Forced convection methods

Typical coil coefficients are listed in Table 11-2. More exact values can be calculated by using the methods for natural convection or forced convection given elsewhere in this section. 

Loop Tests Loop test installations vary widely in size and complexity, but they may be divided into two major categories (c) thermal-convection loops and (b) forced-convection loops. In both types, the liquid medium flows through a continuous loop or harp mounted vertically, one leg being heated whilst the other is cooled to maintain a constant temperature across the system. In the former type, flow is induced by thermal convection, and the flow rate is dependent on the relative heights of the heated and cooled sections, on the temperature gradient and on the physical properties of the liquid. The principle of the thermal convective loop is illustrated in Fig. 19.26. This method was used by De Van and Sessions to study mass transfer of niobium-based alloys in flowing lithium, and by De Van and Jansen to determine the transport rates of nitrogen and carbon between vanadium alloys and stainless steels in liquid sodium. 

Colburn, A.P. Trans. Am. Inst. Chem. Eng. 29 (1933) 174. A method of correlating forced convection heat transfer data and a comparison with fluid friction. 

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... 

Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC, Boca Raton Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New York Shapiro AK (1953) The dynamics and thermodynamics of compressible fluid flow. Wiley, New York... 

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. 

Chen s method was developed from experimental data on forced convective boiling in vertical tubes. It can be applied, with caution, to forced convective boiling in horizontal tubes, and annular conduits (concentric pipes). Butterworth (1977) suggests that, in the absence of more reliable methods, it may be used to estimate the heat-transfer coefficient for forced convective boiling in cross-flow over tube bundles using a suitable cross-flow correlation to predict the forced-convection coefficient. Shah s method was based on data for flow in horizontal and vertical tubes and annuli. 

The forced-convective boiling coefficient will be estimated using Chen s method. 

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

Shitsman, M. E., 1963, On the Methods for Calculating the Critical Heat Flux with Water in Forced Convection, Teploenergetika, August, 70(8). (5)... 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

Despite this, the expected heat transfer coefficients obtainable in a fluidized bed are greater than those for forced convection in a gas (Ditchev and Richardson, 1999) although not as high as in the dynamic dispersion medium (DDM) method described by these authors. Comparative data are presented in Table 3.3. 

Chapter 1 serves as an introduction to both volumes and is a survey of the fundamental principles of electrode kinetics. Chapter 2 deals with mass transport — how material gets to and from an electrode. Chapter 3 provides a review of linear sweep and cyclic voltammetry which constitutes an extensively used experimental technique in the field. Chapter 4 discusses a.c. and pulse methods which are a rich source of electrochemical information. Finally, Chapter 5 discusses the use of electrodes in which there is forced convection, the so-called hydrodynamic electrodes . 

The use of a wetted spherical model affords the opportunity of studying combustion under steady-state conditions. Forced convection of the ambient gas may be employed without distortion of the object. Sufficiently large models may be employed when it is desired to probe the gas zones surrounding the burning sphere. It is apparent that the method is restricted to conditions where polymerization products and carbonaceous residues are not formed. In the application of such models, the conditions of internal circulation, radiant heat transmission, and thermal conductivity of the interior are somewhat altered from those encountered in a liquid droplet. Thus the problem of breakup of the droplet as a result of internal temperature rise cannot be investigated by this method. 

The second part of the book discusses ways in which information concerning electrode processes can be obtained experimentally, and the analysis of these results. Chapter 7 presents some of the important requirements in setting up electrochemical experiments. In Chapters 8—11, the theory and practice of different types of technique are presented hydrodynamic electrodes, using forced convection to increase mass transport and increase reproducibility linear sweep, step and pulse, and impedance methods respectively. Finally in Chapter 12, we give an idea of the vast range of surface analysis techniques that can be employed to aid in investigating electrode processes, some of which can be used in situ, together with photochemical effects on electrode reactions— photoelectrochemistry. 

The boundary layer problem is difficult to solve exactly. There are several approximate methods to solve the problem. This chapter looks at external forced convection, that is, flow outside and around a solid body like a plate. The next chapter discusses flows inside a solid structure such as a pipe, or between two plates. 

Consider laminar forced convective flow over a flat plate at whose surface the heat transfer rate per unit area, qw is constant. Assuming a Prandtl number of 1, use the integral equation method to derive an expression for the variation of surface temperature. Assume two-dimensional flow. 

Oosthuizen, P.H., "Laminar Forced Convective Heat Transfer from Rectangular Blocks Mounted on Opposite Walls of a Channel , Numerical Methods in Thermal Problems, Vol. VI, Part 1, Proc., 6th Int. Conf., Swansea, U.K., July 3-7, pp. 451-461,1989. 

A numerical solution to the laminar boundary layer equations for natural convection can be obtained using basically the same method as applied to forced convection in Chapter 3. Because the details are similar to those given in Chapter 3, they will not be repeated here. 

Before turning to a discussion of other methods of solving the laminar boundary layer equations for combined convection, a series-type solution aimed at determining the effects of small forced velocities on a free convective flow will be considered. In the analysis given above to determine the effect of weak buoyancy forces on a forced flow, the similarity variables for forced convection were applied to the equations for combined convection. Here, the similarity variables that were previously used in obtaining a solution for free convection will be applied to these equations for combined convection. Therefore, the following similarity variable is introduced ... 

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]. 

While Huang and Ozisik solved the spacewise variation of wall heat flux for laminar forced convection problem, Silva Neto and Ozisik [57] used the conjugate gradient method and the adjoint equation simultaneously to solve for the timewise-varying strength of a two plane heat source. 

The discussion and analyses of Chap. 5 have shown how forced-convection heat transfer may be calculated for several cases of practical interest the problems considered, however, were those which could be solved in an analytical fashion. In this way, the principles of the convection process and their relation to fluid dynamics were demonstrated, with primary emphasis being devoted to a clear understanding of physical mechanism. Regrettably, it is not always possible to obtain analytical solutions to convection problems, and the individual is forced to resort to experimental methods to obtain design information, as well as to secure the more elusive data which increase the physical understanding of the heat-transfer processes. 

---