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Numerical study of the heat transfer phenomenon of a rectangular plate including void, notch using finite difference technique

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present study, we have developed a code using Matlab software for solving a rectangular aluminum plate having void, notch, at different boundary conditions discretizing a two dimensional (2D) heat conduction equation by the finite difference technique. We have solved a 2D mixed boundary heat conduction problem analytically using Fourier integrals (Deb Nath et al., 2006; 2007; 2007; Deb Nath and Ahmed, 2008; Deb Nath, 2008; Deb Nath and Afsar, 2009; Deb Nath and Ahmed, 2009; 2009; Deb Nath et al., 2010; Deb Nath, 2013) and the same problem is also solved using the present code developed by the finite difference technique (Ahmed et al., 2005; Deb Nath, 2002; Deb Nath et al., 2008; Ahmed and Deb Nath, 2009; Deb Nath et al., 2011; Mohiuddin et al., 2012). To verify the soundness of the present heat conduction code results using the finite difference method, the distribution of temperature at some sections of a 2D heated plate obtained by the analytical method is compared with those of the plate obtained by the present finite difference method. Interpolation technique is used as an example when the boundary of the plate does not pass through the discretized grid points of the plate. Sometimes hot and cold fluids are passed through rectangular channels in industries and many types of technical equipment. The distribution of temperature of plates including notches, slots with different temperature boundary conditions are studied. Transient heat transfer in several pure metallic plates is also studied to find out the required time to reach equilibrium temperature. So, this study will help find design parameters of such structures.
Rocznik
Strony
733--756
Opis fizyczny
Bibliogr. 41 poz., tab., wykr.
Twórcy
  • Computational Materials Research Initiative, Institute for Materials Research, Tohoku University, JAPAN
autor
  • Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur, INDIA
Bibliografia
  • [1] Ahmed S.R. and Deb Nath S.K. (2009): A simplified analysis of the tire-tread contact problem using displacement potential based finite difference. – Computer Modelling in Engineering and Sciences, vol.44, pp.35-64.
  • [2] Ahmed S. Reaz, Deb Nath S.K. and Uddin M.W. (2005): Optimum shapes of tire treads for avoiding lateral slippage between tires and roads. – Vol.64, pp.729-750.
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  • [8] Blomberg T. (1990): HEAT2- A heat transfer PC- program. – Proceeding of the 2nd Conference on Building Physics in the Nordic Countries, Division of Building Technology, Department of Civil Engineering, The Norwegian Institute of Technology, The University of Tronheim, Alfr, Getz vei3, N-7034 Trondheim, Norway.
  • [9] Blomberg T. (1991): HEAT2- A heat transfer PC-program. – Manual for HEAT2, Department of building physics, Lund University, P.O. Box 118, S-221 00 Lund, Sweden, CoDEN: LUTVDG/(TVBH-7122).
  • [10] Blomberg T. (1993): HEAT3-A three-dimensional heat transfer computer program. – Proceeding of the 3rd conference on building physics in the Nordic countries, Buiding Physics ’93 (Bjarne Saxhof, editor), page 339, Thermal Insulation laboratory, Lyngby, Denmark, ISBN 87-984610-0-1 volume 1.
  • [11] Blomberg T. (1994): HEAT3-A three-dimensional heat transfer computer program Manual for HEAT3. – Department of building physics, Lund University, P.O.Box. 118, S-221 00 Lund, Sweden. CODEN: LUTVDG/(TVBH-7169).
  • [12] Blomberg T. (1994): HEAT2R-A PC-Program for heat conduction in cylindrical coordinates r and z. – Department of Building Physics, LUND University. P.O. BOX 118, S-221 00 Lund, Sweden CODEN: LUTVDG/(TVBH-7178).
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  • [14] Chen C.L. and Lin Y.C. (1998): Solution of two boundary problems using the differential transform method. – J. Optim. Theory, Appl., vol.99, pp.23-35.
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  • [17] Deb Nath S.K. (2002): A study of wear of tire treads. – MSc. Thesis, Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.
  • [18] Deb Nath S.K. (2008): Displacement potential approach to solution of stiffened composite cantilever beams under combined loading. – International Journal of Applied Mechanics and Engineering, vol.13, No.1, pp.21–41.
  • [19] Deb Nath S.K. (2013): Effects of fiber orientation and material isotropy on the analytical elastic solution of a stiffened orthotropic panel subjected to a combined loading. – Advances in Materials Science and Engineering, vol.2013, Article ID 710143,13 pages.
  • [20] Deb Nath S.K., Ahmed S.R. and Afsar A.M. (2006): Displacement potential solution of short stiffened flat composite bars under axial loading. – International Journal of Applied Mechanics and Engineering, vol.11, No.3, pp.557–575.
  • [21] Deb Nath S.K., Afsar A.M. and Ahmed S.R. (2007): Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material. – Journal of Strain Analysis for Engineering Design, vol.42, No.7, pp.529-540.
  • [22] Deb Nath S.K., Afsar A.M. and Ahmed S.R. (2007): Displacement potential approach to the solution of stiffened orthotropic composite panels under uniaxial tensile load. – Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol.221, No.5, pp.869-881.
  • [23] Deb Nath S.K. and Ahmed S.R. (2008): Analytical solution of short guided orthotropic composite columns under eccentric loading using displacement potential formulation. – Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol.222, No.4, pp.425-434.
  • [24] Deb Nath S.K. and Afsar A.M. (2009): Analysis of the effect of fiber orientation on the elastic field in a stiffened orthotropic panel under uniform tension using displacement potential approach. – Mechanics of Advanced Materials and Structures, vol.16, No.4, pp.300-307.
  • [25] Deb Nath S.K. and Ahmed S.R. (2009): Displacement potential solution of stiffened composite struts subjected to eccentric loading. – Applied Mathematical Modelling, vol.33, No.3, pp.1761-1775.
  • [26] Deb Nath S.K. and Ahmed S.R. (2009): Elastic analysis of short orthotropic composite columns subjected to uniform load over a part of the tip. – Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol.223, No.2, pp.95–105.
  • [27] Deb Nath S.K., Ahmed S.R. and Kim S.-G. (2010): Analytical solution of a stiffened orthotropic plate using alternative displacement potential approach. – Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol.224, No.1, pp.89–99.
  • [28] Deb Nath S.K., Akanda M.A.S., Ahmed S.R. and Uddin M.W. (2008): Numerical investigation of bond-line stresses of tire tread section. – International Journal of Applied Mechanics and Engineering, vol.13, pp.43-61.
  • [29] Deb Nath S.K., Ahmed S.R., Kim S-G. and Wong C.H. (2011): Effect of tire material on the prediction of optimum tire tread sections. – International Journal for computational methods in Engineering Science and Mechanics, vol.12, 290-302.
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  • [31] Jordan P.M. (2003): A nonstandard finite difference scheme foe non-linear heat transfer in a thin finite rod. – Journal of Difference Equations and Applications, vol.9, pp.1015-1021.
  • [32] Kalman R.E. (1960): A new approach to linear filtering and prediction problems. – ASME J. Basic Eng., ser. 82d, pp.35-45.
  • [33] Lo C-Y (2011): A study of two-step heat conduction in laser heating using the hybrid differential transform method. – Numerical Heat Transfer, Part B, vol.59, pp.130-146.
  • [34] Mohiuddin M., Uddin M.W., Deb Nath S.K. and Ahmed S.R. (2012): An alternative numerical solution to a screw-thread problem using displacement-potential approach. – International Journal for Computational Methods in Engineering Science and Mechanics, vol.13, pp.254-271.
  • [35] Őzisik M.N. (1989): Boundary Value Problems of Heat Conduction. – New York: Dover.
  • [36] Peng H-S and Chen C.L. (2011): Application of hybrid differential transformation and finite differential transformation and finite difference method on the laser heating problem. – Numerical Heat Transfer, Part A, vol.59, pp.28-42.
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  • [41] Yu L.T. and Chen C.K. (1998): The solution of the Blasius equation by the differential transform method. – Math. Comput. Model, vol.28, pp.101-111.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9d011bd2-3c87-4885-b947-9639d8a07744
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