Mean overall coefficient of heat transfer

Mean overall coefficient of heat transfer, U, of a fluid filled in the container and placed in the atmosphere under isothermal conditions... 

U is called the mean overall coefficient of heat transfer, because it is the coefficient of heat transfer extending over the two kinds of fluid films sandwiching a solid wall in between them. The units of U are cal/(cm -min-K), which are of course the same as those of h. 

In the above example, 1 lb of initial steam should evaporate approximately 1 lb of water in each of the effects A, B and C. In practice however, the evaporation per pound of initial steam, even for a fixed number of effects operated in series, varies widely with conditions, and is best predicted by means of a heat balance.This brings us to the term heat economy. The heat economy of such a system must not be confused with the evaporative capacity of one of the effects. If operated with steam at 220 "F in the heating space and 26 in. vacuum in its vapor space, effect A will evaporate as much water (nearly) as all three effects costing nearly three times its much but it will require approximately three times as much steam and cooling water. The capacity of one or more effects in series is directly proportional to the difference between the condensing temperature of the steam supplied, and the temperature of the boiling solution in the last effect, but also to the overall coefficient of heat transfer from steam to solution. If these factors remain constant, the capacity of one effect is the same as a combination of three effects. 

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. 

Toluene is continuously nitrated to mononitrotoluene in a cast-iron vessel, 1 m diameter, fitted with a propeller agitator 0.3 m diameter rotating at 2.5 Hz. The temperature is maintained at 310 K by circulating 0.5 kg/s cooling water through a stainless steel coil 25 mm o.d. and 22 mm i.d. wound in the form of a helix, 0.80 m in diameter. The conditions are such that the reacting material may be considered to have the same physical properties as 75 per cent sulphuric acid. If the mean water temperatute is 290 K, what is the overall coefficient of heat transfer ... 

A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kg K and the overall coefficient of heat transfer is 1.5 kW/m2 K. 

A solution containing 23 per cent by mass of sodium phosphate is cooled from 313 to 298 K in a Swenson-Walker crystalliser to form crystals of Na3P04.12H20. The solubility of Na3P04 at 298 K is 15.5 kg/100 kg water, and the required product rate of crystals is 0.063 kg/s. The mean heat capacity of the solution is 3.2 kJ/kg deg K and the heat of crystallisation is 146.5 kJ/kg. If cooling water enters and leaves at 288 and 293 K, respectively, and the overall coefficient of heat transfer is 140 W/m2 deg K, what length of crystalliser is required ... 

In a condenser, the rate of heat flow (Q) is proportional to the condenser area (A), the mean temperature difference (A7"m) between the coolant and vapour streams and the overall coefficient of heat transfer ( ) ... 

A cylindrical tank 5 ft in diameter and 5 ft high is full of water at 70°F. The water is to be heated by means of a steam jacket around the sides only. The steam temperature is 230, and the overall coefficient of heat transfer is constant at 40 Btu/ (hr)(ft )(°F). Use Newton s law of cooling (heating) to estimate the heat transfer. Neglecting the heat losses from the top and the bottom, calculate the time necessary to raise the temperature of the tank contents to 170T. Repeat, taking the heat losses from the top and the bottom into account. The air temperature around the tank is 70 F, and the overall coefficient of heat transfer for both the top and the bottom is constant at 10 Btu/(hr)(fF)( F). 

X = Distance through which heat is conducted. See overall coefficient of heat transfer. X also means a pipe or duct fitting (cross) shaped like the letter x. x is also used to mean multiplied by as in a 9 ft x 12 ft x 7 ft ID furnace, xs = excess. As in xs air, xs fuel. 

Attempts have been made to describe rates of drying in the falling-rate period by means of overall coefficients of heat and mass transfer [35] but these have not been too successful owing to the change in the individual resistances to transfer in the solid during the course of the drying. Various expressions for the... 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

Difficult heat-exchange problems occur when one of two fluid streams has a much lower heat-transfer coefficient than the other, A typical case is heating a fixed gas, such as air, by means of condensing steam. The individual coefficient for the steam is typically 100 to 200 times that for the airstream consequently, the overall coefficient is essentially equal to the individual coefiBcient for the air, the capacity of a unit area of heating surface will be low, and many meters or feet of tube will be required to provide reasonable capacity. Other variations of the same problem are found in heating or cooling viscous liquids or in treating a stream of fluid at low flow rate, because of the low rate of heat transfer in laminar flow. 

Calculate the overall heat transfer coefficient for each zone using an appropriate set of heat transfer correlations and an appropriate correlation from Table 17.32. More specifically, if a linear dependence between U and A can be assumed, an arithmetic mean between the terminal U values should be used as a mean value. If both U and T vary linearly with q, the mean U value should be calculated from a logarithmic mean value of the UAT product as indicated in Table 17.32. Next, if both 1IU and T vary linearly with q, the third equation for the mean U value from Table 17.32 should be used. Finally, if U is not a linear function of either A or q, the mean value should be assessed following the procedure described in the section starting on p. 17.47. 

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