Convection theory

New questions have arisen in micro-scale flow and heat transfer. The review by Gad-el-Hak (1999) focused on the physical aspect of the breakdown of the Navier-Stokes equations. Mehendale et al. (1999) concluded that since the heat transfer coefficients were based on the inlet and/or outlet fluid temperatures, rather than on the bulk temperatures in almost all studies, comparison of conventional correlations is problematic. Palm (2001) also suggested several possible explanations for the deviations of micro-scale single-phase heat transfer from convectional theory, including surface roughness and entrance effects. 

Herwig F. (2001) The evolutionary timescale of Sakurai s object a test of convection theory Astrophys. J. 554, L71-L74. 

Kristiansson and Malmqvist (1981) postulate an upward flow of geogas carrying Rn with it in order to explain their field data. However attractive and sensible these convective theories are, data in support of them usually lack one vital analytical component, namely the Ra content of the soils in which the Rn content was measured. Alekseev et al. (1959) report that "thanks to Ra aureoles, it has become possible in individual cases to reveal mineralisation located at considerable depth by means of emanation surveys". 

Convection theory (King, 1966 Kishinevskii, 1951 Moser, 1973c), with E = formal convection coefficient [cm /s]... 

Pebay C, SeUa C, Thouin L, Amatore C (2013) Mass transport at infinite regular arrays of electrodes submitted to natural convection theory and experiments. Anal Chem 85 12062-12069... 

One design for a low temperature convection furnace shown in Figure 4 utilizes an external circulating fan, heating chamber, and duct system. The fan draws air (or a protective atmosphere) from the furnace and passes through the external heating chamber and back into the furnace past the work. This system minimizes the chance that the work receives any direct heat radiation. In theory it is less efficient because the external blower, heating chamber, and ductwork add external surfaces that are subject to heat losses. 

According to the chemical theory of olfaction, the mechanism by which olfaction occurs is the emittance of particles by the odorous substances. These particles are conveyed to the olfactory epithelium by convection, diffusion, or both, and dkecdy or indkectly induce chemical changes in the olfactory receptors. 

A simplified model usiag a stagnant boundary layer assumption and the one-dimension diffusion—convection equation has been used to calculate wall concentration ia an RO module. The iategrated form of this equation, the widely appHed film theory (41), is given ia equation 8. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Consider a vessel containing an agitated liquid. Heat transfer occurs mainly through forced convection in the liquid, conduction through the vessel wall, and forced convection in the jacket media. The heat flow may be based on the basic film theory equation and can be expressed by... 

Mundt, E. 1 992. Convection flows in rooms with temperature gradients Theory and measurements. In Roomvent 92 Proceedings of the Third International Conference on Air Distrihii-tion in Rooms, vol. 3. Aalborg, Denmark. 

The cooling tower cools hot water tvith cool air by countercurrent (or cross-current) fiow of the tw o fluids past each other in a tower filled with packing. This involves both mass and heat transfer. The water surface that exists on the tower packing is covered with an air film assumed to be saturated at the water temperature. The heat is transferred between this film and the main body of air by diffusion and convection. Detailed presentations of the development of cooling tower theory are given in References 39 and 46. 

The linear instability theory of the behavior of a system near the bifurcation point can be successfully applied to many self-organization problems, such as thermal convection in hydrodynamics4 and crystal growth in solution.5 In these theories, various initial fluctuations play important roles. Occasionally the fluctuations arise from the thermal motion of atoms or molecules. If a system reaches an unstable mode over... 

Lin Q, Jiang F, Wang X-Q, Han Z, Tai Y-C, Lew J, Ho C-M (2000) MEMS Thermal Shear-Stress Sensors Experiments, Theory and Modehng, Technical Digest, Solid State Sensors and Actuators Workshop, Hilton Head, SC, 4—8 June 2000, pp 304-307 Lin TY, Yang CY (2007) An experimental investigation of forced convection heat transfer performance in micro-tubes by the method of hquid crystal thermography. Int. J. Heat Mass Transfer 50 4736-4742... 

The data presented in the previous chapters, as well as the data from investigations of single-phase forced convection heat transfer in micro-channels (e.g., Bailey et al. 1995 Guo and Li 2002, 2003 Celata et al. 2004) show that there exist a number of principal problems related to micro-channel flows. Among them there are (1) the dependence of pressure drop on Reynolds number, (2) value of the Poiseuille number and its consistency with prediction of conventional theory, and (3) the value of the critical Reynolds number and its dependence on roughness, fluid properties, etc. 

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

Combining hindered diffusion theory with the diffusion/convection problem in the model pore, Trinh et al. [399] showed how the effective transport coefficients depend upon the ratio of the solute to pore size. Figure 28 shows that as the ratio of solute to pore size approaches unity, the effective mobility function becomes very steep, thus indicating that the resolution in the separation will be enhanced for molecules with size close to the size of the pore. Similar results were found for the effective dispersion, and the implications for the separation of various sizes of molecules were discussed by Trinh et al. [399]. 

A combination of continuum transport theory and the Poisson distribution of solution charges has been popular in interpreting transport of ions or conductivity of electrolytes. Assuming zero gradient in pressure and concentration of other species, the flux of an ion depends on the concentration gradient, the electrical potential gradient, and a convection... 

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