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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 38, 2000 - Issue 2
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Original Articles

AN EFFICIENT METHOD OF COMPUTING EIGENVALUES IN HEAT CONDUCTION

Pages 133-156 | Published online: 29 Oct 2010

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Read on this site (3)

Tien-Mo Shih, Chandrasekhar Thamire, Chao-Ho Sung & An-Lu Ren. (2010) Literature Survey of Numerical Heat Transfer (2000–2009): Part I. Numerical Heat Transfer, Part A: Applications 57:3-4, pages 159-296.
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A. Haji-Sheikh, W.J. Minkowycz & E.M. Sparrow. (2004) A NUMERICAL STUDY OF THE HEAT TRANSFER TO FLUID FLOW THROUGH CIRCULAR POROUS PASSAGES. Numerical Heat Transfer, Part A: Applications 46:10, pages 929-955.
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Robert L. McMasters, Kevin J. Dowding, James V. Beck & David H. Y. Yen. (2002) METHODOLOGY TO GENERATE ACCURATE SOLUTIONS FOR VERIFICATION IN TRANSIENT THREE-DIMENSIONAL HEAT CONDUCTION. Numerical Heat Transfer, Part B: Fundamentals 41:6, pages 521-541.
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Articles from other publishers (44)

George Y. Panasyuk & Kirk L. Yerkes. (2023) Modeling of Uncertainty Propagation for Transient Heat Rejection Problems. Journal of Thermophysics and Heat Transfer, pages 1-9.
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Robert L. McMasters, Filippo de Monte, Giampaolo D'Alessandro & James V. Beck. (2023) The Effect of Biot Number on a Generalized Heat Conduction Solution. ASME Journal of Heat and Mass Transfer 145:9.
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Forest T. Good, Kristopher L. Kuhlman, Tara C. LaForce, Matthew J. Paul & Jason E. Heath. (2023) Analytical solution and parameter estimation for heat of wetting and vapor adsorption during spontaneous imbibition in tuff. International Journal of Heat and Mass Transfer 203, pages 123814.
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A.E Segall. (2023) The Search for a Generalized Analytical Solution for the Inverse Problem; Some Surprisingly Simple Approximate Methods for Problems of Practical Importance. Journal of Physics: Conference Series 2444:1, pages 012013.
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Bart van de Laar & Rik Naus. (2022) On the 1D heat equation for laser-medium interaction including convection and radiation at the boundaries. International Journal of Heat and Mass Transfer 195, pages 123171.
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Peyton Hopson. 2022. Additive Manufacturing in Biomedical Applications. Additive Manufacturing in Biomedical Applications 486 508 .
Amara Chandoul. (2022) Note on the Transcendental Equation with Three Unknowns √2f(z) − 4 = √x − P′(t) + √P(t)(y + 2) ± √ x − P′(t) − √ P(t)(y + 2). WSEAS TRANSACTIONS ON MATHEMATICS 21, pages 356-360.
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Filippo de Monte, Giampaolo D’Alessandro, Sid Becker & Giuseppe Pontrelli. 2022. Modeling of Mass Transport Processes in Biological Media. Modeling of Mass Transport Processes in Biological Media 87 137 .
Zhao Zhao, Yuhang Li, Sujun Dong, Yi Cui & Zheng Dai. (2021) An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters. Applied Mathematics and Mechanics 42:9, pages 1279-1296.
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Giampaolo D’Alessandro & Filippo de Monte. (2020) Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids. Energies 13:24, pages 6484.
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Ingo Ullisch. (2020) A Closed-Form Solution to the Geometric Goat Problem. The Mathematical Intelligencer 42:3, pages 12-16.
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Robert L. McMasters, Filippo de Monte & James V. Beck. (2020) Generalized Solution for Rectangular Three-Dimensional Transient Heat Conduction Problems with Partial Heating. Journal of Thermophysics and Heat Transfer 34:3, pages 516-521.
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Robert L. McMasters, Filippo de Monte & James V. Beck. (2019) Generalized Solution for Two-Dimensional Transient Heat Conduction Problems With Partial Heating Near a Corner. Journal of Heat Transfer 141:7.
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Giampaolo D’Alessandro, Filippo de Monte & Donald E. Amos. (2019) Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High-Conductivity Materials. Mathematical Problems in Engineering 2019, pages 1-15.
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Antonio Campo & Yunesky Masip Macía. (2019) Simple Formulas to Predict Center and Mean Temperatures and Total Heat Transfer in Regular Configurations With Surface Temperature Under Small- and Large-Time Conditions. Journal of Thermal Science and Engineering Applications 11:3.
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G D’Alessandro & F de Monte. (2019) Finite heating duration based-sensitivity analysis in transient heat conduction. Journal of Physics: Conference Series 1224:1, pages 012015.
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Giampaolo D'Alessandro & Filippo de Monte. (2019) Optimal experiment design for thermal property estimation using a boundary condition of the fourth kind with a time-limited heating period. International Journal of Heat and Mass Transfer 134, pages 1268-1282.
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Antonio Campo, Jaime Sieres & Yunesky Masip-Macía. (2019) Plain correlation asymptotes to predict the center and mean temperatures and total heat transfer in simple solid objects with uniform surface temperature at limiting small-time conditions. International Journal of Heat and Mass Transfer 130, pages 733-739.
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Antonio Campo & Yunesky Masip. (2019) Semi-analytical unsteady heat conduction in large plane walls with heat convection exchange. International Journal of Numerical Methods for Heat & Fluid Flow 29:2, pages 536-552.
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Antonio Campo & Müslüm Arıcı. (2018) Numerical analysis of unsteady heat conduction in regular solid bodies comprising natural convection to nearby fluids. Heat Transfer-Asian Research 47:7, pages 887-906.
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Gabriela C. Oliveira, Ana Paula Fernandes & Gilmar Guimaraes. (2017) Thermal behavior analysis of coated cutting tool using analytical solutions. Journal of the Brazilian Society of Mechanical Sciences and Engineering 39:8, pages 3249-3255.
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Tomasz Raszkowski, Agnieszka Samson, Mariusz Zubert, Marcin Janicki & Andrzej Napieralski. (2017) Structure-aware Thermal Model reduction. Structure-aware Thermal Model reduction.
Rogelio Luck, Gregory J. Zdaniuk & Heejin Cho. (2015) An Efficient Method to Find Solutions for Transcendental Equations with Several Roots. International Journal of Engineering Mathematics 2015, pages 1-4.
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Robert L. McMasters & James V. Beck. (2014) A Two-Dimensional Cylindrical Transient Conduction Solution Using Green's Functions. Journal of Heat Transfer 136:10.
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S. Ghalambor, D. Agonafer & A. Haji-Sheikh. (2013) Analytical Thermal Solution to a Nonuniformly Powered Stack Package With Contact Resistance. Journal of Heat Transfer 135:11.
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Filippo de Monte, Giuseppe Pontrelli & Sid Becker. 2013. Transport in Biological Media. Transport in Biological Media 59 118 .
Robert L. McMasters & James V. Beck. (2008) Solutions for Transient Heat Conduction With Solid Body Motion and Convective Boundary Conditions. Journal of Heat Transfer 130:11.
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M Janicki & A Napieralski. (2008) Real time temperature estimation of heat sources in integrated circuits with remote temperature sensors. Journal of Physics: Conference Series 124, pages 012027.
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Feng-Bin Yeh. (2007) Prediction of the transient and steady temperature distributions in a two-layer composite slab in contact with a plasma: exact closed-form solutions. Journal of Physics D: Applied Physics 40:12, pages 3633-3643.
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Marcin Janicki, Gilbert De Mey & Andrzej Napieralski. (2007) Thermal analysis of layered electronic circuits with Green's functions. Microelectronics Journal 38:2, pages 177-184.
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David H. Y. Yen & James V. Beck. (2006) Green’s functions for non-self-adjoint problems in heat conduction with steady motion. Journal of Engineering Mathematics 57:2, pages 115-132.
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Filippo de Monte. (2006) Multi-layer transient heat conduction using transition time scales. International Journal of Thermal Sciences 45:9, pages 882-892.
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M. Janicki & A. Napieralski. (2006) Parametric Thermal Analyses Of Electronic Circuits With Green's Functions. Parametric Thermal Analyses Of Electronic Circuits With Green's Functions.
M. Janicki & A. Napieralski. (2005) Application of green's functions for thermal analysis of electronic circuits. Application of green's functions for thermal analysis of electronic circuits.
Cihat Arslanturk. (2004) Performance analysis and optimization of a thermally non-symmetric annular fin. International Communications in Heat and Mass Transfer 31:8, pages 1143-1153.
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James V. Beck & Robert L. McMasters. (2004) Solutions for multi-dimensional transient heat conduction with solid body motion. International Journal of Heat and Mass Transfer 47:17-18, pages 3757-3768.
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F. de Monte. (2004) Transverse eigenproblem of steady-state heat conduction for multi-dimensional two-layered slabs with automatic computation of eigenvalues. International Journal of Heat and Mass Transfer 47:2, pages 191-201.
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D.H.Y. Yen & J.V. Beck. (2003) Small time approximations of Green's functions for one‐dimensional heat conduction problems with convective boundaries. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 83:8, pages 549-558.
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A Haji-Sheikh, J.V Beck & D Agonafer. (2003) Steady-state heat conduction in multi-layer bodies. International Journal of Heat and Mass Transfer 46:13, pages 2363-2379.
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F. de Monte. (2003) Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results. International Journal of Heat and Mass Transfer 46:8, pages 1455-1469.
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R.J. Goldstein, E.R.G. Eckert, W.E. Ibele, S.V. Patankar, T.W. Simon, T.H. Kuehn, P.J. Strykowski, K.K. Tamma, A. Bar-Cohen, J.V.R. Heberlein, J.H. Davidson, J. Bischof, F.A. Kulacki, U. Kortshagen & S. Garrick. (2002) Heat transfer – a review of 2000 literature. International Journal of Heat and Mass Transfer 45:14, pages 2853-2957.
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A. Haji-Sheikh & J.V. Beck. (2002) Temperature solution in multi-dimensional multi-layer bodies. International Journal of Heat and Mass Transfer 45:9, pages 1865-1877.
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Rogelio Luck & James W. Stevens. (2002) Explicit Solutions for Transcendental Equations. SIAM Review 44:2, pages 227-233.
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Kevin D. Cole & David H. Y. Yen. (2001) Influence Functions for the Infinite and Semi-Infinite Strip. Journal of Thermophysics and Heat Transfer 15:4, pages 431-438.
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