Natural convection introduction

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

The same principle is used for the preparative separation of mixtures of biological materials, the extraction of different individual components from these mixtures, and their purification. In this case one uses an electrophoretic method with continued introduction of individual portions of the mixture and withdrawal of portions of pure fractions. There have been reports that such processes were accomplished in spacecraft where, since gravitational forces are absent, the liquid solutions can be used without the danger of natural convection. 

By introduction of a typical value for D0, 10 r> cm2 s 1, it is seen that the value of 8 after, for example, 5 seconds amounts to 0.1 mm. At times larger than 10-20 seconds, natural convection begins to interfere and the assumption of linear diffusion as the only means of mass transport is no longer strictly valid. At times larger than approximately 1 minute, the deviations from pure diffusion are so serious and unpredictable that the current observed experimentally cannot be related to a practical theoretical model. 

The set of three partial differential equations (the continuity, momentum, and the energy equations) iliai govern natural convection flow over vertical isothermal plates can be reduced to a set of two ordinarj nonlinear differential equations by the introduction of a similarity variable. But the resulting equations must still be solved numerically [Ostrach (1953)]. Interested readers arc referred to advanced books on the topic for detailed discussions [e.g., Kays and Crawford (1993)],... 

In the percolation of a liquid through a bed of solids, mass transfer of the solute from the surfaces of the solid to the liquid in the interstices of the bed takes place by molecular diffusion and by natural convection arising from the density changes created by dissolution. Although these processes are slow, they are much faster than mass transfer in the matrix under the same concentration differences. Concentration gradients in the liquid outside the particles are, therefore, very low. At any point in the bed, the introduction of dilute solution from above and the loss of concentrated solution to below decrease the interstitial concentration by dilution or displacement. This effect can be considered simply to reduce the solute concentration at the jimction of solid and solution, thus imposing a favorable concentration gradient within the matrix. 

As discussed in the introduction, many current-distrihution problems are not described by a simple, convection-diffusion equation or by Laplace s equations. Alavyoon era/. provided an example in which the coupled concentration and potential fields were solved throughout the entire computational domain, along with natural convection flow fields. The equations were solved by evaluating the nonlinear terms at the previous time step. Gu etal. provided an additional study that coupled charge and mass transfer to natural convection. This work is related to... 

Introduction. For the problem depicted in Fig. 4.44, the heat transfer by pure forced convection would increase monotonically with Reynolds number along the curve shown. The heat transfer by pure natural convection from the same surface for various Ra is denoted by the horizontal lines in the figure. If Re is slowly increased from zero in the real problem, the measured values of Nu would at first follow the natural convection curve, since the superimposed forced convection velocities are too feeble to affect the heat transfer. If the forced convection assists the natural convection, the Nu curve in Fig. 4.44 will break upward along path A at larger Re and approach the pure forced convection curve from above. If the flows are opposed, Nu passes through a minimum along path B in Fig. 4.44 and approaches the forced convection curve from below. Mixed convection occurs when the heat transfer is significantly different from that for either pure natural convection or pure forced convection. 

Ernst Schmidt (1892—1975), the German scientist, is known for his pioneering works in the fields of thermodynamics and heat and mass transfer. Some of his noteworthy contributions to heat and mass transfer were developing the analogy between heat and mass transfer, first measurement of velocity and temperature fields in natural convection boundary layer and heat transfer coefficient in droplet condensation, introduction of aluminum foil radiation shielding, and solution of... 

Fig. 8. Perturbation of the axial velocity profile set up by natural convection due to introduction of feed and withdrawal of product and waste. TR = total reflux, E = enricher and S = stripper, with throughput.

Conduction is treated from both the analytical and the numerical viewpoint, so that the reader is afforded the insight which is gained from analytical solutions as well as the important tools of numerical analysis which must often be used in practice. A similar procedure is followed in the presentation of convection heat transfer. An integral analysis of both free- and forced-convection boundary layers is used to present a physical picture of the convection process. From this physical description inferences may be drawn which naturally lead to the presentation of empirical and practical relations for calculating convection heat-transfer coefficients. Because it provides an easier instruction vehicle than other methods, the radiation-network method is used extensively in the introduction of analysis of radiation systems, while a more generalized formulation is given later. 

Tn modeling rivers, streams, and other natural flows for pollution control, A it is often necessary to estimate downstream concentration profiles, in distance and time, of substances which simultaneously undergo reaction and convection after their introduction upstream. These substances might be dissolved or suspended pollutants, microorganisms, oxygen, or other relevant constituents of the aqueous environment. 

Electrically driven convection in nematic liquid crystals [6,7,16] represents an alternative system with particular features listed in the Introduction. At onset, EC represents typically a regular array of convection rolls associated with a spatially periodic modulation of the director and the space charge distribution. Depending on the experimental conditions, the nature of the roll patterns changes, which is particularly reflected in the wide range of possible wavelengths A found. In many cases A scales with the thickness d of the nematic layer, and therefore, it is convenient to introduce a dimensionless wavenumber as q = that will be used throughout the paper. Most of the patterns can be understood in terms of the Carr-Helfrich (CH) mechanism [17, 18] to be discussed below, from which the standard model (SM) has been derived... 

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