Coefficients of heat transfer

Coefficient of heat transfer h Debye circular frequency a>D... 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

U Overall coefficient of heat transfer for outside surface basis U for overall coefficient between liquid-vapor interface and coolant J/(s-m -K) Btu/(h-fF- F)... 

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

Overall Coefficient of Heat Transfer In testing commercial heat-transfer equipment, it is not convenient to measure tube temperatures (t,3 or t4 in Fig. 5-6), and hence the overall performance is expressed as an overall coefficient of heat transfer U based on a convenient area dA, which may be dAi, oi an average of dAi and dA whence, by definition,... 

U is called the overall coefficient of heat transfer, or merelv the overall coefficient. The rate of conduction through the tube wall and scale deposit is given by... 

FIG. 5-7 Radiation coefficients of heat transfer h,.. To convert British thermal units per hoiir-sqiiare foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5,6783 = ( F — 32)/l,8,... 

The physical properties of the liquid, rather than those of the vapor, are used For determining the film coefficient for condensation. Nus-selt [2. Ver. Dt.sch. Ing., 60, 541, 569 (1916)] derived theoretical relationships for predicting the film coefficient of heat transfer for condensation of a pure saturated vapor. A number of simplifying assumptions were used in the derivation. 

Figure 5-9 is a nomograph for determining coefficients of heat transfer for condensation of pure vapors. 

T = absolute temperature. Subscript 1 (or G), radiating surface (or gas) temperature subscript E, exit-gas subscript o, base temperature subscript E, pseudoadiabatic flame temperature based on C averaged from to Te-U = overall coefficient of heat transfer, gas convec tion to refractory wall to ambient air. 

U = coefficient of heat transfer and W,w = flow rate through external exchanger of hot and cold fluids respectively. 

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... 

The value of the coefficient of heat transfer from steam to sheet is determined by the conditions prevailiug on the inside and on the surface of the dryers. Low coefficients may be caused by (1) poor removal of air or other noncoudeusables from the steam in the cyhn-ders, (2) poor removal of condensate, (3) accumulation of oil or rust on the interior of the drums, and (4) accumulation of a fiber lint on the outer surface of the drums. In a test reported by Lewis et al. [Pulp Pap. Mag. Can., 22 (Februaiy 1927)] on a sulfite-paper diyer, in which the actual sheet temperatures were measured, a value of 187 W/(m °C) [33 Btu/(h ft" °F)j was obtained for the coefficient of heat flow between the steam and the paper sheet. 

A droplet Nusselt number = 2, corresponding to pure conduction (Reynolds number = 0) to infinity, is employed for evaluating the coefficient of heat transfer. 

Double-Pipe Scrapea-Surface Crystallizer This type of equipment consists of a double-pipe heat exchanger with an internal agitator fitted with spring-loaded scrapers that wipe the wall of the inner pipe. The cooling hquid passes between the pipes, this annulus being dimensioned to permit reasonable shell-side velocities. The scrapers prevent the buildup of solids and maintain a good film coefficient of heat transfer. The equipment can be operated in a continuous or in a recirculating batch manner. 

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. 

What may be turbulent flow in the heat exchanger for water will reduce to transitional or laminar flow for the heat transfer fluid, reducing the coefficient of heat transfer to a value 70% or more of that for water. 

Figure 5-24B. Forced convection past heat transfer surfaces improves the overall coefficient of heat transfer. By permission, Weber, A. R, Chem. Engr., Oct. 1953, p. 183 [23].

Figure 9-128. Companson of cooling efficiency of several packing materials in terms of the coefficient of heat transfer K a. Used by permission of Plastics Technical Service, The Dow Chemical Co., Midland Mich, with data added from Fuller, A. L., et al. Chemical Engineering Progress, V. 53, No. 10 (1957) p. 501 all rights reserved.

An exchanger has heen examined, and the following individual coefficients and resistances determined. What is the overall coefficient of heat transfer referenced to outside coefficients (Methods for determining these film coefficients are given later). 

These low-fm tubes can be installed and handled in the same manner as plain tubes. The larger diameter fins (5 or more per in.) are usually used in services with very low outside coefficients of heat transfer and require a unit design to accommodate the tube s installation. 

Btu/ (hr) (ft ) (°F) or, heat transfer film coefficient between the insulated or bare pipe and air see Figure 10-171 assume 6 = 0.90 and ambient air = 70°F = surface coefficient of heat transfer,... 

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. 

Inside diameter of tube Velocity Mass velocity Film coefficient of heat transfer h ... 

Radiation arrives at a grey surface of emissivity 0.75 al a constant temperature of 400 K, at the rate of 3 kW/m2. What is the radiosity and the net rate of radiation transfer to the surface What coefficient of heat transfer is required to maintain the surface temperature at 300 K if the rear of the surface is perfectly insulated and the front surface is cooled by convective heat transfer to air at 295 K ... 

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 vessel contains 1 tonm (I Mg) of a liquid of specific heat capacity 4.0 kj/kg K. The vessel is heated by steam at 393 K which is fed to a cod immersed in the agitated liquid and heat is lost to the surroundings at 293 K from the outside o." the vessel. How long dots it take to heat the liquid from 293 to 353 K and what is the maximum temperature to which the liquid can be heated When the liquid temperature has reached 353 K, the steam supply is tinned off for 2 hours (7.2 ks and the vessel cools. How long will it take to reheat the material to 353 K The surface area of the coil is 0 5 m2 and the overall coefficient of heat transfer to the liquid may be taken as 600 W/m2 K. The outside area of Lie vessel is 6 m2 and the coefficient of heat transfer to the surroundings may be taken as 10 W/m2 K. 

Estimate the heat transfer area required for the system considered in Examples 9.1 and 9.36. assuming that no data on the overall coefficient of heat transfer are available. 

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