transfer and friction. At high Reynolds numbers, the distribution of Be is relatively more uniform than at lower Re. For a circular Couette device, the Reynolds number (Re = wr /v) at the transition from laminar to turbulent flow is strongly dependent on the ratio of the gap to the radius of the outer cylinder, — n. The critical Re reaches a value about 50,000 at 1 — n = 0.05. We may control the distribution of the irreversibility by manipulating various operational conditions such as the gap of the Couette device, the Brinkman number, and the boundary conditions (Demirel, 2000). 

Bejan number Brinkman number concentration, cost... 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

Bejan and Tondeur [9] make a number of other observations in their paper. One is that the relation between j and x is not necessarily linear. Another observation is that a similar analysis can show that the force x should be equipartitioned in time, which is another way of saying that the steady state is optimal. Prigogine gave an earlier proof of this principle [11]. The steady state is common in nature and often the favored state in industrial operation. It can be considered to be the "stable state" of nonequilibrium thermodynamics, comparable to the equilibrium state of reversible thermodynamics (see Figure 4.2). Of course, the latter is characterized by Sgen = 0, whereas the former is characterized by a minimum value , larger than zero. 

Poulikakos. D. and Bejan. A.. Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer , J. Heat Transfer. Vol. 105. pp. 476-484. 1983. 

Vertical Cavities (0 = 90°) with UH S 2 and W/L a 5. Except in an end region immediately adjacent to the two vertical plates, the flow in a cavity with L H is everywhere parallel to the horizontal walls, with hot fluid in the upper half of the cavity streaming toward the cold plate and cold fluid in the lower half streaming toward the hot plate (only at very high Rayleigh numbers, where turbulent eddies of a scale smaller than H are possible, will this simple flow pattern break down). The plates at temperatures Th and Tc deflect the streams into boundary layers on each vertical surface. The predictions of Bejan and Tien [16] for adiabatic walls are correlated to within 8 percent by their equation... 

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