Relative Heat Transfer

Some notes on FW and air temperature efficiency are given in the following list. A very simple guideline to the relationship between relative heat transfer surfaces compared with heat absorbed is shown in Table 1.3). 

Fig. 5.43 Relative heat transfer coefficients at the top of horizontal and inclined tubes. Horizontal circles (o) indicate FrLs = 0.9, squares ( ) indicate FrLs = 1-3, triangles (A) indicate FrLS = 2.0. Inclined at j8 = 5° filled circles ( ) indicate FrLs = 0.59, filled squares ( ) indicate FrLs = 1.2, filled triangles (A) indicate FrLs = 2.0. Reprinted from Mosyak and Hetsroni (1999) with permission...

Heat transfer can, of course, be increased by increasing the agitator speed. An increase in speed by 10 will increase the relative heat transfer by 10. The relative power input, however, will increase by 10In viscous systems, therefore, one rapidly reaches the speed of maximum net heat removal beyond which the power input into the batch increases faster than the rate of heat removal out of the batch. In polymerization systems, the practical optimum will be significantly below this speed. The relative decrease in heat transfer coefficient for anchor and turbine agitated systems is shown in Fig. 9 as a function of conversion in polystyrene this was calculated from the previous viscosity relationships. Note that the relative heat transfer coefficient falls off less rapidly with the anchor than with the turbine. The relative heat transfer coefficient falls off very little for the anchor at low Reynolds numbers however, this means a relatively small decrease in ah already low heat transfer coefficient in the laminar region. In the regions where a turbine is effective,... 

Figure 9. Relative heat transfer coefficient vs. percent polystyrene solids hosed on viscosity relationship shown in Figure 8...

Under given external conditions (tube diameter, etc.) the relative heat transfer, on which the velocity and possibility of combustion depend, increases as the combustion velocity decreases. The existence of a limit for the feasibility of combustion at low pressure, depending on the drop in the combustion velocity with decreased pressure, is therefore natural (together with the possibility of existence of an upper limit which depends on the increase in TB as the pressure is raised—see the example of nitroglycerin above). 

Table II. Relative Heat Transfer Rates in a Naptha/AGO Flexible Cracking Furnace0...

Figure 7.2.14. The relation between the relative heat transfer coefficient for boiling PIB solutions in cyclohexane and the Newtonian viscosity of the solutions measured at T=298 K. AT = 16.67 K - PIB Vistanex L-100 in cyclohexane, o - PIB Vistanex L-80 in cyclohexane, X - pure cyclohexane. [Reprinted from H.J. Gannett, and M.C. Williams, Int. J. Heat Mass Transfer, 14, 1001, Copyright 1971, the reference 57, with permission from Elsevier Science]...

These stacked assembly is brazed in a vacuum fiimace to become a rigid core. Headers and nozzles are welded to the side bars. Different types of fins are used for purposes governed by the process limitations such as pressure drop, turbulence and the relative heat transfer. Typical fin types are plain, perforated, serrated and herringbone which are illutrated by Figure 3. 

Fig. 4.23 Influence of moisture content on wall-to-bed heat transfer by means of relative heat transfer coefficients according to Eq. 4.27. Reproduced with permission from Groenewold and Tsotsas (2007).

Figure 11 shows the theoretical relative heat transfer rate of a staggered finned tube heat exchanger as a function of the thermal conductivity of the tube material [36]. A heat exchanger with elements whose thermal conductivity is ten times that of a pure polymer performs at 95% of that expected from stainless steel tubes. Since this levd of thermal conductivity increase is easily obtained with polymer composites, they represent viable candidates with regard to heat transfer. Mesloh has shown exj rimentally, in a forced convection heat exchanger, that an aluminum flake-filled plastic having a thermal conductivity 20 times that of the base polymer has an overall heat transfer rate of 75% of that of an aluminum tube [38]. 

Fig. 11. Theoretical relative heat transfer rate of a staggered finned tube heat exchanger as a function of the relative thermal conductivity of the tube material...

Specifying the hot utility or cold utility or AT m fixes the relative position of the two curves. As with the simple problem in Fig. 6.2, the relative position of the two curves is a degree of freedom at our disposal. Again, the relative position of the two curves can be changed by moving them horizontally relative to each other. Clearly, to consider heat recovery from hot streams into cold, the hot composite must be in a position such that everywhere it is above the cold composite for feasible heat transfer. Thereafter, the relative position of the curves can be chosen. Figure 6.56 shows the curves set to ATn,in = 20°C. The hot and cold utility targets are now increased to 11.5 and 14 MW, respectively. 

Figure 6.6 illustrates what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of AT ir,. When the curves just touch, there is no driving force for heat transfer at one point in the process, which would require an... 

Eurther research on convective transport under low Reynolds number, quasicontinuum conditions is needed before the optimal design of such a micro heat exchanger is possible. The cooling heat exchanger is usually thermally linked to a relatively massive substrate. The effects of this linkage need to be explored and accurate methods of predicting the heat-transfer and pressure-drop performance need to be developed. 

Gas-Cycle Systems. In principle, any permanent gas can be used for the closed gas-cycle refrigeration system however, the prevailing gas that is used is air. In the gas-cycle system operating on the Brayton cycle, all of the heat-transfer operations involve only sensible heat of the gas. Efficiencies are low because of the large volume of gas that must be handled for a relatively small refrigera tion effect. The advantage of air is that it is safe and inexpensive. 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

A low temperature of approach for the network reduces utihties but raises heat-transfer area requirements. Research has shown that for most of the pubhshed problems, utility costs are normally more important than annualized capital costs. For this reason, AI is chosen eady in the network design as part of the first tier of the solution. The temperature of approach, AI, for the network is not necessarily the same as the minimum temperature of approach, AT that should be used for individual exchangers. This difference is significant for industrial problems in which multiple shells may be necessary to exchange the heat requited for a given match (5). The economic choice for AT depends on whether the process environment is heater- or refrigeration-dependent and on the shape of the composite curves, ie, whether approximately parallel or severely pinched. In cmde-oil units, the range of AI is usually 10—20°C. By definition, AT A AT. The best relative value of these temperature differences depends on the particular problem under study. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

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