Transfer coefficients, pipe flow

Compute the process-side heat-transfer coefficient. The correlations for inside (process-side) heat-transfer coefficient in an agitated tank are similar to those for heat transfer in pipe flow, except that the impeller Reynolds number and geometric factors associated with the tank and impeller are used and the coefficients and exponents are different. A typical correlation for the agitated heat-transfer Nusselt number (ANu = htT/k) of a jacketed tank is expressed as... 

The heat transfer coefficient for flow of liquids and gases in pipes in turbulent regime can be estimated accurately by means of the equation ... 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

The pipe has also been used for the transfer of heat between two immiscible liquids in cocurrent flow. For hydrocarbon oil-water, the heat-transfer coefficient is given by... 

At a given Reynolds number, heat transfer coefficients of coils, particularly with turbulent flow, are higher than those of long, straight pipes, due to friction. This also applies to flow through an annular jacket with spiral baffling. 

To reduce the pressure drop, a batch reactor with a half-pipe jacket of length L and flowrate W can be partitioned into a two-zone jacket, each with a length L/2 and each supplied with W jacket flowrate. This doubles the jacket flow at a lower pressure drop in each zone. The flow in each zone can then be increased to increase the outside and overall heat transfer coefficients, which is similar to those of the single-zone jacket. 

Heat transfer through a pipe wall. A pipeline parr 15m long carries water. Its internal diameter d, is 34 mm and its external diameter is 42 mm. The thermal conductivity of the pipe X is 40 W m K". The pipeline is located outdoors, where the outdoor temperature Oao is -8 C. Determine the minimum flow velocity necessary in the pipe to prevent the pipe from freezing. The heat transfer coefficient inside the pipe is = 1000 W m K and outside the pipe = 5 W m" K aiid = 4 W m -K . The specific heat ca-... 

Heat transfer coefficient between a pipe and a wall. Water flows in a pipe d =15 mm) with a velocity of v = 1.0 m s. The mean temperature of water is 0 , = 15 °C, and the wall temperature 6 = 50 °C. Calculate the heat transfer coefficient away from the pipe inlet. For water the properties are... 

Figure 10-50C. Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm . A fluid inside pipes/tubes, turbulent flow only. Note h= average film coefficient, Btu/hr-ft -°F d = inside tube diameter, in. G = mass velocity, Ib/sec/ft v = fluid velocity, ft/sec k = thermal conductivity, Btu/hr (ft )(°F/ft) n, = viscosity, lb/(hr)(ft) Cp = specific heat, Btu/(lb)(°F). (Used by permission Engineering Manual for Dowtherm Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

For the inlet length of a pipe in which the boundary layers are forming, the equations in the previous section will give an approximate value for the heat transfer coefficient. It should be remembered, however, that the flow in the boundary layer at the entrance to the pipe may be streamline and the point of transition to turbulent flow is not easily defined. The results therefore are, at best, approximate. 

In fully developed flow, equations 12.102 and 12.117 can be used, but it is preferable to work in terms of the mean velocity of flow and the ordinary pipe Reynolds number Re. Furthermore, the heat transfer coefficient is generally expressed in terms of a driving force equal to the difference between the bulk fluid temperature and the wall temperature. If the fluid is highly turbulent, however, the bulk temperature will be quite close to the temperature 6S at the axis. 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy. Indicate the assumptions which are made and the conditions under which you would expect it to apply closely. Air at 320 K and atmospheric pressure is flowing through a smooth pipe of 50 mm internal diameter, and the pressure drop over a 4 m length is found to be 150 mm water gauge. By how much would you expect the air temperature to fall over the first metre if the. wall temperature there is 290 K ... 

A 50% glycerol-water mixture is flowing at a Reynolds numher of 1500 through a 25 mm diameter pipe. Plot the mean value of the heat transfer coefficient as a function of pipe length assuming that ... 

A bare thermocouple is used to measure the temperature of a gas flowing through a hot pipe. The heat transfer coefficient bet ween the gas and the thermocouple is proportional to the 0.8 power of the gas velocity and the heat transfer by radiation from the walls to the thermocouple is proportional to the temperature difference. 

The Reynolds number of a gas flowing at 2.5 kg/nrs through a smooth pipe is 20,000. If the specific heat of the gas at constant pressure is 1.67 kJ/kg K, what will the heat transfer coefficient be ... 

An air stream at approximately atmospheric temperature and pressure and containing a low concentration of carbon disulphide vapour is flowing at 38 m/s through a series of 50 mm diameter tubes. The inside of the tubes is covered with a thin film of liquid and both heat and mass transfer are taking place between the gas stream and the liquid film. The film heat transfer coefficient is found to be 100 W/mzK. Using a pipe friction chan and assuming the tubes to behave as smooth surfaces, calculate ... 

The local heat transfer coefficients on the surface of the pipe may not be uniform, though the surface is heated by uniform heat flux. This irregularity is due to the distribution of the air and liquid phase in the pipe. The temperature distribution along the pipe perimeter shows a maximum at the top and a minimum at the bottom of the pipe. In Fig. 5.36a-c, the heat transfer coefficients are plotted versus angle 0. These results were compared to simultaneous visual observations of the flow pat-... 

Figure 5.37a-d illustrates a typical temperature distribution in the range of the angle 0 < 0 < 180° (where 0 = 0° is at the top of the tube). The heat flux was q = 8,000 W/m, the superficial gas velocity was Uqs = 36 m/s. The superficial liquid velocities were 0.016, 0.027, 0.045 and 0.099 m/s, respectively. The flow moves from the right to the left. The color shades are indicative of the wall temperature. Comparison to simultaneous visual observations shows that the distribution of heat transfer coefficient at Uls = 0.0016 m/s corresponds to dryout on the upper part of the pipe. 

Experiments in annular and slug flow were carried out also by Ghajar et al. (2004). The test section was a 25.4 mm stainless steel pipe with a length-to-diameter ratio of 100. The authors showed that heat transfer coefficient increases with increase in liquid superficial velocity not only in annular, but also in slug flow regimes. 

In Fig. 5.39a-d the local heat transfer coefficients derived in the horizontal tube are compared to those obtained in the 8° upward inclined pipe and presented by Hetsroni et al. (2006). The results show a clear improvement of the heat transfer coefficient with the pipe inclination. Taitel and Dukler (1976) showed that the flow regimes are very sensitive to the pipe inclination angle. In the flow regime maps presented in their work, the transition from stratified to annular flow in the inclined tube occurs for a smaller air superficial velocity than for the case of the horizontal tube. 

The pressure-drop and heat-transfer coefficients in empty tube reactors can be calculated using the methods for flow in pipes given in Volume 1. 

Below a Reynolds number of about 2000 the flow in pipes will be laminar. Providing the natural convection effects are small, which will normally be so in forced convection, the following equation can be used to estimate the film heat-transfer coefficient ... 

Chen s method was developed from experimental data on forced convective boiling in vertical tubes. It can be applied, with caution, to forced convective boiling in horizontal tubes, and annular conduits (concentric pipes). Butterworth (1977) suggests that, in the absence of more reliable methods, it may be used to estimate the heat-transfer coefficient for forced convective boiling in cross-flow over tube bundles using a suitable cross-flow correlation to predict the forced-convection coefficient. Shah s method was based on data for flow in horizontal and vertical tubes and annuli. 

The heat transfer coefficient at the inside wall and pressure drop through the coil can be estimated using the correlations for flow through pipes see Section 12.8 and Volume 1, Chapters 3 and 9. Correlations for forced convection in coiled pipes are also given in the Engineering Sciences Data Unit Design Guide, ESDU 78031 (2001). 

The design of devices to promote cocurrent drop flows for heating or cooling a two-phase system, or for direct-contact heat transfer between two liquids, is difficult. The study by Wilke et al. (W7) is typical of the approach frequently used to analyze these processes. Wilke et al. described the direct-contact heat transfer between Aroclor (a heavy organic liquid) and seawater in a 3-in. pipe. No attempt was made to describe the flow pattern that existed in the system. The interfacial heat-transfer coefficient was defined by... 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3. Determine the volume required to produce 2 million lb of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 hr annually with 97% conversion of the A fed to the reactor. The feed enters at 163 C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperature of 160 °C. The overall heat transfer coefficient based on the... 

In order to investigate the dependence of a fast reaction on the nature of the metal, Iwasita et al. [3] measured the kinetics of the [Ru(NH,3)6]2+/3+ couple on six different metals. Since this reaction is very fast, with rate constants of the order of 1 cm s-1, a turbulent pipe flow method (see Chapter 14) was used to achieve rapid mass transport. The results are summarized in Table 8.1 within the experimental accuracy both the rate constants and the transfer coefficients are independent of the nature of the metal. This remains true if the electrode surfaces axe modified by metal atoms deposited at underpotential [4]. It should be noted that the metals investigated have quite different chemical characteristics Pt, and Pd are transition metals Au, Ag, Cu are sd metals Hg and the adsorbates T1 and Pb are sp metals. The rate constant on mercury involved a greater error than the others... 

In Figure 8.3, the oxygen transfer coefficient, KLa, the flow velocity, u, the bulk water DO concentration and the DO consumption rate of the biofilm, ry, are all plotted versus the flow, Q, under steady state conditions in a gravity sewer pipe under the conditions given. 

If the pipe fluid continues to flow, then forced convection with the moving fluid providing very effective cooling to the pipe. The heat transfer coefficient is then high, and depends on the flow velocity. 

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