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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Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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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