Thermal convection, streaming

Fig.1 shows a column type for discontinuous or batchwise separation process. A trough of polypropylene or another suitable material is divided vertically to the length axis (separation direction) by means of diaphragms of polypropylene gauze to prevent the thermal convection in this direction. The diaphragms are welded on polypropylene frames and are fitted like slides into plates of polypropylene through which the cooling pipes pass. The counter current liquid streams with a constant rate from the cathode to the anode if cations are to be separated and vice versa. 

Piezoelectric fans are small, low-power, relatively low-noise, solid-state devices that provide viable thermal management solutions for a variety of portable electronic appliances, including laptop computers and cellular phones. In these fans piezoceramic patches are bonded onto thin, low-frequency flexible blades driven at resonance frequency, thereby creating an air stream directed at the electronics components. Thereby, up to 100% improvement over natural convective heat transfer can be achieved (Acikalin et al. 2004). 

Next one needs an expression for (xA — xA"). The difference in concentration between the two streams results from two effects thermal diffusion, which tends to increase the concentration difference, and convection, which tends to decrease it. Each of these effects is considered separately by obtaining an approximate integrated form of the steady state equation of continuity as applied to that particular process. If the only effect tending to produce a concentration difference were thermal diffusion, then according to Eq. (131) dxA/dx = — (kT/T)(d,T/dx) this expression may be written in difference form over the distance from x = — ( 4)a to x — + (M)° thus ... 

In predicting convective thermal transport to turbulent streams it has usually been sufficient to determine the corresponding thermal flux at the boundary for a specified area. Such methods have been refined by many workers and ably summarized by McAdams (Ml) and Jakob (Jl). 

Oosthuizen, P.H., Combined Forced and Free Convective Heat Transfer from a Horizontal Cylinder in an Axiai Stream , Proc. 3rd Int. Conf. Num. Methods in Thermal Problems, Vol. 3, Pineridge Press, Swansea, U.K., pp. 529-539. 1983. 

Natural convection occurs when a fluid is in contact with a solid surface of different temperature. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Ra = p AT gx3/ va and the Prandtl number Pr = v/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion p (K-1) the difference AT between the surface (Ts) and free stream (Te) temperatures (K or °C) the acceleration of gravity g(m/s2) a characteristic dimension x of the surface (m) the kinematic viscosity v(m2/s) and the thermal diffusivity a(m2/s). The volumetric coefficient of expansion for an ideal gas is p = 1/T, where T is absolute temperature. For a given geometry,... 

While the wave length, phase speed and group velocity is similar for the first modes in Tables 6.1 and 6.2, the spatial growth rate has increased significantly due to added instability via buoyancy effect. The second mode of these two tables are also similarly related, while the third mode of Table 6.1 has disappeared for the case of mixed convection. Disappearance of modes have been identified in Sengupta et al. (1997) as related to waves attaining phase speed equal to the free stream speed. The third mode of Table 6.2 can be related to the thermal mode (fourth) of Table 6.1. We note that the thermal mode propagate at lower speeds compared to hydrodynamic modes. 

For the present investigation the characteristic temperature difference for free convection, AT, is taken as Too—JTsI, and the gas-phase properties are evaluated at the mean temperature Tg = 1/2 (r — Tg). The thermal coeflBcient of volumetric expaimon of the gas, which appears in the Grashof number is taken as 1/Tg. Equations 30, 31, and 32 state that the gas film thickness which surrounds the droplet is infinite when the droplet is motionless relative to the gas stream and when gravity is absent. As the relative velocity increases, the film thickness becomes smaller. 

They subsequently (2) developed a one-dimensional mathematical model in the form of coupled differential and integro-differential equations, based on a gross mechanism for the chemical kinetics and on thermal feedback by wall-to-wall radiation, conduction in the tube wall, and convection between the gas stream and the wall. This model yielded results by numerical integration which were in good agreement with the experimental measurements for the 9.53-mm tube. For this tube diameter, the flows of unbumed gas for stable flames were in the turbulent regime. 

But before the virtues of the results and the approach are extolled, the method must be described in detail. Let us therefore return to a systematic development of the ideas necessary to solve transport (heat or mass transfer) problems (and ultimately also fluid flow problems) in the strong-convection limit. To do this, we begin again with the already-familiar problem of heat transfer from a solid sphere in a uniform streaming flow at sufficiently low Reynolds number that the velocity field in the domain of interest can be approximated adequately by Stokes solution of the creeping-flow problem. In the present case we consider the limit Pe I. The resulting analysis will introduce us to the main ideas of thermal (or mass transfer) boundary-layer theory. 

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