Forced convection flow turbulent

In physical as well as mathematical modeling of transport phenomena, it is important to consider the existence or otherwise in the real process, any possible flow transition from laminar to turbulent flow, natural convection to forced convection, or subsonic to supersonic flow. This is because of the significant impact that such transitions may have on the process. 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

In problems of forced convection, it is usually the cooling mass flow that has to be found to determine the temperature difference between the cooling substance and the wall for a given heat flow. In turbulent pipe flow, the iol-low ing equation is valid ... 

H7. Hines, W. S., Forced convection and peak nucleate boiling heat transfer characteristics for hydrazine flowing turbulently in a round tube at pressures to 1000 psia, Rept. No. 2059, Rocketdyne, Canoga Park, California (1959). 

In forced convection, circulating currents are produced by an external agency such as an agitator in a reaction vessel or as a result of turbulent flow in a pipe. In general, the magnitude of the circulation in forced convection is greater, and higher rates of heat transfer are obtained than in natural convection. 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

The first example pertains to forced convection in pipe flow. It is found that the rate of heat transfer between the pipe wall and a fluid flowing (turbulent flow) through the pipe depends on the following factors the average fluid velocity (u) the pipe diameter (d) the... 

In the second example, let the case of forced convective mass transfer in pipe flow be considered. Let it be assumed that the turbulent flow of the fluid, B, through the pipe is accompanied by a gradual dissolution of the material, A, of the pipe wall. Experimental... 

The rotation rate should ensure forced convection on the one hand, but laminar flow on the other, so that it remains well below the conditions of the critical Reynolds number, above which turbulent flow sets in ... 

ESDU 92003 (1993) Forced convection heat transfer in straight tubes. Part 1 turbulent flow. 

Fouad and Ibl (F6) have suggested that the transfer rate in free-convective turbulent flow should follow a Ra1/3 dependence. Experimentally they found a slightly lower dependence, probably due to the partly laminar regime on such plates. Because the exponent is not determined by theoretical considerations, there is considerable variation in the coefficients of turbulent, free convection correlations. Among other factors, inaccuracies in the calculation of the density-driving force may be responsible for discrepancies. This is particularly likely for the case of the ferricyanide reduction reaction. 

This expression applies to the transport of any conserved quantity Q, e.g., mass, energy, momentum, or charge. The rate of transport of Q per unit area normal to the direction of transport is called the flux of Q. This transport equation can be applied on a microscopic or molecular scale to a stationary medium or a fluid in laminar flow, in which the mechanism for the transport of Q is the intermolecular forces of attraction between molecules or groups of molecules. It also applies to fluids in turbulent flow, on a turbulent convective scale, in which the mechanism for transport is the result of the motion of turbulent eddies in the fluid that move in three directions and carry Q with them. 

In process operations, simultaneous transfer of momentum, heat, and mass occur within the walls of the equipment vessels and exchangers. Transfer processes usually take place with turbulent flow, under forced convection, with or without radiation heat transfer. One of the purposes of engineering science is to provide measurements, interpretations and theories which are useful in the design of equipment and processes, in terms of the residence time required in a given process apparatus. This is why we are concerned here with the coefficients of the governing rate laws that permit such design calculations. 

Clearly, the solution of this equation at forced-convection electrodes will depend on whether the fluid flow is laminar, in the transition regime, or turbulent. Since virtually all kinetic investigations have been performed in the laminar flow region, no further mention will be made of turbulent flow. The reader interested in mass transport under turbulent flow is recommended to consult refs. 14 and 15. 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be... 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

There are various purposes of using a stirred vessel, and the required mixing effect depends on the purpose. For any mixing purpose, rapid and homogeneous dispersion is required. In a stirred vessel, forced convection by the rotation of an impeller occurs, that is, each element of the fluid has an individual velocity finally, turbulent flow based on the shear stress accelerates the mixing. Therefore, the shape of the impeller has a very important effect on the mixing state. However, there are various types of impeller shapes, and traditional impellers are classified into three types ... 

A deeper insight into the physical nature of the process. By representing experimental data in a dimensionless form, physical states (e.g. turbulent or laminar flow range, suspension state, heat transfer by natural or by forced convection, and so on) can be delimited from each other and the limits quantified. In this manner, the domain of individual physical quantities also becomes apparent. 

As explained in Chapter 1, natural or free convective heat transfer is heat transfer between a surface and a fluid moving over it with the fluid motion caused entirely by the buoyancy forces that arise due to the density changes that result from the temperature variations in the flow, [1] to [5]. Natural convective flows, like all viscous flows, can be either laminar or turbulent as indicated in Fig. 8.1. However, because of the low velocities that usually exist in natural convective flows, laminar natural convective flows occur more frequently in practice than laminar forced convective flows. In this chapter attention will therefore be initially focused on laminar natural convective flows. 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

In using these equations, the forms of the velocity and temperature profiles in the boundary layer are assumed. Now, in turbulent forced convective boundary layer flows it has been found that the velocity profile is well described by ... 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

Because, for flow over a heated surface. r>ulc>x is positive and ST/ y is negative. S will normally be a negative. Hence, in assisting flow, the buoyancy forces will tend to decrease e and e, i.e., to damp the turbulence, and thus to decrease the heat transfer rate below the purely forced convective flow value. However, the buoyancy force in the momentum equation tends to increase thle mean velocity and, therefore, to increase the heat transfer rate. In turbulent assisting flow over a flat plate, this can lead to a Nusselt number variation with Reynolds number that resembles that shown in Fig. 9.22. 

Numerically predicted variation of Nusselt number variation with Reynolds number in turbulent assisting mixed convective flow over a vertical plate. (Based on results obtained by Patel K., Armaly B.F., and Chen T.S., Transition from Turbulent Natural to Turbulent Forced Convection Adjacent to an Isothermal Vertical Plate , ASME HTD, Vol. 324, pp. 51-56, 1996. With permission.)... 

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