Modes of heat transfer

Conduction is the principal mechanism of heat transfer in solids. In liquids, conduction is frequently augmented by convection as circulating currents are set up due to density differences, while in gases, because of 

2 Convection. Heat is transferred by moving fluids and therefore only occurs in gases and liquids. A moving fluid takes thermal energy with it, and when it contacts another fluid or a surface at a different temperature, heat is transferred. There are two types of convection  

3 Radiation. All bodies emit and absorb electromagnetic radiation, such as infrared, ultraviolet and visible light. The predominant 

---

If the dominant mode of heat transfer to the soHds is convection between the wall and the soHds, then the characteristic time for a dry system is... 

Operation of a reactor in steady state or under transient conditions is governed by the mode of heat transfer, which varies with the coolant type and behavior within fuel assembHes (30). QuaHtative understanding of the different regimes using water cooling can be gained by examining heat flux, q, as a function of the difference in temperature between a heated surface and the saturation temperature of water (Eig. 1). 

In fossil fuel-fired boilers there are two regions defined by the mode of heat transfer. Fuel is burned in the furnace or radiant section of the boiler. The walls of this section of the boiler are constmcted of vertical, or near vertical, tubes in which water is boiled. Heat is transferred radiatively from the fire to the waterwaH of the boiler. When the hot gas leaves the radiant section of the boiler, it goes to the convective section. In the convective section, heat is transferred to tubes in the gas path. Superheating and reheating are in the convective section of the boiler. The economizer, which can be considered as a gas-heated feedwater heater, is the last element in the convective zone of the boiler. 

Batch reaclors are tanks, usually provided with agitation and some mode of heat transfer to maintain temperature within a desirable range. They are primarily employed for relatively slow reactions of several hours duration, since the downtime for filling and emptying large equipment may be an hour or so. Agitation maintains uniformity and improves heat transfer. Modes of heat transfer are illustrated in Figs. 23-1 and 23-2. 

Thermal design concerns itself with sizing the equipment to effect the heat transfer necessaiy to cany on the process. The design equation is the familiar one basic to all modes of heat transfer, namely,... 

The hterature to date offers practically no such values. However, enough proprietaiy work has been performed to present a rehable evaluation for the comparison of mechanisms (see Introduction Modes of Heat Transfer ). 

Some modes of heat transfer to stirred tank reacdors are shown in Fig. 23-1 and to packed bed reactors in Fig. 23-2. Temperature and composition profiles of some processes are shown in Fig. 23-3. Operating data, catalysts, and reaction times are stated for a number of industrial reaction processes in Table 23-1. 

Convection is influenced by the fluid flow adjacent to the solid surface. To appreciate the mechanics of this mode of heat transfer, the nature of the fluid flow in relation to the particular flow process must be known. Consideration of the flow structure created by the passage of a turbulent fluid over a smooth solid surface shows (see Fig. 4.24)... 

Contact temperature measurement is based on a sensor or a probe, which is in direct contact with the fluid or material. A basic factor to understand is that in using the contact measurement principle, the result of measurement is the temperature of the measurement sensor itself. In unfavorable situations, the sensor temperature is not necessarily close to the fluid or material temperature, which is the point of interest. The reason for this is that the sensor usually has a heat transfer connection with other surrounding temperatures by radiation, conduction, or convection, or a combination of these. As a consequence, heat flow to or from the sensor will influence the sensor temperature. The sensor temperature will stabilize to a level different from the measured medium temperature. The expressions radiation error and conduction error relate to the mode of heat transfer involved. Careful planning of the measurements will assist in avoiding these errors. 

Tlie growfii and spread of fires occurs fiuough heat transfer or tlie migration of burning materials. There are fiuee main modes of heat transfer conduction, convection, and radiation. 

Heat transfer is the energy flow that occurs between bodies as a result of a temperature difference. There are three commonly accepted modes of heat transfer conduction, convection, and radiation. Although it is common to have two or even all three modes ot heat transfer present in a given process, we will initiate the discussion as though each mode of heat transfer is distinct. 

Convective heat transfer occurs when a fluid (gas or liquid) is in contact with a body at a different temperature. As a simple example, consider that you are swimming in water at 21°C (70°F), you observe that your body feels cooler than it would if you were in still air at 21°C (70°F). Also, you have observed that you feel cooler in your automobile when the air-conditioner vent is blowing directly at you than when the air stream is directed away from you. Both ot these observations are directly related to convective heat transfer, and we might hypothesize that the rate of energy loss from our body due to this mode of heat transfer is dependent on not only the temperature difference but also the typie of surrounding fluid and the velocity of the fluid. We can thus define the unit heat transfer for convection, q/A, as follows ... 

Convection requires a fluid, either liquid or gaseous, which is free to move between the hot and cold bodies. This mode of heat transfer is very complex and depends firstly on whether the flow of fluid is natural , i.e. caused by thermal currents set up in the fluid as it expands, or forced by fans or pumps. Other parameters are the density, specific heat capacity and viscosity of the fluid and the shape of the interacting surface. 

Two-phase flows are classified by the void (bubble) distributions. Basic modes of void distribution are bubbles suspended in the liquid stream liquid droplets suspended in the vapor stream and liquid and vapor existing intermittently. The typical combinations of these modes as they develop in flow channels are called flow patterns. The various flow patterns exert different effects on the hydrodynamic conditions near the heated wall thus they produce different frictional pressure drops and different modes of heat transfer and boiling crises. Significant progress has been made in determining flow-pattern transition and modeling. 

Summary of experimental data Film boiling correlations have been quite successfully developed with ordinary liquids. Since the thermal properties of metal vapors are not markedly different from those of ordinary liquids, it can be expected that the accepted correlations are applicable to liquid metals with a possible change of proportionality constants. In addition, film boiling data for liquid metals generally show considerably higher heat transfer coefficients than is predicted by the available theoretical correlations for hc. Radiant heat contribution obviously contributes to some of the difference (Fig. 2.40). There is a third mode of heat transfer that does not exist with ordinary liquids, namely, heat transport by the combined process of chemical dimerization and mass diffusion (Eq. 2-162). 

The primary mode of heat transfer at the wall is forced convection of the vapor phase. As the liquid does not wet the heating surface during film boiling, heat transfer due to drop-wall collisions is relatively small, resulting in low wall-drop heat transfer (only a few percent of the total heat input). Most of the droplet evaporation occurs because of vapor-drop heat transfer. Just after dryout, the... 

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

Since the other modes of heat transfer discussed depend upon the difference in temperature, Tx - T2, it would be convenient to express radiative heat exchange in terms of Tx - T2 rather than in terms of the difference in fourth powers of temperature. For this purpose, we express the difference in fourth powers of temperature as... 

The other mode of heat transfer is conduction. The conductive heat flux is, by Fourier s law,... 

Conduction is the primary mode of heat transfer through solid material. Conduction occurs by two mechanisms ... 

Consider a tube heated uniformly at a heat flux q/A fed with saturated water at the base at a velocity Fo. For this velocity and heat flux, nucleate boiling will take place, and a temperature difference aTo will be established. At some distance up the tube vaporization will occur and increase the volumetric flow of material and hence the velocity to, say, Fi. The line for forced convective heat transfer meets the boiling curve below the heat flux of q/A and so nucleate boiling will still be the mode of heat transfer and the temperature difference AT, and hence the heat transfer... 

A final mode of heat transfer in tubular reactors is the feed-cooled reactor, where the hot products from the reactor are cooled by the feed before it enters the reactor. As shown in Figure S-22, the cold feed in the jacket is preheated by the reaction in the inner tube or a heat exchanger is used for this purpose before the reactor. Temperature profiles for feed cooling are shown in Figure 5-22. 

---