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Research Papers: Heat and Mass Transfer

Simulating Heat Transfer Through Periodic Structures With Different Wall Temperatures: A Temperature Decomposition Method

[+] Author and Article Information
Ping Li

Bharti School of Engineering,
Laurentian University,
935 Ramsey Lake Road,
Sudbury, P3E 2C6 ON, Canada

Junfeng Zhang

Bharti School of Engineering,
Laurentian University,
935 Ramsey Lake Road,
Sudbury, P3E 2C6 ON, Canada
e-mail: jzhang@laurentian.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 11, 2017; final manuscript received May 1, 2018; published online July 23, 2018. Assoc. Editor: Guihua Tang.

J. Heat Transfer 140(11), 112002 (Jul 23, 2018) (9 pages) Paper No: HT-17-1746; doi: 10.1115/1.4040257 History: Received December 11, 2017; Revised May 01, 2018

To simulate heat transfer processes through periodic devices with nonuniform wall temperature distributions, we propose to decompose the regular temperature into two parts: namely the transient part and the equilibrium part. These two parts can be solved independently under their individual wall and inlet/outlet conditions. By calculating the flow field and the two component functions in one periodic module, one can easily generate the distributions of regular temperature in one or multiple modules. The algorithm and implementation are described in details, and the method is discussed thoroughly from mathematical, physical, and numerical aspects. Sample simulations are also presented to demonstrate the capacity and usefulness of this method for future simulations of thermal periodic flows using various numerical schemes.

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References

Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2006, Fundamentals of Heat and Mass Transfer, Wiley, New York.
Soumerai, H. , 1978, Practical Thermodynamics Tools for Heat Exchanger Design Engineers, Wiley, New York.
Ahmed, M. A. , Yaseen, M. M. , and Yusoff, M. Z. , 2017, “Numerical Study of Convective Heat Transfer From Tube Bank in Cross Flow Using Nanofluid,” Case Stud. Therm. Eng., 10, pp. 560–569. [CrossRef]
Adhama, A. M. , Mohd-Ghazali, N. , and Ahmad, R. , 2013, “Thermal and Hydrodynamic Analysis of Microchannel Heat Sinks: A Review,” Renewable Sustainable Energy Rev., 21, pp. 614–622. [CrossRef]
Wang, R. , Wang, W. , Wang, J. , and Zhu, Z. , 2018, “ Analysis and Optimization of Trapezoidal Grooved Microchannel Heat Sink Using Nanofluids in a Micro Solar Cell,” Entropy, 20(1), p. 9. [CrossRef]
Ahmed, M. A. , Yusoff, M. Z. , Ng, K. C. , and Shuaib, N. H. , 2015, “Numerical Investigations on the Turbulent Forced Convection of Nanofluids Flow in a Triangular-Corrugated Channel,” Case Stud. Therm. Eng., 6, pp. 212–225. [CrossRef]
Patankar, S. V. , Liu, C. H. , and Sparrow, E. M. , 1977, “Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area,” ASME J. Heat Transfer, 99(2), pp. 180–186. [CrossRef]
Bahaidarah, H. M. S. , Anand, N. K. , and Chen, H. C. , 2005, “ Numerical Study of Heat and Momentum Transfer in Channels with Wavy Walls,” Numer. Heat Transfer A, 47(5), pp. 417–439. [CrossRef]
Stalio, E. , 2002, “ Direct Numerical Simulation of Heat Transfer Enhancing Surfaces,” Ph.D. thesis, University of Bologna, Bologna, Italy.
Stalio, E. , and Piller, M. , 2007, “Direct Numerical Simulation of Heat Transfer in Converging–Diverging Wavy Channels,” ASME J. Heat Transfer, 129(7), pp. 769–777. [CrossRef]
Wang, G. , and Vanka, S. P. , 1995, “Convective Heat Transfer in Periodic Wavy Passages,” Int. J. Heat Mass Transfer, 38(17), pp. 3219–3230. [CrossRef]
Ramgadia, A. G. , and Saha, A. K. , 2013, “Numerical Study of Fully Developed Flow and Heat Transfer in a Wavy Passage,” Int. J. Therm. Sci., 67, pp. 152–166. [CrossRef]
Wang, Z. , Shang, H. , and Zhang, J. , 2017, “Lattice Boltzmann Simulations of Heat Transfer in Fully Developed Periodic Incompressible Flows,” Phys. Rev. E, 95(6–1), p. 063309. [CrossRef] [PubMed]
Angeli, D. , Stalio, E. , Corticelli, M. A. , and Barozzi, G. S. , 2015, “A Fast Algorithm for Direct Numerical Simulation of Natural Convection Flows in Arbitrarily-Shaped Periodic Domains,” J. Phys. Conf. Ser., 655, p. 012054. [CrossRef]
Greiner, M. , Faulkner, R. J. , Van, V. T. , Tufo, H. M. , and Fischer, P. F. , 2000, “Simulations of Three-Dimensional Flow and Augmented Heat Transfer in a Symmetrically Grooved Channel,” ASME J. Heat Transfer, 122(4), pp. 653–660. [CrossRef]
Adachi, T. , and Uehara, H. , 2001, “Correlation Between Heat Transfer and Pressure Drop in Channels With Periodically Grooved Parts,” Int. J. Heat Mass Transfer, 44(22), pp. 4333–4343. [CrossRef]
Zhang, J. , 2011, “Lattice Boltzmann Method for Microfluidics: Models and Applications,” Microfluid. Nanofluid., 10(1), pp. 1–28. [CrossRef]
Chen, Q. , Zhang, X. , and Zhang, J. , 2013, “Improved Treatments for General Boundary Conditions in the Lattice Boltzmann Method for Convection-Diffusion and Heat Transfer Processes,” Phys. Rev. E, 88(3), p. 033304. [CrossRef]
Niceno, B. , and Nobile, E. , 2001, “Numerical Analysis of Fluid Flow and Heat Transfer in Periodic Wavy Channels,” Int. J. Heat Fluid Flow, 22(2), pp. 156–157. [CrossRef]
Chen, Q. , Zhang, X. , and Zhang, J. , 2015, “Effects of Reynolds and Prandtl Numbers on Heat Transfer Around a Circular Cylinder by the Simplified Thermal Lattice Boltzmann Model,” Commun. Comput. Phys., 17(4), pp. 937–959. [CrossRef]
Cao, Y. , and Zhang, Y. , 2017, “Investigation on the Natural Convection in Horizontal Concentric Annulus Using the Variable Property-Based Lattice Boltzmann Flux Solver,” Int. J. Heat Mass Transfer, 111, pp. 1260–1271. [CrossRef]
Saha, A. K. , and Acharya, S. , 2005, “Unsteady RANS Simulation of Turbulent Flow and Heat Transfer in Ribbed Coolant Passages of Different Aspect Ratios,” Int. J. Heat Mass Transfer, 48(23–24), pp. 4704–4725. [CrossRef]
He, X. , Chen, S. , and Doolen, G. D. , 1998, “A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit,” J. Comput. Phys., 146(1), pp. 282–300. [CrossRef]
Succi, S. , 2001, The Lattice Boltzmann Equation, Oxford University Press, Oxford, UK.
Guo, Z. , and Shu, C. , 2013, Lattice Boltzmann Method and Its Applications in Engineering, World Scientific Publishing, Singapore. [CrossRef]
Li, Q. , Luo, K. , Kang, Q. , He, Y. , Chen, Q. , and Liu, Q. , 2016, “Lattice Boltzmann Methods for Multiphase Flow and Phase-Change Heat Transfer,” Prog. Energy Combust. Sci., 52, pp. 62–105. [CrossRef]
Yin, X. , and Zhang, J. , 2012, “An Improved Bounce-Back Scheme for Complex Boundary Conditions in Lattice Boltzmann Method,” J. Comput. Phys., 231(11), pp. 4295–4503. [CrossRef]

Figures

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Fig. 1

Schematic illustration of the periodic flow passage. The vertical dashed lines are plotted to divide the flow passage into individual periodic modules. The coordinate system is set with the x direction in the flow direction and the y direction in the transverse direction.

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Fig. 2

Velocity (a) and temperature (b) distributions from the long-channel direct simulation, and the bulk temperature Tm (c) and relative errors ET and Eu (d) along the channel

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Fig. 3

Comparison of temperature profiles from the long-channel direct simulation (solid lines) and the decomposition method prediction (dashed lines) at several streamwise locations as shown in labels: (a) x/H = 0.5, (b) x/H = 1, (c) x/H = 1.5, (d) x/H = 2, (e) x/H = 3, (f) x/H = 4, (g) x/H = 8, (h) x/H = 12, and (i) x/H = 20

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Fig. 4

The temperature distribution over three periodic modules (a) and the streamwise variations (b) at y=−L/12 (top), 0 (middle), and L/12 (bottom). The background color patches in (a) and the lines in (b) are from the three-module simulation, and the isothermal contour lines in (a) and the symbols in (b) are from the one-module simulation. The vertical dashed lines in (b) are displayed to indicate individual periodic modules.

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Fig. 5

The simulated flow streamlines (a), function θ (b), and function γ (c) using one periodic module. The cylinders are colored to indicate the surface temperature distributions given in Eq. (36) for the hot and cold sides.

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Fig. 6

Comparison of the simulated velocity (a) and temperature (b) profiles for the two-cylinder system using three different resolutions D = 20 (solid lines), 40 (dashed lines), and 80 (dash-dotted lines) at x=3H/4. The difference among these three sets of results is negligible.

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Fig. 7

Temperature fields ((a) and (b)) in the 10H-long domain and the temperature variations (c) at three different vertical positions: y=3H/16 above the cylinders (solid lines), y=−3H/16 below the cylinders (dashed lines), and y=−H/2 along the domain bottom (dash-dotted lines). The vertical positions y=3H/16 and y=−3H/16 are indicated, respectively, by the black and white short bars at the left and right domain ends in (a) and (b). Both heating (b and blue lines in c) and cooling (a and red lines in c) have been considered. These results are all obtained from the same one-module simulation shown in Fig. 5. The vertical dashed lines in (c) are displayed to indicate individual periodic modules. Also in (c) labeled arrows are employed as references for discussion convenience in the text.

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