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Research Papers: Heat and Mass Transfer

A Novel Numerical Approach for Convective and Radiative Heat Transfer Analysis of Fluid Flow Problems Within Triangular Cavities Using Natural Element Method

[+] Author and Article Information
Ardeshir Moftakhari

Cockrell School of Engineering,
Department of Civil, Architectural and
Environmental Engineering,
University of Texas at Austin,
Austin, TX 78712
e-mail: ardeshir_2010@yahoo.com

Cyrus Aghanajafi

School of Mechanical Engineering,
K. N. Toosi University of Technology,
Tehran 64499, Iran

Ardalan Moftakhari Chaei Ghazvin

Department of Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09111, Germany

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 6, 2016; final manuscript received February 14, 2017; published online April 11, 2017. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 139(8), 082002 (Apr 11, 2017) (13 pages) Paper No: HT-16-1634; doi: 10.1115/1.4036057 History: Received October 06, 2016; Revised February 14, 2017

Thermal analysis of fluid flow is always regarded as an important research issue within cavities in order to become familiar with the characteristics of fluid flow phenomenon in enclosures. This research paper investigates the fluid and heat transfer analysis of fluid flow inside a triangular cavity using natural element methodology (NEM). This Galerkin-based methodology has been introduced for a decade and almost demonstrated its efficiency in the numerical heat transfer analysis of problems in most engineering sciences. The fluid flow contains natural convection along with conduction and radiation heat transfer with medium's walls, which have absorbing, emitting, semitransparent, and nonscattering characteristics. The final results investigate the effects of radiative and natural convection heat transfer on the fluid flow pattern as expressed in Rayleigh number, stream function, strength of natural convection regime, etc., which are checked with other similar studies presented in the literature and shows how promising NEM can be as an efficient numerical approach to improve computational precision when dealing with fluid mechanic problems.

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References

Tan, H. P. , and Lallemand, M. , 1989, “ Transient Radiative—Conductive Heat Transfer in Flat Glasses Submitted to Temperature, Flux and Mixed Boundary Conditions,” Int. J. Heat Mass Transfer, 32(5), pp. 795–810. [CrossRef]
Anteby, I. , Shai, I. , and Arbel, A. , 2000, “ Numerical Calculations for Combined Conduction and Radiation Transient Heat Transfer in a Semitransparent Medium,” Numer. Heat Transfer: Part A, 37(4), pp. 359–371. [CrossRef]
Joudi, K. A. , Hussein, I. A. , and Farhan, A. A. , 2004, “ Computational Model for a Prism Shaped Storage Solar Collector With a Right Triangular Cross Section,” Energy Convers. Manage., 45(3), pp. 391–409. [CrossRef]
Kontogeorgos, D. A. , Keramida, E. P. , and Founti, M. A. , 2007, “ Assessment of Simplified Thermal Radiation Models for Engineering Calculations in Natural Gas-Fired Furnace,” Int. J. Heat Mass Transfer, 50(25–26), pp. 5260–5268. [CrossRef]
Lei, C. , and Patterson, J. C. , 2002, “ Natural Convection in a Reservoir Sidearm Subject to Solar Radiation: Experimental Observations,” Exp. Fluids, 32(5), pp. 590–599. [CrossRef]
Karyakin, Y. E. , Sokovishin, Y. A. , and Martynenko, O. G. , 1998, “ Transient Natural Convection in Triangular Enclosures,” Int. J. Heat Mass Transfer, 31(9), pp. 1759–1766. [CrossRef]
Holtzman, G. A. , Hill, R. W. , and Ball, K. S. , 2000, “ Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above,” ASME J. Heat Transfer, 122(3), p. 485. [CrossRef]
Bejan, A. , 2004, Convection Heat Transfer, 3rd ed., Wiley, Hoboken, NJ.
Kent, E. F. , 2009, “ Numerical Analysis of Laminar Natural Convection in Isosceles Triangular Enclosures for Cold Base and Hot Inclined Walls,” Mech. Res. Commun., 36(4), pp. 497–508.
Kaluri, R. S. , Anandalakshmi, R. , and Basak, T. , 2010, “ Bejan's Heatline Analysis of Natural Convection in Right-Angled Triangular Enclosures: Effects of Aspect-Ratio and Thermal Boundary Conditions,” Int. J. Therm. Sci., 49(9), pp. 1576–1592. [CrossRef]
Basak, T. , Roy, S. , Babu, S. K. , and Balakrishnan, A. R. , 2008, “ Finite Element Analysis of Natural Convection Flow in a Isosceles Triangular Enclosure Due to Uniform and Non-Uniform Heating at the Side Walls,” Int. J. Heat Mass Transfer, 51(17–18), pp. 4496–4505. [CrossRef]
Saha, S. C. , and Khan, M. M. K. , 2011, “ A Review of Natural Convection and Heat Transfer in Attic-Shaped Space,” Energy Build., 43(10), pp. 2564–2571. [CrossRef]
Singh, I. V. , 2004, “ A Numerical Solution of Composite Heat Transfer Problems Using Meshless Method,” Int. J. Heat Mass Transfer, 47(10–11), pp. 2123–2138. [CrossRef]
Mishra, S. C. , and Roy, H. K. , 2007, “ Solving Transient Conduction and Radiation Heat Transfer Problems Using the Lattice Boltzmann Method and the Finite Volume Method,” J. Comput. Phys., 223(1), pp. 89–107. [CrossRef]
Siegel, R. , and Howell, J. R. , 1992, Thermal Radiation Heat Transfer, 3rd ed., Hemisphere, Washington, DC.
Modest, M. F. , 2003, Radiative Heat Transfer, 2nd ed., Academic Press, New York.
Traugott, S. C. , 1966, “ Radiative Heat-Flux Potential for Nongrey Gas,” AIAA J., 4(3), pp. 541–542. [CrossRef]
Lauriat, G. , 1980, “ A Numerical Study of a Thermal Insulation Enclosure: Influence of the Radiative Transfer,” ASME HTD, 8, pp. 55–62.
Lauriat, G. , 1982, “ Combined Radiation-Convection in Gray Fluids Enclosed in Vertical Cavities,” ASME J. Heat Transfer, 104(4), pp. 609–615. [CrossRef]
Fusegi, T. , Farouk, B. , and Kuwahara, K. , 1991, “ 3-d Natural Convection Radiation Interactions in a Cube Filled With Gas-Soot Mixtures,” Fire Saf. Sci., 3, pp. 365–374. [CrossRef]
Saleem, M. , Hossain, M. A. , Saha, C. , and Gu, Y. T. , 2014, “ Heat Transfer Analysis of Viscous Incompressible Fluid by Combined Natural Convection and Radiation in an Open Cavity,” Math. Probl. Eng., 2014, pp. 1–14. [CrossRef]
Sieres, J. , Campo, A. , Ridouane, E. H. , and Fernández-Seara, J. , 2007, “ Effect of Surface Radiation on Buoyant Convection in Vertical Triangular Cavities With Variable Aperture Angles,” Int. J. Heat Mass Transfer, 50(25–26), pp. 5139–5149. [CrossRef]
Liu, L. H. , Tan, J. Y. , and Li, B. X. , 2006, “ Meshless Approach for Coupled Radiative and Conductive Heat Transfer in One-Dimensional Graded Index Medium,” J. Quant. Spectrosc. Radiat. Transfer, 101(2), pp. 237–248. [CrossRef]
Braun, J. , and Sambridge, M. , 1995, “ A Numerical Method for Solving Partial Differential Equations on Highly Irregular Evolving Grids,” Nature, 376, pp. 655–660. [CrossRef]
Sukumar, N. , Moran, B. , and Belytschko, T. , 1998, “ The Natural Element Method in Solid Mechanics,” Int. J. Numer. Methods Eng., 43(5), pp. 839–887. [CrossRef]
Belikov, V. V., Ivanov, V. D., Kontorovich, V. K., Korytnik, S. A., and Yu Semenov A., 1997, “ The Non-Sibsonian Interpolation: A New Method of Interpolation of the Values of a Function on an Arbitrary Set of Points,” Comput. Math. Math. Phys., 37(1), pp. 9–15.
Hiyoshi, H. , and Sugihara, K. , 1999, “ Two Generalizations of an Interpolant Based on Voronoi Diagrams,” Int. J. Shape Model., 5(2), pp. 219–231. [CrossRef]
Sukumar, N. , 2003, “ Voronoi Cell Finite Difference Method for the Diffusion Operator on Arbitrary Unstructured Grids,” Int. J. Numer. Methods Eng., 57(1), pp. 1–34. [CrossRef]
Somireddy, M., and Rajagopal, A. , 2012, “ Meshless Natural Neighbor Galerkin Method for the Bending and Vibration Analysis of Composite Plates,” Compos. Struct., 111, pp. 138–146.
Weidong, W. , and Cheng, G. , 2013, “ Application of Natural Element Method in Numerical Simulation of Crack Propagation,” Adv. Mech. Eng., 5, pp. 1–6.
Zhang, Y. , Yi, H. L. , and Tan, H. P. , 2013, “ Natural Element Method for Radiative Heat Transfer in Two-Dimensional Semitransparent Medium,” Int. J. Heat Mass Transfer, 56(1–2), pp. 411–423. [CrossRef]
Zhang, Y. , Yi, H. L. , and Tan, H. P. , 2014, “ Natural Element Method Analysis for Coupled Radiative and Conductive Heat Transfer in Semitransparent Medium With Irregular Geometries,” Int. J. Therm. Sci., 76, pp. 30–42. [CrossRef]
Basak, T. , Roy, S. , Babu, S. K. , and Balakrishnan, A. R. , 2006, “ Effects of Thermal Boundary Conditions on Natural Convection Flows Within a Square Cavity,” Int. J. Heat Mass Transfer, 49(23–24), pp. 4525–4535. [CrossRef]
Amlin, D. W. , and Korpela, S. A. , 1979, “ Influence of Thermal Radiation on the Temperature Distribution in a Semitransparent Solid,” ASME J. Heat Transfer, 101(1), pp. 76–80. [CrossRef]
Gonzalez, D. , and Cueto, E. , 2007, “ A Natural Element Updated Lagrangian Strategy for Free-Surface Fluid Dynamics,” J. Comput. Phys., 223(1), pp. 127–150. [CrossRef]
Lewis, R. W. , Nithiarasu, P. , and Seetharamu, K. N. , 2004, Fundamentals of the Finite Element Method for Heat and Fluid Flow, Wiley, New York.
Wan, D. C. , Patnaik, B. S. V. , and Wei, G. W. A. , 2001, “ A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution,” Numer. Heat Transfer, Part B, 40(3), pp. 199–228. [CrossRef]
Moftakhari, A. , Torabi, F. , and Aghanajafi, C. , 2016, “ A Novel Energy Simulation Approach for Thermal Design of Buildings Equipped With Radiative Panels Using Inverse Methodology,” Energy Build., 113, pp. 169–181. [CrossRef]
Moftakhari, A. , and Aghanajafi, C. , 2016, “ An Inverse Parameter Estimation Method for Building Thermal Analysis,” ASME J. Sol. Energy Eng., 138(2), p. 021004. [CrossRef]
Moftakhari, A. , Aghanajafi, C. , and Ghazvin, A. M. C. , 2016, “ An Innovative Inverse Analysis Technique for Building Cooling Design With HVAC Systems,” Sci. Technol. Built Environ., 22(3), pp. 299–316. [CrossRef]
Moftakhari, A. , Aghanajafi, C. , and Ghazvin, A. M. C. , 2016, “ Inverse Heat Transfer Analysis of Radiator Central Heating Systems Inside Residential Buildings Using Sensitivity Analysis,” Inverse Probl. Sci. Eng., 25(4), pp. 580–607.
Moftakhari, A. , Aghanajafi, C. , and Ghazvin, A. M. C. , 2016, “ Thermal Analysis of HVAC and Solar Panels Using Genetic Optimization Algorithm,” J. Mech. Sci. Technol., 30(3), pp. 1405–1412. [CrossRef]
Moftakhari, A. , Aghanajafi, C. , and Ghazvin, A. M. C. , 2015, “ A Comparative Study of HVAC and Radiant Systems for Heating Buildings in Different Climates of Iran,” Indian J. Nat. Sci. (IJONS), 6(31), pp. 8615–8633.
Moftakhari, A. , and Aghanajafi, C. , 2015, “ Inverse Design of Residential Room With Radiative Panels,” The 7th Conference on Efficient, Clean and Renewable Energy, Tehran, Iran, pp. 75–83.
Moftakhari, A. , Aghanajafi, C. , and Ghazvin, A. M. C. , 2015, “ The Use of Solar Radiative Panels for Heating Residential Buildings in Different Climates of Iran,” The 2nd International Conference and Exhibition on Solar Energy, University of Tehran, Tehran, Iran, Aug. 30–31, pp. 61–66.
Moftakhari, A. , and Aghanajafi, C. , 2015, “ Building Energy Consumption Using Generic Algorithm,” The 1st Conference on Heating, Ventilation, Air Conditioning (HVAC) and Heating and Cooling Installation, Tehran, Iran, pp. 101–108.
Moftakhari, A. , and Aghanajafi, C. , 2015, “ Inverse Design of Conductivity Coefficient in Building Equipped With Solar Panels,” The 6th International Conference on Heating, Ventilation, Air Conditioning (ICHVAC), Tehran, Iran, May 26–28, pp. 21–29.
Moftakhari, A. , and Aghanajafi, C. , 2015, “ Thermal Analysis of a Residential Room Equipped With Solar Panel Using Generic Algorithm,” The 6th International Conference on Heating, Ventilation, Air Conditioning (ICHVAC), Tehran, Iran, May 26–28, pp. 39–48.
Moftakhari, A. , and Ghazvin, A. M. C. , 2015, “ Estimation of Building Energy Consumption Using PSO Optimization Algorithm,” The 7th Conference on Efficient, Clean and Renewable Energy, Tehran, Iran, pp. 56–63.
Moftakhari, A. , and Aghanajafi, C. , 2015, “ Thermal Simulation of Residential Buildings Equipped With Fan Coils Using Inverse Analysis,” The 1st Conference on Heating, Ventilation, Air Conditioning (HVAC) and Heating and Cooling Installation, Tehran, Iran, pp. 98–105.

Figures

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Fig. 1

The Voronoi diagram for node number 5

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Fig. 2

The Delaunay triangulation for seven nodes

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Fig. 3

The second-order Voronoi diagram for point (x)

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Fig. 4

The second-order of the Voronoi diagram

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Fig. 5

The geometry and boundary conditions for the triangular cavity

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Fig. 6

The error function changes per time

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Fig. 7

The geometry and boundary conditions of the study by Lauriat [18]

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Fig. 8

Mean temperature profile on the horizontal line passing from the cavity center (y = H/2): (a) present study versus Lauriat for radiation and (b) present study versus Lauriat versus Basak et al. for only natural convection

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Fig. 9

Stream line contour comparison in the triangular cavity: (a) present study and (b) Basak et al. study [33]

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Fig. 10

Stream line contour comparison in the triangular cavity: (a) Ra=104, (b) Ra=105, and (c) Ra=106

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Fig. 11

Temperature contours of a nonradiative medium for different Rayleigh numbers: (a) Ra=104, (b) Ra=105, and (c) Ra=106

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Fig. 12

Stream line contours of a radiative medium for different Planck numbers: (a) qr=0, (b) NCR = 10, and (c) NCR = 0.4

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Fig. 13

Temperature contours of a radiative medium for different Planck numbers: (a) qr= 0, (b) NCR = 10, and (c) NCR = 0.4

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Fig. 14

The changes in Nusselt number versus Planck number: (a) local Nusselt number for cold walls and (b) local Nusselt number for warm walls

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Fig. 15

Average Nusselt number versus Planck number

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Fig. 16

The changes of average Nusselt number versus dimensionless mean temperature: (a) warm walls and (b) cold walls

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Fig. 17

The effects of variable optical thickness and emissivity on combined convection and radiation captured by NEM: (a) Nusselt number versus variable optical thickness and (b) Nusselt number versus variable emissivity coefficient

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