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Research Papers

A Meshless Method for Modeling Convective Heat Transfer

[+] Author and Article Information
Darrell W. Pepper

Professor and Director
NCACM, UNLV,
Las Vegas, NV 89154
e-mail: darrell.pepper@unlv.edu

Xiuling Wang

Assistant Professor
Department of Mechanical Engineering,
Purdue University Calumet,
Hammond, IN 46323
e-mail: wangx@purduecal.edu

D. B. Carrington

Research Scientist
T-3 Fluid Dynamics and Solid Mechanics Group, LANL,
Los Alamos, NM 87545
e-mail: dcarring@lanl.gov

1Currently Distinguished Visiting Professor, U.S. Air Force Academy, CO 80840.

Manuscript received October 19, 2010; final manuscript received July 7, 2012; published online December 6, 2012. Assoc. Editor: Akshai Runchal.

J. Heat Transfer 135(1), 011003 (Dec 06, 2012) (9 pages) Paper No: HT-10-1486; doi: 10.1115/1.4007650 History: Received October 19, 2010; Revised July 07, 2012

A meshless method is used in a projection-based approach to solve the primitive equations for fluid flow with heat transfer. The method is easy to implement in a matlab format. Radial basis functions are used to solve two benchmark test cases: natural convection in a square enclosure and flow with forced convection over a backward facing step. The results are compared with two popular and widely used commercial codes: comsol, a finite element-based model, and fluent, a finite volume-based model.

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Figures

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Fig. 1

Irregular domain discretized using (a) three-noded triangular finite elements, (b) boundary element, and (c) arbitrary interior and boundary points using a meshless method

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Fig. 2

Nodal placement within (a) patches and (b) clipping circles

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Fig. 3

Steady-state conduction in a two-dimensional plate

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Fig. 4

Natural convection within an enclosed cavity

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Fig. 5

31 × 31 point distribution for natural convection in a square cavity (a) comsol mesh, (b) fluent mesh, and (c) meshless node distribution

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Fig. 6

Velocity vectors for natural convection for Ra = 103 in a square cavity using (a) comsol (b) fluent, and (c) meshless

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Fig. 7

Velocity profiles for Ra = 104 along (a) vertical and (b) horizontal central lines

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Fig. 8

Isotherms for natural convection in a square cavity for Ra = 104 using (a) meshless, (b) comsol, and (c) fluent (right vertical wall heated)

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Fig. 9

Problem configuration for forced convection in a backward facing step

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Fig. 10

Typical mesh for backward facing step solution: (a) COMSOL mesh of 388 elements, (b) FLUENT mesh of 284, and (c) 284 nodes for the meshless method

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Fig. 11

Velocity profiles for Re = 800

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Fig. 12

Temperature profiles for Re = 800

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Fig. 13

Isotherms for backward step flow using (a) meshless, (b) comsol, and (c) fluent

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