Forced convection heat transfer variations

In this lecture, the effects of the abovementioned dimensionless parameters, namely, Knudsen, Peclet, and Brinkman numbers representing rarefaction, axial conduction, and viscous dissipation, respectively, will be analyzed on forced convection heat transfer in microchannel gaseous slip flow under constant wall temperature and constant wall heat flux boundary conditions. Nusselt number will be used as the dimensionless convection heat transfer coefficient. A majority of the results will be presented as the variation of Nusselt number along the channel for various Kn, Pe, and Br values. The lecture is divided into three major sections for convective heat transfer in microscale slip flow. First, the principal results for microtubes will be presented. Then, the effect of roughness on the microchannel wall on heat transfer will be explained. Finally, the variation of the thermophysical properties of the fluid will be considered. 

R. Oskay and S. Kakac, Effect of viscosity variations on forced convection heat transfer in pipe flow, METU Journal of Pure and Applied Sciences 6, 211-230 (1973). 

Unfortunately, satisfactory analytical methods for practical prediction of forced convection heat transfer at supercritical pressures have not yet been developed due to the difficulty in dealing with steep property variations, especially in turbulent flows and at high heat fluxes. Therefore, generalized correlations based on experimental data are used for HTC calculations at supercritical pressures. 

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. 

Mass transfer from a flowing fluid to the surface of another substance, or between two substances that are barely miscible, depends on the properties of the materials involved and the type of flow. As in the case of convective heat transfer the flow can be forced from outside through, for example, a compressor or a pump. This is known as mass transfer in forced convection. If however mass transfer is caused by a change in the density due to pressure or temperature variations, then we would speak of mass transfer in free convection. 

The combined CFD—DEM approach was extended to investigate the effects of some important parameters closely related to the van der Waals force such as particle size and Hamaker constant (Hou et al., 2012a). The heat transfer characteristics of cohesive particles were demonstrated in three flow regimes in Fig. 19. It revealed that the convective heat transfer is dominant for large particles while the conductive heat transfer becomes important with the decrease of particle size. This is mainly attributed to the increase of surface area per unit volume. Two transitional points with the increase of Hamaker constant were found in the variation of heat fluxes by convective and conductive heat transfer modes as shown in Fig. 20. 

Only a small number of solutions for the laminar forced convection problem and experimental investigations are available in the literature with some variations in the associated thermophysical properties. To the authors knowledge, for example, no experimental study is available to clarify the effect of the Prandtl number on the heat transfer in micro-channels with different duct geometries. 

Free or natural convection occurs when fluid motion is generated predominantly by body forces caused by density variations, under the earth s gravitational field. In the absence of the gravitational field, body forces may be caused by surface tension. The subject material here is focussed on heat transfer with motion produced by buoyancy forces. 

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. 

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. 

Air at a temperature of 10°C flows upward at a velocity of 0.8 m/s over a wide vertical 15-cm high flat plate which is maintained at a uniform surface temperature of 50°C. Plot the variation of the local heat transfer rate with distance along the plate from the leading edge. Also show the variations that would exist in purely forced and purely free convective now. 

Close agreement of the observed and predicted variations for the normalized droplet surface area are shown in Figure 7 for both pure diffusion and forced-convection modes of gas-phase heat and mass transfer. Whereas the consistency of normalized surface area predictions for both... 

Convection is called forced convection if Ihe fluid is forced to flow over the surface by external means such as a fan, pump, or the wind. In contrast, convection is called natural (or free) convection if the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid (Fig. 1 33). For example, in the absence of a fan, heat transfer from the surface of the hot block in Fig. 1-32 is by natural convection since any motion in the air in this case is due to the rise of Ihe warmer (and thus lighter) air near the surface and the fall of the cooler (and thus heavier) air to fill its place. Heat transfer between the block and the surrounding air is by conduction if the temperature difference between Ihe air and the block is not large enough to overcome the resistance of air to movement and thus to initiate natural convection currents. 

Kakag S., Y. Yener, 1973, Exact solution of the transient forced convection energy equation for time wise variation of inlet temperature, Int. J. Heat Mass Transfer 16, 2205-2214. 

Kaka , S., Cotta, R.M., Hatay, F.F. md Li, W. (1990), Unsteady Forced Convection in Ducts for a Sinusoidal Variation of Inlet Temperature, 9 Int Heat Transfer Conf, Paper 8-MC-01, pp. 265-270, Jerusalem, Israel, August. 

Heat is transferred from or to a region by the motion of fluids and the phenomenon of convection. In natural convection, the movement is caused by buoyancy forces induced by variations in the density of the fluid these variations are caused by differences in temperature. In forced convection, movement is created by an external agency such as a pump. 

The temperature dependence of the fluid density is especially important in heat transfer caused by natural or free convection. In contrast to the previous case of forced convection, where the fluid is forced at speed by a blower or pump, free convective flow exists due to density changes in the earth s gravitational field, which originate from the variation in temperature. This is how, for example, a quiescent fluid next to a hot wall is heated. The density of the fluid adjacent to the wall is lowered, causing an upward flow in the gravitational field to develop. 

The mechanism of heat flow in forced convection outside tubes differs from that of flow inside tubes, because of differences in the fluid-flow mechanism. As has been shown on pages 59 and 106 no form drag exists inside tubes except perhaps for a short distance at the entrance end, and all friction is wall friction. Because of the lack of form friction, there is no variation in the local heat transfer at different points in a given circumference, and a close analogy exists between friction and heat transfer. An increase in heat transfer is obtainable at the expense of added friction simply by increasing the fluid velocity. Also, a sharp distinction exists between laminar and turbulent flow, which calls for different treatment of heat-transfer relations for the two flow regimes. 

FIGURE 15.95 Variation of heat transfer coefficient with quality in the forced convective region (from Kenning and Cooper [233], with permission of Elsevier Science). 

FIGURE 15.111 Variation of heat transfer coefficient with composition in the forced convective boiling of R134a/R123 mixtures (from Fujita and Tsutsui [279], with permission from Taylor Francis, Washington, DC. All rights reserved). 

The time variation of enthalpy per m (left hand side of the equation) is caused by forced convection (first term on the right hand side), the effective heat transfer (second term on the right hand side) and the heat release caused by the chemical reaction (third term on the right hand side) )i is the effective coefficient of thermal conductivity of the mixture of substances in W/(m K), p is its density in kg/m, Cp the corresponding heat capacity at constant pressure in J/(kg K) and AHrj the enthalpy of reaction of reaction j in J/kg (with a negative sign for exothermic reactions). 

Convection. Most industrial processes rely more heavily on convection for the transfer of heat. Here, the process is aided by the bulk movement of fluid. Natural convection takes place when the transfer of heat itself causes variations in the density of the fluid. The resulting flow, under the influence of gravity, transfers heat from one zone to another. When the fluid is forced into motion by an outside agency such as a pump or an agitator, we have forced convection. Most of the applications of interest here rely on forced convection. 

Convection involves the transfer of heat by the motion and mixing of macroscopic portions of a fluid (i.e., the flow of a fluid past a solid boundary). The term natural convection is used if this motion and mixing is cansed by density variations resnlting from temperature differences within the fluid. The term forced convection is used if this motion and mixing is cansed by an outside force, such as a pump or fan (as shown in Figure 6.4). The transfer of heat from a hot-water radiator to a room is an example of heat transfer by natural convection. The transfer of heat from the surface... 

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