Cooling heat transfer calculations

A one-dimensional heat transfer calculation was also performed from the centerline of the coolant channel to the centerline of the fuel compact for the average channel at the outlet of the core. For this configuration, the coolant temperature was fixed at 1000°C. The NGNP result is given in Fig. 3.15, compared with the same distribution for a 600 MW(t) and a 2400 MW(t) AHTR. In all cases, the narrow gap between the fuel compact and the graphite matrix is assumed to be filled with helium. These eurves show that for the average channel, the 2400 MW(t) AHTR fuel temperature will be at least 30°C cooler than that of the helium-cooled NGNP. 

These results were used as the starting conditions for the heat transfer calculation. They gave a maximum temperature of 820°K in the TNT and 910°K in the Plexiglas. The temperature in the gas was lowered to a maximum of 2000°K within 3 /nsec, and insufficient reaction had occurred to make the first cell decompose. At later times the explosive surface cooled as heat was being conducted away faster than it was furnished by the hot gas and explosive decomposition. 

Because mixing involves viscous heat generation and simultaneous cooling, heat transfer measurement is a necessary part of calculating the energy balance. 

The relationship between heat transfer and the boundary layer species distribution should be emphasized. As vaporization occurs, chemical species are transported to the boundary layer and act to cool by transpiration. These gaseous products may undergo additional thermochemical reactions with the boundary-layer gas, further impacting heat transfer. Thus species concentrations are needed for accurate calculation of transport properties, as well as for calculations of convective heating and radiative transport. 

Vertical Tubes For the following cases Reynolds number < 2100 and is calculated by using F = Wp/ KD. The Nusselt equation for the heat-transfer coefficient for condensate films may be written in the following ways (using liquid physical properties and where L is the cooled lengm and At is — t,) ... 

Equivalent-Area Concept The preceding equations for batch operations, particularly Eq. 11-35 can be appliedforthe calculation of heat loss from tanks which are allowed to cool over an extended period of time. However, different surfaces of a tank, snch as the top (which would not be in contact with the tank contents) and the bottom, may have coefficients of heat transfer which are different from those of the vertical tank walls. The simplest way to resolve this difficulty is to nse an equivalent area A in the appropriate equations where... 

A low-boiling-point liquid, in boiling off, has a good heat transfer coefficient to help cool the wall and buy time. Calculate the time required to heat up the liquid and vaporize the inventory. If the time is less than 15 minutes... 

Fig. 6 shows both the actual cycle (shown in dashed lines) and the idealised cycle, which consists of two isosteres and two isobars. Heat flows in J/kg adsorbent q) are shown as shaded arrows. For most purposes, analysis of the ideal cycle gives an adequate estimate of the COP and cooling or heating per kg of adsorbent. An accurate calculation of the path of the actual cycle needs information on the dead volume of the whole system and of the heat transfer characteristics of the condenser and evaporator. General trends are more apparent from an analysis of the idealised cycle. 

Calculating the heat transfer and water evaporation rates are illustrated by the following example. A cooling tower eools 900 gpm of water from 95 to 85 F. The problem is to determine what the heat rejeetion is, and also what is the evaporation rate. The heat rejeetion is ealeulated as follows ... 

Calculate the time required to cool the batch described in Example 7-12 if an external heat exchanger with a heat transfer surface of 200 ft (18.58 m ) is available. The batch material is circulated through the exchanger at the rate of 25,000 Ib/hr (11,339.8 kg/hr). The overall... 

Most polymer processing methods involve heating and cooling of the polymer melt. So far the effect of the surroundings on the melt has been assumed to be small and experience in the situations analysed has proved this to be a reasonable assumption. However, in most polymer flow studies it is preferable to consider the effect of heat transfer between the melt and its surroundings. It is not proposed to do a detailed analysis of heat transfer techniques here, since these are dealt with in many standard texts on this subject. Instead some simple methods which may be used for heat flow calculations involving plastics are demonstrated. 

A lace of polyethylene is extruded with a diameter of 3 mm and a temperature of 190°C. If its centre-line must be cooled to 70°C before it can be granulated effectively, calculate the required length of the water bath if the water temperature is 20°C. The haul-off speed is 0.4 tn/s and it may be assumed that the heat transfer from the plastic to the water is by conduction only. 

But it app>ears that thermal efficiency does tend towards a maximum level with increasing combustion temperature. More realistic calculations of highly cooled turbines are given in the next chapter, after a brief description of the heat transfer analysis involved in the determination of cooling flow quantities. 

In Chapter 4 calculations were made on the overall efficiency of CBT plants with turbine cooling, the fraction of cooling air (tp) being assumed arbitrarily. In this chapter, we outline more realistic calculations, with the cooling air fraction i/r being estimated from heat transfer analysis and experiments. 

The outer and inner tubes extend from separate stationary tube sheets. The process fluid is heated or cooled by heat transfer to/from the outer tube s outside surface. The overall heat transfer coefficient for the O.D. of the inner tube is found in the same manner as for the double-pipe exchanger. The equivalent diameter of the annulus uses the perimeter of the O.D. of the inner tube and the I.D. of the inner tube. Kem presents calculation details. 

If it is required to know the area needed for the transfer of heat at a specified rate, the temperature difference AT, and the value of the overall heat-transfer coefficient must be known. Thus the calculation of the value of U is a key requirement in any design problem in which heating or cooling is involved. A large part of the study of heat transfer is therefore devoted to the evaluation of this coefficient. 

A heat exchanger is required to cool 20 kg/s of water from 360 K to 340 K by means of 25 kg/s water entering at 300 K. If the overall coefficient of heat transfer is constant at 2 kW/m2K, calculate the surface area required in < a) a countercurrent concentric tube exchanger, and (b) a co-current flow concentric tube exchanger. 

In the problems which have been considered so far, it has been assumed that the conditions at any point in the system remain constant with respect to time. The case of heat transfer by conduction in a medium in which the temperature is changing with time is now considered. This problem is of importance in the calculation of the temperature distribution in a body which is being heated or cooled. If, in an element of dimensions dr by dy by dr (Figure 9.9), the temperature at the point (x, y, z) is 9 and at the point (x + dx, y + dy, r. + dr) is (9 4- d6>), then assuming that the thermal conductivity k is constant and that no heat is generated in the medium, the rate of conduction of heat through the element is ... 

Then, the quantity of heat that could be removed in batch reactors whose volume varies from 11 to 1 m is calculated. In order to compare with experimental results, the temperature gradient is fixed at 45 °C (beyond which water in the utility stream would freeze and another cooling fluid should be used). The maximum global heat-transfer coefficient is estimated at an optimistic value of 500 W m K h The calculated value of the global heat transfer area of each batch reactor. A, is in the same range as the one given by the Schweich relation [35] ... 

Typical results of calculations using this model are shown in Fig. 5.4-67. The discontinuity of the d77<7f-curves corresponds to the complete consumption of the reactant (5 = 0). This is followed by cooling to temperature T,-. If the initial temperature is sufficiently high, the reaction proceeds rapidly. Consequently, the rate of heat evolution is so high that the rate of heat transfer to the coolant can be considered negligible. 

Example 15.1 A hot stream is to be cooled from 300 to 100°C by exchange with a cold stream being heated from 60 to 200°C in a single unit. 1-2 shell-and-tube heat exchangers are to be used subject to IP =0.9. The duty for the exchanger is 3.5 MW and the overall heat transfer coefficient is estimated to be 100 W-m 2-K 1. Calculate ... 

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