A meshless finite difference method is developed for solving conjugate heat transfer problems. Starting with an arbitrary distribution of mesh points, derivatives are evaluated using a weighted least-squares procedure. The resulting system of algebraic equations is sparse and is solved using an algebraic multigrid method. The implementation of the Neumann, Dirichlet, and mixed boundary conditions within this framework is described. For conjugate heat transfer problems, continuity of the heat flux and temperature are imposed on mesh points at multimaterial interfaces. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. The method improves on existing meshless methods for conjugate heat conduction by eliminating spurious oscillations previously observed. Metrics for accuracy are provided and future extensions are discussed.
Skip Nav Destination
e-mail: vvc@purdue.edu
e-mail: jmurthy@ecn.purdue.edu
e-mail: smathur@purdue.edu
Article navigation
Research Papers
A Meshless Finite Difference Method for Conjugate Heat Conduction Problems
Chandrashekhar Varanasi,
Chandrashekhar Varanasi
School of Mechanical Engineering,
e-mail: vvc@purdue.edu
Purdue University
, West Lafayette, IN 47906
Search for other works by this author on:
Jayathi Y. Murthy,
Jayathi Y. Murthy
School of Mechanical Engineering,
e-mail: jmurthy@ecn.purdue.edu
Purdue University
, West Lafayette, IN 47906
Search for other works by this author on:
Sanjay Mathur
Sanjay Mathur
School of Mechanical Engineering,
e-mail: smathur@purdue.edu
Purdue University
, West Lafayette, IN 47906
Search for other works by this author on:
Chandrashekhar Varanasi
School of Mechanical Engineering,
Purdue University
, West Lafayette, IN 47906e-mail: vvc@purdue.edu
Jayathi Y. Murthy
School of Mechanical Engineering,
Purdue University
, West Lafayette, IN 47906e-mail: jmurthy@ecn.purdue.edu
Sanjay Mathur
School of Mechanical Engineering,
Purdue University
, West Lafayette, IN 47906e-mail: smathur@purdue.edu
J. Heat Transfer. Aug 2010, 132(8): 081303 (13 pages)
Published Online: June 9, 2010
Article history
Received:
April 15, 2009
Revised:
February 25, 2010
Online:
June 9, 2010
Published:
June 9, 2010
Citation
Varanasi, C., Murthy, J. Y., and Mathur, S. (June 9, 2010). "A Meshless Finite Difference Method for Conjugate Heat Conduction Problems." ASME. J. Heat Transfer. August 2010; 132(8): 081303. https://doi.org/10.1115/1.4001363
Download citation file:
Get Email Alerts
Cited By
On Prof. Roop Mahajan's 80th Birthday
J. Heat Mass Transfer
Thermal Hydraulic Performance and Characteristics of a Microchannel Heat Exchanger: Experimental and Numerical Investigations
J. Heat Mass Transfer (February 2025)
Related Articles
Multiquadric
Collocation Method for Time-Dependent Heat Conduction Problems With Temperature-Dependent Thermal
Properties
J. Heat Transfer (February,2007)
Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem
J. Heat Transfer (June,2003)
BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain
J. Pressure Vessel Technol (February,2003)
On the Determination of Thermal Conductivity From Frequency Domain Thermoreflectance Experiments
J. Heat Transfer (January,2022)
Related Proceedings Papers
Related Chapters
Introduction
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
Approximate Analysis of Plates
Design of Plate and Shell Structures
Steady Heat Conduction with Variable Heat Conductivity
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow