Pressure Drop and Heat Transfer in a Single-Phase Flow

3 Pressure Drop and Heat Transfer in a Single-Phase Flow 

Many correlations have been proposed in literature for the friction factor and heat transfer, based on experimental investigations on liquid and gas flow in microchannels. Garimella and Sobhan (2003) presented a comprehensive review of these investigations conducted over the past decade. 

According to Schlichting and Gersten s (2000) equation, the friction factor is  

For developed laminar flow in smooth channels of t/h 1 mm, the product ARe = const. Its value depends on the geometry of the channel. For a circular pipe ARe = 64, where Re = Gdh/v is the Reynolds number, and v is the kinematic viscosity. 

Transition from laminar to turbulent flow occurs when the friction factor exceeds the low ARe range. In Fig. 2.20a the results obtained for a mbe of diameter 705 pm by Maynes and Webb (2002) are compared against the value accepted for laminar flow A = 64/Re. Based on the above data, one can conclude that the transition occurs at Tie 2,100. 

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Experimental and numerical study of the pressure drop and heat transfer in a single-phase micro-channel heat sink by Qu and Mudawar (2002a,b) demonstrated that the conventional Navier-Stokes and energy equations can adequately predict the fluid flow and heat transfer characteristics. 

Pressure drop and heat transfer in a single-phase incompressible flow. According to conventional theory, continuum-based models for channels should apply as long as the Knudsen number is lower than 0.01. For air at atmospheric pressure, Kn is typically lower than 0.01 for channels with hydraulic diameters greater than 7 pm. From descriptions of much research, it is clear that there is a great amount of variation in the results that have been obtained. It was not clear whether the differences between measured and predicted values were due to determined phenomenon or due to errors and uncertainties in the reported data. The reasons why some experimental investigations of micro-channel flow and heat transfer have discrepancies between standard models and measurements will be discussed in the next chapters. 

Qu W, Mudawar I (2002) Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. Int J Heat Mass Transfer 45 2549-2565 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Ren L, Qu W, Li D (2001) Interfacial electro kinetic effects on liquid flow in micro-channels. Int J Heat Mass Transfer 44 3125-3134... 

T. S. Ravigururajan and A. E. Bergles, Development and Verification of General Correlations for Pressure Drop and Heat Transfer in Single-Phase Turbulent Flow in Enhanced Tubes, Experimental Thermal and Fluid Science (13) 55-70,1996. 

The geometry of coiled-tube heat exchangers can be varied widely to obtain optimum flow conditions for all streams and still meet heat transfer and pressure drop requirements. However, optimization of a coiled-tube heat exchanger design is very involved and complex. There are numerous variables, such as tube and shell flow velocities, tube diameter, tube pitch, and layer spacer diameter. Other considerations include single-phase and two-phase flow, condensation on either the tube or shell side, and boiling or evaporation on either the tube or shell side. Additional complications come into play when multicomponent streams are present, as in natural gas liquefaction, since mass transfer accompanies the heat transfer in the two-phase region. 

The data presented in the previous chapters, as well as the data from investigations of single-phase forced convection heat transfer in micro-channels (e.g., Bailey et al. 1995 Guo and Li 2002, 2003 Celata et al. 2004) show that there exist a number of principal problems related to micro-channel flows. Among them there are (1) the dependence of pressure drop on Reynolds number, (2) value of the Poiseuille number and its consistency with prediction of conventional theory, and (3) the value of the critical Reynolds number and its dependence on roughness, fluid properties, etc. 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

In two-phase flow, most investigations are carried out in one dimension in the steady state with constant flow rates. The system may or may not be isothermal, and heat and mass may be transferred either from liquid to gas, or vice versa. The assumption is commonly made that the pressure is constant at a given cross section of the pipe. Momentum and energy balances can then be written separately for each phase, and with the constraint that the static pressure drop, dP, is identical for both phases over the same increment of flow length dz, these balances can be added to give over-all expressions. However, it will be seen that the resulting over-all balances do not have the simple relationships to each other that exist for single-phase flow. 

Estimate thermofluid characteristics of liquid-vapor phase change and related heat transfer processes such as circulation rate in natural or forced internal or external fluid circulation, pressure drops, and single- and two-phase vapor-liquid flow conditions. The initial analysis should be based on a rough estimation of the surface area from the energy balance... 

Single-phase flow of either gas or liquid on the tube side is generally well represented by either the Colburn correlation or modified forms of the Dittus-Boelter relationships. Table 5.3 provides suggested heat transfer and corresponding pressure drop relationships for a coiled-tube heat exchanger with either banks of staggered or in-line tubes in the annulus space as detailed by Fig. 5.5. 

Currently the standard TRACE code heat transfer (Dittus-Boelter) and fluid pressure drop (Churchill and Moody) correlations are applied to the gas cooler. Use of the Churchill correlation and Moody curves, and mathematical representations of the curves, for calculation of the single-phase friction factor in a variety of flow-channel geometries is a common engineering practice. Information on the TRACE default correlations is available in the TRACE theory manual (Reference 12-9). A surface roughness of 2E-6 m is used with the TRACE single phase friction correlations. In order to match the HB24 pressure drop prediction, additional frictional flow factors are included in the hydraulic model. The TRACE model also includes plenums to provide a location to specify form loss factors for the gas cooler. The heat transfer and pressure drop correlations would have been updated as the cooler design was determined and as test data was collected. 

On the other hand Bao et al. (2000) reported that the measured heat transfer coefficients for the air-water system are always higher than would be expected for the corresponding single-phase liquid flow, so that the addition of air can be considered to have an enhancing effect. This paper reports an experimental study of non-boiling air-water flows in a narrow horizontal tube (diameter 1.95 mm). Results are presented for pressure drop characteristics and for local heat transfer coefficients over a wide range of gas superficial velocity (0.1-50m/s), liquid superficial velocity (0.08-0.5 m/s) and wall heat flux (3-58 kW/m ). 

The details of the specific features of the heat transfer coefficient, and pressure drop estimation have been covered throughout the previous chapters. The objective of this chapter is to summarize important theoretical solutions, results of numerical calculations and experimental correlations that are common in micro-channel devices. These results are assessed from the practical point of view so that they provide a sound basis and guidelines for the evaluation of heat transfer and pressure drop characteristics of single-phase gas-liquid and steam-liquid flows. 

R. F. Lopina and A. E. Bergles, Heat Transfer and Pressure Drop in Tape Generated Swirl Flow of Single-Phase Water, J. Heat Transfer (91) 434-442,1969. 

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