Heat-transfer coefficients accuracy

Liquid viscosity is one of the most difficult properties to calculate with accuracy, yet it has an important role in the calculation of heat transfer coefficients and pressure drop. No single method is satisfactory for all temperature and viscosity ranges. We will distinguish three cases for pure hydrocarbons and petroleum fractions ... 

It is assumed that process conditions and physical properties are known and the following are known or specified tube outside diameter D, tube geometrical arrangement (unit cell), shell inside diameter D shell outer tube limit baffle cut 4, baffle spacing and number of sealing strips N,. The effective tube length between tube sheets L may be either specified or calculated after the heat-transfer coefficient has been determined. If additional specific information (e.g., tube-baffle clearance) is available, the exact values (instead of estimates) of certain parameters may be used in the calculation with some improvement in accuracy. To complete the rating, it is necessary to know also the tube material and wall thickness or inside diameter. 

Typical film coefficients can be used to build rough overall heat transfer coefficients. This should suffice in most cases to establish that the design is within ballpark accuracy. Later, for final design, certain critical services will be checked in detail. Typical film resistances for shell and tube heat exchangers and overall heat transfer coefficients for air cooled heat exchangers are shown in Chapter 2, Heat Exchangers. 

This method for vertical thermosiphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients 30 percent, which is about the same range of accuracy for most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. See Figures 10-110 and 10-111. 

Whenever possible, streamline conditions of flow are avoided in heat exchangers because of the very low heat transfer coefficients which are obtained. With very viscous liquids, however, turbulent conditions can be produced only if a very high pressure drop across the plant is permissible. In the processing industries, streamline flow in heat exchangers is most commonly experienced with heavy oils and brines at low temperatures. Since the viscosity of these materials is critically dependent on temperature, the equations would not be expected to apply with a high degree of accuracy. 

In experiments of flow and heat transfer in micro-channels, some parameters, such as the Reynolds number, heat transfer coefficient, and Nusselt number, are difficult to obtain with high accuracy. The channel hydraulic diameter measurement error may play a very important role in the uncertainty of the friction factor (Hetsroni... 

Figure 6.31 compares the measured heat transfer coefficient by Lee and Mudawar (2005b) in two-phase flow of R-134a to predictions based on previous studies. The predictive accuracy of a correlation was measured by the mean absoiute error, defined as... 

There are 12 equations in all (overall material and energy balances side A and B energy balances coil 1 to 8 energy balances) and 36 variables. However, the heat transfer coefficients are not known with any great accuracy. Further, both the side and coil heat transfer coefficients depend on the fire-box temperature. It is therefore necessary to calculate values for the heat transfer coefficients from the data. This effectively reduces the number of independent equations to 11. 

The results show clearly that a much better design can be obtained with a variable heat transfer coefficient. The length of the original reactor is now at its upper bound, which translates into increased conversion of nitrogen to ammonia. This is reflected in the exit ammonia concentration of 23.93 mol %, a 15.2% increase over the initial value. Further, this also represents a 15.4% increase over the corresponding result with a constant U case. The final objective function value of 5.6359 denotes a 12.25% rise over the initial value. In addition, the accuracy of the approximation profiles and adequacy of the final element partitions are also evident. 

Since wall thicknesses of heat exchangers are relatively small and the accuracy of heat transfer coefficients may not be great, the ratio of radii in Eq. (8.21) often is ignored, so that the equation for the overall coefficient becomes simply... 

This Stanton number is then used in Eq. (5-125), (5-126), or (5-127) to calculate the heat-transfer coefficient. When calculating the enthalpies for use in the above relations, the total enthalpy must be used i.e., chemical energy of dissociation as well as internal thermal energy must be included. The reference-enthalpy method has proved successful for calculating high-speed heat transfer with an accuracy of better than 10 percent. 

Figure 11 shows a prediction by J. M. Healzer and W. M. Kays (private communication) of the heat-transfer coefficient (based on enthalpy difference) in an adiabatic rocket nozzle boundary-layer flow, made with an extended MVFN method, no chemical reactions being considered. The accuracy of this prediction attests to the value of such methods in contemporary engineering analysis. 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

Discussion Note that the heat losses prevent the plate temperature from rising above 33.4 C. Also, the combined heat transfer coefficient accounts for the effects of both convection and radiation, and thus it is very convenient to use in heat transfer calculations when its value is known with reasonable accuracy. 

The height of the cells fot a finite-difference solution of the temperature in the rectangular solid shown in Fig. P5-127 is oiic-lialf the cell width to improve the accuracy of the solution. If the left surface is exposed to air at 7, with a heat transfer coefficient of h, the correct finite-difference heat conduction energy balance for node 5 is... 

In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Saber.sky (1963)]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8-71 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with/for /> 4/sn,ooih [Norris (1970)1 and correlations developed specifically for rough tubes should be used when more accuracy is desired. 

The entry lengths for turbulent flow are typically short, often just 10 tube diameters long, and thus the Nusselt number determined for fully developed turbulent flow can be used approximately for the entire tube. This simple approach gives reasonable results for pressure drop and heat transfer for long tubes and conservative re.sults for short ones. Correlations for the friction and heat transfer coefficients for the entrance regions are available in the literature for better accuracy. 

The overall volumetric heat transfer coefficient is obtained by combining a gas and liquid coefficient. Woods provides a value of 3 kW/m °C for a typical volumetric overall heat transfer coefficient for a packed tower under the above conditions (see Table 3-18). For greater accuracy values for the individual gas and liquid volumetric heat transfer coefficient may be obtained using the relations... 

The heat transfer coefficients h are shown in Figures 3, 4, 5 and 6 plotted against AT - T - Tg. For small AT, accuracy is limited by thermocouple calibration error, which we estimate to be within 0.2 K. Thus, estimated errors in h range from 2 % at AT - 30 K, to ... 

Example 2.6 A steel plate with the material properties A = 15.0 W/Km and a = 3.75 10-6 m2/s is 28 = 270mm thick and has a constant initial temperature o At time to the plate is brought into contact with a fluid which has a temperature s < o that is constant with respect to time. The heat transfer coefficient at both surfaces of the plate is a = 75W/m2K. The temperatures during the cooling of the plate are to be numerically determined. Simple initial and boundary conditions were intentionally chosen, so that the accuracy of the finite difference method could be checked when compared to the explicit solution of the case dealt with in section 2.3.3. 

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