The Convective Heat Transfer Coefficient

Consider a fluid flowing over a surface which is maintained at a temperature that is different from that of the bulk of the fluid as shown in Fig. 1.8. 

If the temperature at some point on the surface is Tw and if the rate at which heat is being transferred locally at this point from the surface to the fluid per unit surface 

In this equation Tf is some convenient fluid temperature which will be more precisely defined at a later stage [11],[12],[13],[14],[15]. 

The heat transfer rate, q, is taken as positive in the direction wall-to-fluid so that it will have the same sign as(Tw -T/) and h will always, therefore, be positive. A number of names have been applied to h including convective heat transfer coefficient , heat transfer coefficient , film coefficient , film conductance , and unit thermal convective conductance . The heat transfer coefficient, h, has the units W/m2-K or, since its definition only involves temperature differences, W/m2oC, in the SI system of units. In the imperial system of units, h has the units Btu/ft2-hr-°F. 

It must be clearly understood that h is not only dependent on the fluid involved in the process but is also strongly dependent on, among other things, the shape of the surface over which the fluid is flowing and on the velocity of the fluid. 

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Table 2. Values of the Convective Heat-Transfer Coefficient ...

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

The values of CJs are experimentally determined for all uncertain parameters. The larger the value of O, the larger the data spread, and the greater the level of uncertainty. This effect of data spread must be incorporated into the design of a heat exchanger. For example, consider the convective heat-transfer coefficient, where the probabiUty of the tme value of h falling below the mean value h is of concern. Or consider the effect of tube wall thickness, /, where a value of /greater than the mean value /is of concern. 

To the extent that radiation contributes to droplet heatup, equation 28 gives a conservative estimate of the time requirements. The parameter ( ) reflects the dependence of the convective heat-transfer coefficient on the Reynolds number ... 

The convective wave cycle was described in 5.2.4 but its heat transfer properties not quantified. Critoph and Thorpe [22] and Thorpe [23] have measured the convective heat transfer coefficient between flowing gas and the grains within the bed. Preliminary results imply that the pressure drop through the bed can be expressed by a modified Ergun equation ... 

Tj is the surface temperature of the panel, Tj, the thermometer bulb temperature, Tj the air temperature, and T the temperature of the walls of the building. F is the view factor from the bulb to the heating panel, e is the emissivity of the thermometer bulb at temperature T cr is the Stefan-Boltzmann constant (5.67 X 10 W m K " ), and is the convective heat transfer coefficient from bulb to air. 

A = area of the heating panel and h is the convective heat transfer coefficient. 

Solution One of the most critical and important quantities to calculate in Eq. (8.32) is the convective heat transfer coefficient. It depends on the temperature conditions and also on the width of the panel. Tables 8.11 and 8.12 collect the calculated heat transfer coefficients in different conditions. 

The Convective Heat Transfer Coefficient between the Plate and Flowing Air... 

The kind of convective heat transfer—forced convection or natural (at floor, wall, or ceiling)—must be considered and taken into account by selecting appropriate values for the convective heat transfer coefficient see Eq. (11.14)). Thus, the heat transfer coefficient implicitly assumes the flow situation at the surface. Normally, coefficients for convective heat transfer are considered as a preset constant parameter (the coefficient may be defined as variable, however, depending on other parameters). Therefore, the selection of appropriate values is crucial. Values for heat transfer coefficients can be found in several references a comprehensive summary is given in Daskalaki. ... 

Figure 3 illustrates some additional capability of the flow code. Here no pressure gradient is Imposed (this is then drag or "Couette flow only), but we also compute the temperatures resulting from Internal viscous dissipation. The shear rate in this case is just 7 — 3u/3y — U/H. The associated stress is.r — 177 = i/CU/H), and the thermal dissipation is then Q - r7 - i/CU/H). Figure 3 also shows the temperature profile which is obtained if the upper boundary exhibits a convective rather than fixed condition. The convective heat transfer coefficient h was set to unity this corresponds to a "Nusselt Number" Nu - (hH/k) - 1. 

Here the proportionality constant h is called the convective heat transfer coefficient. In S.I. units, h is expressed in Wm 2 K. The rate equation may be expressed as... 

Calculate the convective heat transfer coefficient using simple methods, such as assuming convection only, or Chens method see Section 12.11.3. 

The parameter h which combines several effects, must be at least as large as the convective heat transfer coefficient (hc calculated from the jH factor correlations discussed in Section 12.5. It is given by an expression of the following form... 

Equations 12.7.20 to 12.7.23 may be used to evaluate the parameter h. We begin by converting the convective heat transfer coefficient hC9 determined in Illustration 12.6, to British Engineering Units. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

All correlations based on ambient temperature data where thermal radiation is negligible should be considered to represent only the convective heat transfer coefficient hc. 

The simplest correlations are of the form shown by Eq. (15), in attempts to recognize the strong influence of solid concentration (i.e., suspension density) on the convective heat transfer coefficient. Some examples of this type of correlation, for heat transfer at vertical wall of fast fluidized beds are ... 

For laminar conditions of slow flow, as in candle flames, the heat transfer between a fluid and a surface is predominately conductive. In general, conduction always prevails, but in the unsteadiness of turbulent flow, the time-averaged conductive heat flux between a fluid and a stationary surface is called convection. Convection depends on the flow field that is responsible for the fluid temperature gradient near the surface. This dependence is contained in the convection heat transfer coefficient hc defined by... 

The process of steady flame propagation into a premixed system is depicted in Figure 4.12 for a moving control volume bounding the combustion region <5r. The heat loss in this case is only considered to the duct wall. With h as the convection heat transfer coefficient, the loss rate can be written as... 

Let us examine methanol. Its flashpoint temperature is 12 to 16 °C (285-289 K) or, say, 15 °C. If this is in an open cup, then the concentration near the surface is Xl = 6.7 %. Performed under normal room temperatures of, say, 25 °C, the temperature profile would be as in Figure 6.2. This must be the case because heat must be added from the air to cause this evaporated fuel vapor at the surface. This decrease in temperature of an evaporating surface below its environment is sometimes referred to as evaporative cooling. If the convective heat transfer coefficient, typical of natural convection, is,... 

The convective heat transfer coefficient may be approximated as that due to heat transfer without the presence of mass transfer. This assumption is acceptable when the evaporation rate is small, such as drying in normal air, and for conditions of piloted ignition, since XL is typically small. Mass transfer due to diffusion is still present and can be approximated by... 

Calculate the time to ignite (piloted) for the materials listed below if the irradiance is 30 kW/ m2 and the initial temperature is 25 °C. The materials are thick and the convective heat transfer coefficient is 15 W/m2 K. Compute the critical flux for ignition as well. 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

H is defined as the convective heat transfer coefficient. This proportionality constant contains all the nonlinearities associated with convection /A is the area of the surfaces in contact Tsurf is the temperature of the hot surface Tamb is the ambient fluid temperature... 

Hubbard, L. J. and Farkas, B. E. (1999). A method for determining the convective heat transfer coefficient during immersion frying. ]. Food Process Eng. 22, 201-214. 

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