Heat flux by convection

In the above equation, represents the heat flux by conduction through the porous medium, and represents the heat flux by convection of the fluid mixture. The y direction is assumed to be of unit length. 

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. 

The transfer of heat by radiation in general can be said to occur simultaneously with heat transfer by convection and conduction. Transfer by radiation tends to become more important than that by the other two mechanisms as the temperature increases. It is useful to gain an appreciation of the basic definitions of the energy flux terms, the surface property terms and their relationships while discussing radiative heat transfer. With this objective, reference may be made to Table 3.4 in which these are presented. 

If the reactive gas produced at the burning surface of an energehc material reacts slowly in the gas phase and generates a luminous flame, the distance Lg between the burning surface and the luminous flame front is termed the flame stand-off distance. In the gas phase shown in Fig. 3.9, the temperature gradient appears to be small and the temperature increases relatively slowly. In this case, heat flux by conduction, the first term in Eq. (3.41), is neglected. Similarly, the rate of mass diffusion, the first term in Eq. (3.42), is assumed to be small compared with the rate of mass convection, the second term in Eq. (3.42). Thus, one gets... 

Fig. 5.25 Temperature gradient, conductive heat flux, convective heat flux, and heat flux by chemical reaction as a function of distance from the burning surface at 3 MPa (initial temperatures 243 K and 343 K) for BAMO/ THF = 60 40 copolymer.

The time may control in the case of ignition by a very large radiative heat flux or a shock wave. For small heat fluxes or convective heat transfer the last term of Eq. (2.8) is essential. 

In many applications heat transfer by convection must be considered in addition to radiative heat transfer. This is, for example, the case where a radiator releases heat to a room which is at a lower temperature. Radiative heat exchange takes place between the radiator and the walls of the room, whilst at the same time heat is transferred to the air by convection. These two kinds of heat transfer are parallel to each other and so the heat flow by convection and that by radiation are added together in order to find the total heat exchanged. The heat flux then becomes... 

In convective vaporization, the same boiling regimes are encountered, but modified by the net motion of the two-phase fluid past the surface. At low velocities or high heat fluxes, the convection effect is small, and nucleate boiling dominates. At higher velocities, the heat-transfer rate is dominated by the two-phase mixture sweeping across the surface. It is still important to avoid transition and film boiling, but the onset of these phenomena is complicated by many factors. (See [1, 34].)... 

Number of researchers reports the liquid forced convection inside narrow channels is a most valuable form of heat removal from heat sinks [13-16]. However, the respective key issues are the maximum attainable heat flux by using liquid forced convection, and its value in comparison with the preeminent alternatives of boiling critical heat fluxes. We believe that maximum heat flux could be accomplished by using the inverted meniscus principle of evaporation coupled with excluding of vapor... 

Find the local Nusselt number for free convection of a vertical plate subjected to a constant wall heat flux by using linear profiles for cases Pr > 1 (Fig. 5P-5). Compare the result with Eq. (5.104). 

Another method of determining the convective heat flux by direct measurement involves adding a radiant shield between the heat source and the heat flux gauge to exclude radiation from being received by the gauge. The problem is that the shield often disturbs the flow and the measured flux is not representative of the actual convective flow. Anofher problem is that the surface temperature under the shield will be lower than it would be without the shield, so the measurement would need to be done quickly before fhe wall femperature under the shield drops too much. In addition, although radiation from fhe primary source (burners) may be shielded, the rest of fhe furnace walls may still contribute radiation to the gauge. 

Heat transfer by convection is a complex process but the analysis is simplified by the boundary layer concept. All resistance to heat transfer on the fluid side of a hot surface is supposed to be concentrated in a thin film of fluid close to the solid surface. Transfer within the film is by conduction. The temperature profile for such a process is shown in Figure 7.27. The thickness of the thermal boundary layer is not generally equal to that of the hydrodynamic boundary layer. The heat flux could be expressed as... 

For volume zone, i, the balance equation expresses that the ineoming radiation flux from the other volume, 1, and surface zones, k, minus the adiation flux to the other gas and surface zones plus the net heat release is equal to zero. The net heat release in the zone includes the heat of combustion plus heating of the flue gas and minus heat delivered by convection to the adjaeent surface zones. A volume equation is then ... 

The ratio of the convective heat flux to the heat flux by pure conduction without fluid motion gives the Nusselt number (here with the distance L between the two plates as characteristic length) ... 

To be precise, the convective term for the transport of liquid water should be added to the left-hand side of Equation 4.282. This would lower the conductive heat flux by the value q , and the same value would appear as the convective heat flux. Note that the total heat flux of Equation 4.298 would not change, since this flux is determined by the rate of heat production in the CL only. 

In practice, the analysis of heat transfer by convection is treated anpiricaUy (by direct observation). Convection heat transfer is treated empirically because of the factors that affect the stagnant film thickness such as fluid velocity, fluid viscosity, heat flux, surface roughness, and the type of flow (single phase/double phase). 

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