### Enhancement of Algorithm and Investigation of Heat Transfer Through Fins

^{(*)}

*Corresponding author*

**DOI's assignment:**

*the author of the article can submit here a request for assignment of a DOI number to this resource!*

**Cost of the service: euros 10,00 (for a DOI)**

#### Abstract

Finite Element Method (FEM) and Differential Quadrature Method (DQM) are two very important numerical solution techniques to solve engineering and physical science problems. Usually elements are sub-divided uniformly in FEM (Conventional FEM, CFEM) to obtain temperature distribution behavior in a fin or plate. Hence, extra computational complexity is needed to obtain a fair solution with required accuracy. In this paper, non-uniform sub-elements are considered to enhance the CFEM algorithm to reduce the computational complexity. The proposed algorithm is known as Efficient FEM (EFEM).This EFEM is applied for the solution of one-dimensional heat transfer problem in convection-tip thin rectangular fin. Exact solutions are also obtained for comparison purpose. The obtained results are compared with CFEM and Efficient DQM (EDQM), with non-uniform mesh generation. It is found that the EFEM exhibits more accurate results than CFEM, EDQM and agrees with exact solution showing its potentiality *Copyright © 2013 Praise Worthy Prize - All rights reserved.*

#### Keywords

#### Full Text:

PDF#### References

G. Strang, G.J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Inc., 1997).

http://dx.doi.org/10.1002/zamm.19750551121

R. Tirupathi, P.E. Chandrupatla, Introduction to Finite Elements in Engineering (Prentice-Hall International, 1997).

Mathematics of Finite Element Method, 2004, Available at: http://math.nist.gov/mcsd/savg/tutorial/ansys/FEM/ (Accessed on 19 October 2006).

B. Li, Numerical Method for a Parabolic Stochastic Partial Differential Equation (Chalmers Finite Element Center, 2004).

F. Fairag, Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method, arXiv: math.NA/0109109, Vol. 1, n. 17, September 2001.

http://dx.doi.org/10.1137/s1064827500370895

S. Park, Development and Applications of Finite Elements in Time Domain, PhD Thesis, Faculty of the Virginia Polytechnic Institute and State University, Virginia, December, 1996. Available in the Library, Virginia Polytechnic Institute and State University.

R. Bellman, J. Casti, Differential quadrature and long-term integration, J Math and Appl., Vol. 34, pp. 235-238, 1971.

http://dx.doi.org/10.1016/0022-247x(71)90110-7

R. Bellman, J. Casti, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, J Comput Phys, Vol. 10, pp. 40-52, 1972.

http://dx.doi.org/10.1016/0021-9991(72)90089-7

C.W. Bert, S.K. Jang, A.G. Striz, Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature, J Comput Mech, Vol. 5, pp. 217-226, 1989.

http://dx.doi.org/10.1007/bf01046487

C.W. Bert, M. Malik, Fast computing technique for the transient response of gas-lubricated journal bearings, Proceedings of the U.S. National Congress of Applied Mechanics, Seattle, WA, pp. 298, June 26-July 1, 1994.

C. Shu, W. Chen, H. Xue, H. Du, Numerical analysis of grid distribution effect on the accuracy of Differential Quadrature analysis of beams and plates by error estimation of derivative approximation, Int. Journal of Numer. Methods Engineering, Vol. 51, n. 2, pp. 159-179, 2001.

http://dx.doi.org/10.1002/nme.150

M.M. Fakir, M.K. Mawlood, W. Asrar, S. Basri, A.A. Omar, Triangular Fin Temperature Distribution by the Method of Differential Quadrature, Journal Mekanikal, Malaysia, Vo. 15, pp. 20-31, 2003.

M.M. Fakir, M.K. Mawlood, W. Asrar, S. Basri, A.A. Omar, Rectangular Fin Temperature Distribution by the Method of Differential Quadrature, The Journal of the Institute of Engineers, Malaysia (IEM), Vol. 63, n. 4, pp. 41-47, 2002.

E. Hinton, D. R. J. Owen, An Introduction to Finite Element Computations (Pineridge Press Limited, Swansea, U.K., 1985).

http://dx.doi.org/10.1002/nme.1620150815

S. Tiwari, G. Biswas, P. L. N. Prasad, S. Basu, Numerical Prediction of Flow and Heat Transfer in a Rectangular Channel With a Built-In Circular Tube, ASME Journal of Heat Transfer, Vol. 125, n. 3, pp. 413-421, 2003.

http://dx.doi.org/10.1115/1.1571087

B. L. Wang, Z. H. Tian, Application of Finite Element-Finite Difference Method to the determination of Transient Temperature Field in Functionally Graded Materials, Journal of Finite Elements in Analysis and Design, Vol. 41, pp. 335-349, 2005.

http://dx.doi.org/10.1016/j.finel.2004.07.001

S. H. Lo, W. X. Wang, Finite Element Mesh Generation over Intersecting Curved Surfaces by Tracing of Neighbours, Journal of Finite Elements in Analysis and Design, Vol 41, pp. 351-370, 2005.

http://dx.doi.org/10.1016/j.finel.2004.07.002

M. N. Ozisik, Heat Transfer: A Basic Approach (McGraw-Hill, 1985).

Wen J, Li Y, Wang S, Zhou A, Experimental investigation of header configuration improvement in plate-fin heat exchanger, Applied Thermal Engineering, 2007.

http://dx.doi.org/10.1016/j.applthermaleng.2007.01.004

Wen J, Study of flow distribution and its improvement in plate-fin heat exchanger, Cryogenics, 2004.

http://dx.doi.org/10.1016/j.cryogenics.2004.04.009

Wen J, Li Y, Zhou A, Zhang K, An experimental and numerical investigation of flow patterns in the entrance of plate-fin heat exchanger, International Journal of Heat and Mass Transfer, 2006.

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2005.10.029

Kim NH, Han SP, Distribution of air–water annular flow in a header of a parallel flow heat exchanger, International Journal of Heat and Mass Transfer, 2008.

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.05.028

Ding WK, Fan JF, He YL, Tao WQ, Zheng YX, Gao YF, A general simulation model for performance prediction of plate fin-and-tube heat exchanger with complex circuit configuration, Applied Thermal Engineering, 2011.

http://dx.doi.org/10.1016/j.applthermaleng.2011.01.045

M.M. Fakir, S, Basri, R. Varatharajoo, A.A. Jaafar, A.S. Mohd. Rafie and D.L.A. Majid, Extended Conventional Finite Element Method vs. Differential Quadrature Method Comparison in Two dimensional Heat Transfer Problem. (2008) International Review of Aerospace Engineering (IREASE), 1 (2), pp. 200-205.

M.M. Fakir, S, Basri, R. Varatharajoo, A.A. Jaafar, A.S. M. Rafie and D.L.A. Majid, Comparison of Optimum Finite Element Method vs. Differential Quadrature Method in Two-dimensional Heat Transfer Problem, (2008) International Review of Mechanical Engineering (IREME), 2 (3), pp. 483-488.

Sidik, N.A.C., Samion, S.B., Cubic interpolation profile method for prediction of thermal fluid flow through porous media, (2013) International Review of Mechanical Engineering (IREME), 7 (3), pp. 563-569.

Sivakumar, K., Natarajan, E., Kulasekharan, N., CFD simulation and experimental investigation of convection heat transfer in a rectangular convergent channel with staggered ribs, (2013) International Review of Mechanical Engineering (IREME), 7 (3), pp. 541-548.

Dia, S., Mbow, C., Effects of the heated surface on the unsteady two dimensional natural convection in enclosures bounded by two paraboloids of revolution, (2013) International Review of Mechanical Engineering (IREME), 7 (2), pp. 384-391.

Sathyanarayanan, S., Vimala Juliet, A., Finite element analysis and modeling of Mems pressure sensor for intraocular pressure, (2013) International Review of Mechanical Engineering (IREME), 7 (1), pp. 243-247.

Sukri, M.F., Salim, M.A., Mohd Rosli, M.A., Azraai, S.B., Mat Dan, R., An analytical investigation of overall thermal transfer value on commercial building in Malaysia, (2012) International Review of Mechanical Engineering (IREME), 6 (5), pp. 1050-1056.

El-Askary, W.A., Balabel, A., Wilson, S., Numerical and experimental investigation of thermo-fluid characteristics of air jet impingement on a heated flat plate subjected to a periodic oscillation, (2012) International Review of Mechanical Engineering (IREME), 6 (3), pp. 440-448.

Tabarki, M., Ben Mabrouk, S., Numerical modeling of heat and mass transfer phenomena in heated enclosures, (2012) International Review of Mechanical Engineering (IREME), 6 (2), pp. 291-301.

Setareh, M., Isvandzibaei, M.R., FEM Method for Symmetrical Boundary Conditions Two FGM Circular Cylindrical Shell, (2011) International Review of Mechanical Engineering (IREME), 5 (6), pp. 1102-1108.

Hamzehei, M., Raki, M., Study and simulation of thermal buckling in a thin rectangular FGM plate, (2011) International Review of Mechanical Engineering (IREME), 5 (5), pp. 918-926.

Deshmukh, P.A., Warkhedkar, R.M., Thermal performance of pin fin heat sinks: A review of literature, (2011) International Review of Mechanical Engineering (IREME), 5 (4), pp. 726-732.

### Refbacks

- There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com**Copyright © 2005-2022 Praise Worthy Prize**