Heating from below

Convection. Heat transfer by convection arises from the mixing of elements of fluid. If this mixing occurs as a result of density differences as, for example, when a pool of liquid is heated from below, the process is known as natural convection. If the mixing results from eddy movement in the fluid, for example when a fluid flows through a pipe heated on the outside, it is called forced convection. It is important to note that convection requires mixing of fluid elements, and is not governed by temperature difference alone as is the case in conduction and radiation. 

The formation of Benard convection cells takes place as follows if water is heated from below in a vessel, macroscopic convection currents occur under certain conditions seen from above, these have the structure of uniform, honeycombshaped cells. 

The final product is a fine powder that is shown to be Co304 by FTIR. The paler color observed at the top of the particle in Figure 1.6g arises because the sample is heated from below. 

Tray or shelf dryers are commonly used for granular materials and for individual articles. The material is placed on a series of trays which may be heated from below by steam coils and drying is carried out by the circulation of air over the material. In some cases, the air is heated and then passed once through the oven, although, in the majority of dryers, some recirculation of air takes place, and the air is reheated before it is passed over each shelf. As air is passed over the wet material, both its temperature and its humidity change. This process of air humidification is discussed in Volume 1, Chapter 13. 

G.H. Evans and S. Paolucci. The Thermoconvective Instability of Plane Poiseuille Flow Heated from Below A Proposed Benchmark Solution for Open Boundary Flows. Int. J. Num. Meth. Fluids, 11 1001-1013,1990. 

BENARD CONVECTION CELLS. When a layer of liquid is heated from below, the onset of convection is marked by the appearance of a regular array of hexagonal cells, the liquid rising in the center and falling near the wall of each cell. The criterion for the appearance of the cells is that the Rayleigh number should exceed 1700 (for rigid boundaries). 

Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below (with A.G. Salinger, S. Brandon, and J.J. Derby). Proc. Roy. Soc. A442,313-341 (1992). 

Horizontal Reactors. Horizontal reactor flow may involve both transverse and longitudinal rolls, as well as time-periodic flows. Insights into these phenomena may be gained from previous analysis of idealized, analogous systems, as well as from recent experiments and computations. Analytical studies of flow between two plates of infinite size differentially heated from below (180) and horizontal channel flow (181) indicate that the development of transverse and longitudinal rolls depends on the relative and absolute magnitudes of the dimensionless Rayleigh and Reynolds numbers, Ra and Re, as well as the aspect ratio. 

Previous computations (189) show that the critical value of Rat for non-Boussinesq conditions is approximately the same as that for a Boussinesq fluid in a box heated from below, at least when H2 is the carrier gas. Thus, results from the stability analysis of the classical Rayleigh-Benard problem of a two-dimensional fluid layer heated from below (see reference 190 for a review) may be used to indicate the type of behavior to be expected in a horizontal reactor with insulated side walls. As anticipated from this analysis, an increase in the reactor height from 2 to 4 cm raises the value of Rat to 4768, which is beyond the stability limit, Rat critical = 2056, for a box of aspect ratio 2 (188). The trajectories show the development of buoyancy-driven axial rolls that are symmetric about the midplane and rotating inward. For larger values of Rat (>6000), transitions to three-dimensional or time-de-... 

Most of the early experiments with salvinorin A were performed by inhaling the vaporized crystal using the following technique. The salvinorin A was placed on the center of a piece of thick aluminum foil, which was heated from below with a butane micro-torch or "jet flame" lighten As the salvinorin A turned to a white vapor, the vapors were inhaled through a 15mm diameter glass tube. This technique requires careful performance. If one inhales before the crystal has been melted, the solid material wilt be taken into the mouth and will not produce the desired effects. However, if one waits more than a... 

Heating from below the liquidus can be considered as the opposite to cooling from above the liquidus. Heating path of composition p is illustrated below. Others may be determined in the same manner. 

Wafers are transported, in Inconel trays, on a moving belt through a reactant gas flow while being heated from below by quartz radiant heaters. Reactant gases are introduced through a unique disperser head design. Details of the gas introduction are shown in Figure 2. 

Before starting to discuss (116), we make an observation. The fast time evolution (116) is also observed in driven systems that cannot be described on the level Ath- For example, let us consider the Rayleigh-Benard system (i.e., a horizontal layer of a fluid heated from below). It is well established experimentally that this externally driven system does not reach thermodynamic equilibrium states but its behavior is well described on the level of fluid mechanics (by Boussinesq equations). This means that if we describe it on a more microscopic level, say the level of kinetic theory, then we shall observe the approach to the level of fluid mechanics. Consequently, the comments that we shall make below about (116) apply also to driven systems and to other types of systems that are prevented from reaching thermodynamical equilibrium states (as, e.g., glasses where internal constraints prevent the approach to Ath)-... 

Pellew, A. and Southwell, R.V., On Maintained Convection Motion in a Fluid Heated from Below , Proc. R. Soc. London, Vol. A176, pp. 312-343, 1940. 

Schmidt, E., Free Convection in Horizontal Fluid Spaces Heated from Below , Proc. Int. Heat Trans. Conf., Boulder, Colo., ASME, 1961. 

Narusawa. U., Numerical Analysis of Mixed Convection at the Entrance Region of a Rectangular Duct Heated from Below", Int. J. Heat and Mass Transfer, Vol. 36, pp. 2375-2380, 1993. 

STABILITY OF HORIZONTAL POROUS LAYERS HEATED FROM BELOW... 

Consider an essentially infinite horizontal layer of saturated porous medium that is heated from below and cooled from the top. The situation is shown in Fig. 10.33. 

Naylor, D. and Oosthuizen, P.H.. Free Convection in an Enclosure Partly Filled with a Porous Medium and Partially Heated from Below ", Proc. 10th Int. Heat Trans. Conf. Brighton. UK, Vol. 5, pp. 351-356, 1994. 

Elder, J.W., Steady Free Convection in a Porous Medium Heated from Below , J. Fluid Mech., Vol. 27, pp. 29-48. 1967. 

Yen, Y.C., Effects of Density Inversion on Free Convective Heat Transfer in Porous Layer Heated from Below , Int. J. Heat Mass Transfer. Vol. 17. pp. 1349-1356,... 

Lai. F.C and Kulacki, F.A., Experimental Study of Free and Mixed Convection in Horizontal Porous Layers Locally Heated from Below , Int. J. Heat and Mass Trans.. Vol. 34, pp. 525-541, 1991. 

Flfl. 7- 12 Benard-cell pattern in enclosed fluid layer heated from below, from Ref. 33... 

The diagram shows a solid being heated from below its freezing point. Which line segment shows the gas and liquid phases existing at the same time (See Figure 2.)... 

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