Effective area for heat transfer

The rate of heat transfer is most conveniently expressed in terms of an overall heat transfer coefficient, the effective area for heat transfer and an overall temperature difference, or driving force, where... 

The effective area for heat transfer is linearly proportional to the gassed height of the cylindrical portion in the tank ... 

Heat exchange with the surroundings is expressed here in terms of the surroundings temperature 7, the overall heat-transfer coefficient U, and the effective area for heat transfer A. The heat of reaction AH and the rate of reaction do not appear directly in Eq. (3-4). However, their effects are reflected in the difference in the enthalpies of the feed and product streams, since these streams will have different compositions. That is, to calculate the enthalpy of the product stream it is necessary to know AH and the rate r. Therefore it is more convenient to replace Hp — Hg with the appropriate r, r, and AH. This is accomplished by considering the enthalpy change when feed at Tp is first heated to and then changed in composition to that of the product. Expressed mathematically, the first contribution is Cp Tg — Tp) and the second is x — Xp)AH M. Hence... 

The effective area for heat transfer from a finned surface is the sum of the prime area (the tube surface between the fins) and the finned area multiplied by the fin efficiency ... 

It is estimated that the uncertainty in the effective area for heat transfer does not exceed 4.5%, and uncertainty in any given temperature difference does no exceed 0.1 K. Corresponding uncertainty in any value of the heat transfer coefficient depends principally upon the magnitude of the temperature difference and becomes largest as the critical pressures are approached, since AT s for peak flux are of the order of 1 K. 

With a load placed in a furnace or oven, its effective area for heat transfer is determined by its location relative to other loads, the sidewalls, and the end walls. 

Before eonsidering the effects of water injection in an EGT type plant, it is worthwhile to refer to the earlier studies on the performanee of some dry recuperative cycles. Fig. 6.6 shows the T..s diagram of a [CBT i X r cyele, with a heat exchanger effectiveness of unity. It is implied that the surface area for heat transfer is very large, so that the outlet temperature on the cold side is the same as the inlet temperature on the hot side. However, due to the higher specific heat of the hot gas, its outlet temperature is higher than the inlet temperature of the cold air. 

For the common problem of heat transfer between a fluid and a tube wall, the boundary layers are limited in thickness to the radius of the pipe and, furthermore, the effective area for heat flow decreases with distance from the surface. The problem can conveniently be divided into two parts. Firstly, heat transfer in the entry length in which the boundary layers are developing, and, secondly, heat transfer under conditions of fully developed flow. Boundary layer flow is discussed in Chapter 11. 

In principle, however, the effective surface area for heat transfer from the single monomer is decreased by the contact area between the particles. The fractal dimension of the aggregates varies in different systems and depends on the evolution process. For dense aggregates, heat transfer rates are decreased due to the reduced heat exchange area compared to primary particles only connected by point contact in a chain like structure (Liu et al., 2006a-c). This leads to an overestimation of... 

The coated particles are contained in graphite, which acts as a structural material and also provides a relatively large effective surface area for heat transfer to the coolant. 

The flow cross-section within a given spiral channel is constant and at the designers discretion. A further important feature is that the effective disc area for heat transfer is enhanced by the inter-spiral walls which act as very efficient fins. From a mechanical point of view the spiral fins also serve to reinforce the disc surface so that it remains undistorted by the differential pressure forces between the heating channel and the process fluid - an inherent problem with the splitter plate design. 

As a result of the volumetric expansion of the glass, the surface area and the volume increase. Owing to the increased surface area for heat transfer, the heat exchange increases. However, it can be calculated that this effect is very small. The increase of the volume, however, has a sigiuficant effect on the mercuiy level. The volumetric expansion coefficient of mercury is 1.8 x lO K , the value for glass is in the order of 0.1-0.3 X 10 K . By ignoring the volumetric expansion of glass, an error is made in the order of 10%. A possible solution is to use a modified value for mercuiy, which is the difference between the two expansion coefficients. 

A = effective surface area for heat and mass transfer in m L = latent heat of vaporization at in kj/kg k = mass-transfer coefficient in kg/ (sm kPa) t = mean source temperature for all components of heat transfer in K t = Hquid surface temperature in K p = Hquid vapor pressure at in kPa p = partial pressure of vapor in the gas environment in kPa. It is often useful to express this relationship in terms of dry basis moisture change. For vaporization from a layer of material ... 

Sindlady, heating surface area needs are not direcdy proportional to the number of effects used. For some types of evaporator, heat-transfer coefficients decline with temperature difference as effects are added the surface needed in each effect increases. On the other hand, heat-transfer coefficients increase with temperature level. In a single effect, all evaporation takes place at a temperature near that of the heat sink, whereas in a double effect half the evaporation takes place at this temperature and the other half at a higher temperature, thereby improving the mean evaporating temperature. Other factors to be considered are the BPR, which is additive in a multiple-effect evaporator and therefore reduces the net AT available for heat transfer as the number of effects is increased, and the reduced demand for steam and cooling water and hence the capital costs of these auxiUaries as the number of effects is increased. 

The area added by the fin is not as efficient for heat transfer as bare tube surface owing to resistance to conduction through the fin. The effective heat-transfer area is... 

An alternate means of reboiler control is to remove the control valve from the steam line and provide a condensate level controller for the chest cascaded from the tray temperature. The alternate method uses A tube surface for control, with the condensate covering more or less tube surface to vary the area exposed to condensing stream. Condensing area is many times more effective for heat transfer than area covered by relatively stagnant condensate. The reboiler must have extra surface to allow part of its surface to be derated for control purposes. 

The thickness of the tube sheet will reduce the effective length of the tube slightly, and this should be allowed for when calculating the area available for heat transfer. As a first approximation the length of the tubes can be reduced by 25 mm for each tube sheet. 

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