# Convection Heat Transfer Coefficient Modeling Biology Essay

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Modern research development for refrigeration systems that is the investigation of alternative technologies to apply for the refrigeration, such as in cooling electronic components, vehicles, space shuttles, and household refrigerators and also air condition for human. Thermoacoustic refrigerator is a class of a new cooling technology, which offers a revolutionary solution for the current problems of energy consumption and also able to reduce environmental impact. For operating of this refrigeration technology is using the acoustic energy and air at atmospheric pressure or other inert gases such as the helium as working fluid to create the temperature gradient across a device which is called the stack to migration heat from the low temperature reservoir to ambient at a higher temperature. This is quite simple to use when compare with the current vapor compression system which use the shaft power and a Freon to operate as above.

The development of the thermoacoustic system has accelerated since a theoretical model was developed in the 1988 and became available to determine the power and heat fluxes in thermoacoustics devices. Although the based on the thermoacoustic principle and some standing-wave thermoacoustic refrigerator prototypes showed that higher efficiencies are feasible if high power density is used or if an optimum mixture of inert gasses is used. Nevertheless, the development in a class of thermoacoustic refrigeration systems is not an easy issue to improving efficiency for refrigeration applications. Due to the one major disadvantage and bottleneck to development of this system is that it requires the use of two heat exchangers placed on each side of the stack surface for the heat transfer process. Hot and cold heat exchangers in the thermoacoustic refrigerator are responsibility to transfer heat from the oscillatory of gas to external heat source or sink. So, the behavior of gas in a thermoacoustic resonator is identified to oscillatory flow which is a form of a reciprocating flow. Therefore, the steady flow design methodology for the compact heat exchangers, such as LMTD method or effectiveness-NTU method cannot be applied directly. Namely, if heat exchanges of the thermoacoustic system is designed in a way that without the optimal method for designing or absent knowledge of the heat transfer characteristics in forms of oscillating flow at heat exchangers, it may be lead to reduce in the number of the gas particles enter into the stack due to the gas particles blockage. This may cause thermal performance problems of the thermoacoustic refrigerator. Therefore, the evaluation of the heat transfer coefficient of the heat exchanger in oscillating flow and develop to a new heat transfer correlation in term of dimensionless parameters is important with the system performance. Because it can be helpful to understand heat transfer characteristics at the heat exchanger and assist in determining the optimum design of the heat exchanger for the thermoacoustic refrigerator.

## OBJECTIVES

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To analyze the factors that influences the convection heat transfer coefficient in oscillatory flows through the heat exchanger of the thermoacoustic refrigerator.

To develop a mathematical model for predicting the convection heat transfer coefficient of heat exchangers in oscillatory flows for the thermoacoustic refrigerator.

## LITERATURE REVIEW

In 1980, Nikolaus Rott presented sound theoretical foundation applicable to the study of both thermoacoustic heat pump and refrigerators and prime movers in the low amplitude regime (Swift, G. W., 1988). Rott's theory is still the main mathematical descriptions used in the study of thermoacoustic systems. After that, in 1986, the first a standing-wave thermoacoustic refrigerator prototype was constructed based on Rott's theory by Hofler. This prototype can be created the maximum second law efficiency, defined as the ratios of coefficient of performance (COP) and the Canot COP, was 12.6%. In addition, in his Ph.D. work, the optimum quarter wavelength resonance tube was developed to solve the performance problem of a standing-wave thermoacoustic refrigerator. This resonance tube consists of a small diameter tube portion, a large diameter tube portion and a sphere bulb. The smaller diameter tube can be helped reduce the losses that are proportional to the surface area of the resonance tube.

Swift, G. W.(1988) has produced an inclusive article addressing important aspects of thermoacoustic engines and its applications. This article is provided a principal design devices based on the linearization of the equation of mass, momentum and energy conservation. This linear theory, based on Rott's work, is the basis for the design methodology of all the thermoacoustic devices built so far.

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Wetzel, M. and C. Herman, (1997) developed an algorithm for optimizing the design of thermoacoustic refrigerators. They used a short stack boundary approximation to obtain an optimized of the thermoacoustic core or stack, which the results of the short stack boundary approximation, developed by Swift, G. W., (1988), yields equations of the enthalpy flux and work flux. Also, they found parameters of 19 independent from these equations. From the results of calculated on 19 design variable, the performance of thermoacoustic refrigerator depend on stack length, stack position, mean pressure and Prandtl number. In addition, they claim that one reason that these efficiencies have not yet been achieved in devices built to date is the poor performance of the heat exchangers attached at both ends of the stack.

Poese and Garrett, (2000) performed performance measurements on a small thermoacoustic refrigerator driven at drive ratios up to 6%. The results of measurements are compared to a DELTAE computer model of the low-amplitude. This pressure ratio corresponded to 30 W of cooling power which was five times as large as reported for the Space ThermoAcoustic Refrigerator (STAR) in 1993

In 2002, Tijani, M. E. H. et al., published two articles which is presented the method optimization for the design device(Tijani, M. E. H. et al., 2002a), which is similar to methods of Wetzel, M. and C. Herman (1997), and decribed the construction of a small standing wave thermoacoustic refrigerators(Tijani, M. E. H. et al., 2002b). Their thermoacoustic refrigerator prototype got more influence from Hofler, T. J., (1986) and Swift, G. W., (1988). However, its resonator tube is modified by adjusting a taper angle of instead of the sphere bulb designed by Hofler, T. J. They claim that their a new buffer volume, which has taper angle of , can be reduced irreversibilities. Tijani achieved temperature as low as -65 with a cooling capacity 4 W. In addition, in Tijani's Ph.D work (2001), the effect of some importance parameters, such as the spacing of the stack plate and the Prandtl number were studied.

Russell, D. A. and P. Weibull.,(2002) built a low cost thermoacoustic refrigerator for demonstration purposes. This thermoacoustic refrigerator was built from a boxed loudspeaker, acrylic tubing and sheet, a roll of 35 mm film, fishing line, an aluminium plug, and two thermocouples. Temperature differences across the stack of more than 15°C were achieved after running the thermoacoustic refrigerator for several minutes. However, their thermoacoustic refrigerator prototype was lack the heat exchangers

Tu, Q. et al., (2005) studied the frequency characteristic of loudspeaker thermoacoustic refrigerator. The prototype machine, which is 38 mm in diameter and 437.5 mm length, has the length of hot heat exchanger stack and cold heat exchanger are 2 mm,46 mm, 2mm respectively. The results show that the stack, working fluid, resonator length and loudspeaker have influence on frequency of system.

Herman, C. and Z. Travnicek,(2006) described the thermodynamic and heat transfer issues relevant in improving the performance of the thermoacoustic system. They shows that the maximum COP depended on the acoustic power efficiency, electroacoustic efficiency and effectiveness of the cold heat exchanger. In addition, small Prandtl number values able to lead to high values of COP in thermoacoustic refrigerators.

Nsofor, E. C. and A. Ali, (2009) performed experiments on performance of thermoacoustic refrigerator. They design their thermoacoustic refrigerator is similar to Tijani's prototype. The stack of 59 mm diameter was tested on pressures of 3 to 5 bar of helium gas and 250 to 500 Hz of the frequency. The result indicated that the high pressure alone in the system does not necessarily in higher cooling load and temperature at the ends of stack as it varies with frequency for constanst mean pressure in the system.

Assawamartbunlue, K. and P. Kanjanawadee, (2009) tested a miniature thermoacoustic refrigerator at difference of the plate spacing, diameter and length of the stack. The shape of the stack is spiral. This prototype used the air as working fluid without the hot and cold heat exchangers mounted in a resonator tube. They claim that plate spacing of the stack is very important on performance of thermoacoustic refrigerator. Whereas the length of the stack is not much important on performance of thermoacoustic refrigerator.

Wantha, C. and K. Assawamartbunlue, (2011) have performed experiments to investigate the factors have affected on temperature difference of a stack in the standing-wave thermoacoustic refrigerator. They found that the resonance frequency is the factor that influence on the temperature difference of the stack. But the experimental results shown the actual resonance frequency to build the thermoacoustic effect on the stack is not equal to the basic formula for calculation in a half-wave length of the sound wave. The resonance tube length is elongated to compensate for some effects that occur in the tube of thermoacoustic refrigerator.

## Heat transfer at heat exchangers

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Examples of our workThe performance of standing-wave thermoacoustic refrigerators is still limited; one reason for this is that the lacking of the knowledge of heat transfer in oscillating flow, particularly heat transfer between the acoustic wave and the heat exchangers at heat exchanger-stack junction.

Swift, G. W.,(1988) recommends an optimum width for the heat exchangers should be matched with peak-to-peak displacement amplitude. The convective heat transfer coefficient between gas and solid wall of thermoacoustic heat exchangers can be estimated using a basic simple boundary layer conduction heat transfer model is suggested by Swift, G.W. The convective coefficient should be roughly equal to:

(1)

Where is the thermal conductivity of the gas and is the thermal penetration depth.

Ishikawa, H. and P. A. Hobson, (1996) used the second law of thermodynamics to analysis the optimum heat exchangers in a thermoacoustic engine. They found an optimum dimensionless expression of its surface area by minimizing entropy generation at the heat exchangers due to the thermodynamic irreversibility, viscous and thermoacoustic losses.

Wetzel, M. and C. Herman (1999, 2000) performed experiments to estimate a local heat fluxes at edge of a single stack plate and visualized the time-dependent temperature profile in oscillating flow using holographic interferometry (HI) combined with high-speed cinematography. The results showed that the heat transfer process is different between in oscillating flow and steady flow.

Poese and Garrett (2000) proposed a modified a basic correlation of the laminar flow over length of the flat plate. The modified correlation was obtained by assumption that the time-averaged value of convective heat transfer coefficient was relevant to heat transfer in oscillating flow, and averaging a laminar correlation during half a period.

Paek, I.(2005) estimated heat transfer coefficient for microchannel heat exchangers in standing wave thermoacoustic refrigerator prototype. This prototype is approximately one half-wavelength long. The cross sectional area of the stack section was 200 cm2. The system was driven by a moving-magnet CFIC Model B-300 electro-mechanical transducer. The experiments were performed in three helium and argon mixture (44%He, 33%He, 22%He) with three different mean pressures (0.67MPa, 1.33MPa, 2MPa). The results showed that the Colburn-j factor obtained from boundary layer conduction model did not accurately predict the heat transfer coefficient. Results from the study yield the expression:

(2)

For about, where is Colburn-j factor determined from measurements in oscillating flow and is Reynolds number of the particle velocity.

Piccolo, A. and G. Pistone, (2006) have performed numerical investigations to estimation of heat transfer coefficient and optimal length for the parallel-plate heat exchanger of thermoacoustic systems. Their results showed that the optimal length of the parallel-plate heat exchanger is a function of plate spacing, and also concluded that the length of the exchanger should match the peak-to-peak acoustic displacement amplitude. Then after that, in (Piccolo, A., 2011)(Piccolo, A., 2011)(Piccolo, A., 2011)(Piccolo, A., 2011)(Piccolo, A., 2011)(Piccolo, A., 2011)(Piccolo, A., 2011)2011, Piccolo, A,(2011) performed numerical analysis again with parallel-plate heat exchanger through 2D numerical model based on the linear thermoacoustic theory. The results showed that their Colburn-j factor from the numerical model was compared with experiments data ,it can be predicted within 36% and 49% respectivily at moderate and high acoustic Reynolds numbers.

Akhavanbazaz, M. et al., (2007) studied the impact of heat exchanger surface area on the performance of a thermoacoustic refrigerator. They build the spiral and letter M shapes of heat exchangers and placed them at the ends of the stack. Diameter of the stack was set equal to internal diameter of the resonance tube was 6.3 cm. The experiments show that the gas blockage has effect on the temperature difference across the stack ends. The larger thermal contact area or higher gas blockage increases the heat exchanger between the fluid of heat exchangers and the stack, but increases the work input to the stack and reduces the cooling power.

Nsofor, E. C. et al., (2007) constructed a heat exchanger with the same shape as a parallel plate stack. The inside and outside diameter of the heat exchanger tube are 59mm and 65 mm respectively, and the width of copper fins is 6.6 mm and 0.15 mm thick. This heat exchanger was only located at the hot side of the resonator and the experiments were performed in six different mean pressures in pure helium gas. They developed a model for this heat exchanger and tested it. The results showed that the heat transfer coefficient for the heat exchanger is higher under greater mean pressures and at the resonant frequency where the highest dynamic pressure takes place. They assume that this higher heat transfer coefficient is due to a greater number of gas particles being in contact with the heat exchanger surface. A correlation of Nusselt number representing the data within 18% was proposed.

(3)

For , at hot end of the stack.

From the literature review on a thermoacoustic performance shows that the enhancement of standing wave thermoacoustic refrigerator performances is limited understanding of factors involved in the heat transfer at heat exchangers. Several researches shows that there is no comprehensive analytical on heat transfer at heat exchangers random porous medium stack using porous media modeling

Therefore, the enhancement of thermoacoustic refrigerator performances requires a better understanding of such flows, particularly at high amplitudes by many factors such as the efficiency of acoustic driver

Ben and Jerry's Ice Cream funded a project at the Pennsylvania State University to make a travelling-wave thermoacoustic refrigerator to use in a commercial application was an ice-cream cabinet. This refrigerator has a cooling capacity of 119 W and an overall COP of 19% of Carnot's.

However, several researches show that the linear thermoacoustic theory is limited at low amplitude acoustic pressure. Namely, at high values of the drive ratio () nonlinear effect appear at end of the stack and has effect on efficiency of thermoacoustic systems. The enhancement of thermoacoustic refrigerator performances requires a better understanding of such flows, particularly at high amplitudes.

This papers still lack a study of heat exchangers

Thermoacoustic theory

Akhavanbazaz, M., M.H.K. Siddiqui and R.B. Bhat. 2007. The Impact of Gas Blockage on the Performance of a Thermoacoustic Refrigerator. Experimental Thermal and Fluid Science 32 (1): 231-239.

Assawamartbunlue, K. and P. Kanjanawadee. 2009. Experimental Demonstration of Thermoacoustic Cooling. Journal of Research in Engineering and Technology 6 (1): 1-24.

Herman, C. and Z. Travnicek. 2006. Cool Sound: The Future of Refrigeration? Thermodynamic and Heat Transfer Issues in Thermoacoustic Refrigeration. Heat and Mass Transfer 42 (6): 492-500.

Hofler, T.J. 1986. Thermoacoustic Refrigerator Design and Performance. Ph.D Thesis, University of California at San Diego.

Ishikawa, H. and P.A. Hobson. 1996. Optimisation of Heat Exchanger Design in a Thermoacoustic Engine Using a Second Law Analysis. International Communications in Heat and Mass Transfer 23 (3): 325-334.

Nsofor, E.C. and A. Ali. 2009. Experimental Study on the Performance of the Thermoacoustic Refrigerating System. Applied Thermal Engineering 29 (13): 2672-2679.

Nsofor, E.C., S. Celik and X. Wang. 2007. Experimental Study on the Heat Transfer at the Heat Exchanger of the Thermoacoustic Refrigerating System. Applied Thermal Engineering 27 (14-15): 2435-2442.

Paek, I. 2005. Performance Characterization of Thermoacoustic Cooler Components and Systems. Ph.D. Dissertation, Purdue University.

Piccolo, A. 2011. Numerical Computation for Parallel Plate Thermoacoustic Heat Exchangers in Standing Wave Oscillatory Flow. International Journal of Heat and Mass Transfer 54 (21-22): 4518-4530.

Piccolo, A. and G. Pistone. 2006. Estimation of Heat Transfer Coefficients in Oscillating Flows: The Thermoacoustic Case. International Journal of Heat and Mass Transfer 49 (9-10): 1631-1642.

Poese and Garrett. 2000. Performance Measurements on a Thermoacoustic Refrigerator Driven at High Amplitudes. J Acoust Soc Am 107 (5 Pt 1): 2480-2486.

Russell, D.A. and P. Weibull. 2002. Tabletop Thermoacoustic Refrigerator for Demonstrations. American Journal of Physics 70 (12): 1231-1233.

Swift, G.W. 1988. Thermoacoustic Engines. The Journal of the Acoustical Society of America 84 (4): 1145-1180.

Tijani, M.E.H. 2001. Loudspeaker-Driven Thermo-Acoustic Refrigeration. Ph.D Dissertation, Eindhoven University of Technology.

Tijani, M.E.H., J.C.H. Zeegers and A.T.A.M. de Waele. 2002a. Design of Thermoacoustic Refrigerators. Cryogenics 42 (1): 49-57.

Tijani, M.E.H., J.C.H. Zeegers and A.T.A.M. de Waele. 2002b. Construction and Performance of a Thermoacoustic Refrigerator. Cryogenics 42 (1): 59-66.

Tu, Q., V. Gusev, M. Bruneau, C. Zhang, L. Zhao and F. Guo. 2005. Experimental and Theoretical Investigation on Frequency Characteristic of Loudspeaker-Driven Thermoacoustic Refrigerator. Cryogenics 45 (12): 739-746.

Wantha, C. and K. Assawamartbunlue. 2011. The Impact of the Resonance Tube on Performance of a Thermoacoustic Stack. Frontiers in Heat and Mass Transfer 2 (4): 1-8.

Wetzel, M. and C. Herman. 1997. Design Optimization of Thermoacoustic Refrigerators. International Journal of Refrigeration 20 (1): 3-21.

Wetzel, M. and C. Herman. 1999. Experimental Study of Thermoacoustic Effects on a Single Plate Part Ii : Heat Transfer. Heat and Mass Transfer 35 (6): 433-441.

Wetzel, M. and C. Herman. 2000. Experimental Study of Thermoacoustic Effects on a Single Plate Part I: Temperature Fields. Heat and Mass Transfer 36 (1): 7-20.