Convective mixing temperature fields

The horizontal structure of the field of the minimal water temperatures (the core of the CIL) of the Black Sea in the extreme months of the annual cycle (February and August) is presented in Figs. 6a and 6b. The February field of the minimal water temperatures (Fig. 6a) is similar to the surface temperature field (Fig. 5a). Meanwhile, a detailed analysis shows that they are not fully identical from the northwest to the southeast the excess of the surface temperature over the minimal value grows up to 1.0 °C. The depth of the temperature minimum location increases in the same direction down to 70-80 m. This points to the absence of CIL water renewal owing to the winter convective mixing over some part of the Black Sea area. 

Effect of flow direction on the temperature field around a heated cylinder. (From Krause, J.R., "An Interferometric Study of Mixed Convection from a Horizontal Cylinder to a Cross Flow of Air , M.E.Sc. Thesis, The University of Western Ontario. London. Ontario. Canada. 1985. By... 

The above equations can be solved using numerical methods, i.e., using the same basic procedures as used with forced convection. There is, however, one major difference between the procedures used in forced convection and in mixed convection. In forced convection, the velocity field is independent of the temperature field because fluid properties are here being assumed constant. Thus, in forced convection it is possible to first solve for the momentum and continuity equations and then, once this solution is obtained, to solve for the temperature distribution in tike flow. However, in combined convection, because of the presence of the temperature-dependent buoyancy force term in the momentum equation, all of the equations must be solved simultaneously. Studies of flows for which the boundary layer equations are not applicable are described in [24] to [43]. 

These are the well-known Orr-Sommerfeld equations for mixed convection flows, that show the disturbance normal velocity and the temperature fields to be coupled, constituting a sixth order differential system. Equations (6.4.10) and (6.4.11) are to be solved subject to the six boundary conditions ... 

In all flows involving heat transfer and, therefore, temperature changes, the buoyancy forces arising from the gravitational field will, of course, exist. The term forced convection is only applied to flows in which the effects of these buoyancy forces are negligible. In some flows in which a forced velocity exists, the effects of these buoyancy forces will, however, not be negligible and such flows are termed combined- or mixed free and forced convective flows. The various types of convective heat transfer are illustrated in Fig. 1.5. 

We first obtain the mean flow by solving the coupled DDEs (6.3.11) and (6.3.13) by standard four-stage Runge-Kutta method. These equations have been solved by taking maximum similarity co-ordinate, r max = 12 equally divided into 4000 sub-intervals. For different Re and K, mean flow has been obtained here. Fixing K, instead of Gr, is motivated by our discussion in the introduction where we have noted that for instability of mixed-convection boundary layers, K is more relevant than Gr. As we have investigated the mixed convection problem in air, we have fixed the value of Pr = 0.7 for all cases. Obtained mean-field results for the non-dimensional velocity and temperature are shown in Fig. 6.1. 

Diffusion, which occurrs in essentially all matter, is one of the most ubiquitous phenomena in nature. It is the process of transport of materials driven by an external force field and the gradients of pressure, temperature, and concentration. It is the net transport of material that occurs within a single phase in the absence of mixing either by mechanical means or by convection. The rates of different technical as well as many physical, chemical, and biological processes are directly influenced by diffusive mass transfer, and also the efficiency and quality of processes are governed by diffusion [1]. 

The basic concept of diffusion refers to the net transport of material within a single phase in the absence of mixing (by mechanical means or by convection). Both experiment and theory have shown that diffusion can result from pressure gradients (pressure diffusion), temperature gradients (thermal diffusion), external force fields (forced diffusion), and concentration gradients. Only the last type is considered in this book that is, the discussion is limited to diffusion caused by the concentration difference between two points in a stagnant solution. This process, called molecular diffusion, is described by Pick s laws. His first law relates the flux of a chemical to the concentration gradient ... 

The flow field in the experiment SUCOS-3D must be reconstructed from the measured temperatures because no velocity measurements were performed. Other than in SUCOS-2D here we find in the experiment the highest temperatures not in the horizontal side area, but below the tilted roof. Fig. 7. Therefore, a different behavior of the natural convection has to be deduced We have at least to expect stronger mixing between cold counter-current downward flow with hot rising fluid in the chimney. 

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