AN APPLICATION OF ALGORITHMS OF ADAMS AND GEAR METHODS ON BOUNDARY LAYER CONVECTIVE HEAT TRANSFER WITH PRESSURE GRADIENT USING HOMOTOPY PERTURBATION METHOD (HPM) OVER A FLAT PLATE

Authors

  • Amber Nehan Kashif Department of Mathematics, Faculty of Science, University of Kordofan, 51111 El Obeid, Sudan
  • Zainal Abdul Aziz UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Faisal Salah Department of Mathematics, Faculty of Science, University of Kordofan, 51111 El Obeid, Sudan
  • K. K. Viswanathan Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box No. 27235, Safat 13133, Kuwait

DOI:

https://doi.org/10.11113/jt.v80.10204

Keywords:

Adams Method (AM), Gear Method (GM), Homotopy Perturbation Method (HPM), pressure gradient parameter, convective heat transfer

Abstract

Boundary layer flow of convective heat transfer with pressure gradient over a flat plate is solved with an application of algorithms of Adams Method (AM) and Gear Method (GM) using Homotopy Perturbation Method (HPM). The distributions of temperature and velocity in the boundary layer are examined, particularly on the influences due to Prandtl number (Pr) and pressure gradient (m). Consequently, the equations of momentum and energy are resolved concurrently. These HPM outcomes have been compared with the previous published work in the literature; and these are found to be in good agreement with the results obtained from numerical methods.

Author Biographies

  • Amber Nehan Kashif, Department of Mathematics, Faculty of Science, University of Kordofan, 51111 El Obeid, Sudan
    Department of Mathematics, Faculty of Science
  • Zainal Abdul Aziz, UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
    Dept. of Mathematical Sciences
  • Faisal Salah, Department of Mathematics, Faculty of Science, University of Kordofan, 51111 El Obeid, Sudan
    Department of Mathematics, Faculty of Science
  • K. K. Viswanathan, Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box No. 27235, Safat 13133, Kuwait
    Associate Professor,Dept. of Mathematics

References

Fathizadeh, M. and Rashidi, F. 2009. Boundary Layer Convective Heat Transfer with Pressure Gradient using Homotopy Perturbation Method (HPM) over a Flat Plate. Chaos, Solitons & Fractals. 42(4): 2413-2419.

Matthew, B., Olyvia, D., Viral, P., Joel, S. and Van, B. E. 2007. Adams and Gear Methods for Solving ODEs with Mathematica. http://controls.engin.umich.edu/wiki/index.php.Solving_ODEs_with_Mathematica.

Shagaiya, Y. and Daniel, S. 2015. Presence of Pressure Gradient on Laminar Boundary Layer over a Permeable Surface with Convective Boundary Condition. Am. J. Heat Mass Transf. 2(1): 1-14.

Aminikhah, H. and Jamalian, A. 2012. An Analytical Approximation for Boundary Layer Flow Convection Heat and Mass Transfer Over a Flat Plate. J. Math. Comput. Sci. 5(4): 241-257.

Aziz, A. 2009. A Similarity Solution for Laminar Thermal Boundary Layer over a Flat Plate with a Convective Surface Boundary Condition. Commun. Nonlinear Sci. Numer. Simul. 14(4): 1064-1068.

Mirgolbabaei, H. and Barari, A. 2010. Analytical Solution of Forced-convective Boundary-layer Flow over a Flat Plate. Arch. Civ. Mech. Eng. X(2): 41-51.

Jiya, M. and Oyubu, J. 2012. Adomian Decomposition Method for the Solution of Boundary Layer Convective Heat Transfer Flow over a Flat Plate. Int. J. Appl. 2(8): 54-62.

Fathizadeh, M. and Aroujalian, A. 2012. Study of Boundary Layer Convective Heat Transfer with Low Pressure Gradient Over a Flat Plate Via He’s Homotopy Perturbation Method. Iran. J. Chem. Eng. 9(1): 33-39.

Esmaeilpour, M. and Ganji, D. D. 2007. Application of He’s Homotopy Perturbation Method to Boundary Layer Flow and Convection Heat Transfer over a Flat Plate. Phys. Lett. A. 372: 33-38.

Desale, S. V. and Pradhan, V. H. 2013. Implicit Finite Difference Solution of Boundary Layer Heat Flow over a Flat Plate. Int. J. Eng. Res. Appl. 3(6): 1611-1616.

Mukhopadhyay, S. 2013. MHD Boundary Layer Flow and Heat Transfer over an Exponentially Stretching Sheet Embedded in a Thermally Stratified Medium. Alexandria Eng. J. 52(3): 259-265.

Biliana, B. and Roslinda, N. 2009. Numerical Solution of the Boundary Layer Flow over an Exponentially Stretching Sheet with Thermal Radiation. Eur. J. Sci. Res. 33(4): 710-717.

Bhattacharyya, K. 2011. Dual Solutions in Boundary Layer Stagnation-Point Flow and Mass Transfer with Chemical Reaction Past a Stretching/Shrinking Sheet. Int. Commun. Heat Mass Transf. 38(7): 917-922.

Bhattacharyya, K. 2011. Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet. Chinese Phys. Lett. 28(7): 074701.

Ishak, A. 2010. Similarity Solutions for Flow and Heat Transfer Over a Permeable Surface with Convective Boundary Condition. Appl. Math. Comput. 217(2): 837-842.

He, J. H. 2006. Some Asymptotic Methods for Strongly Nonlinear Equations. Int. J. Mod. Phys. B. 20(10): 1141-1199.

He, J. H. 2006. New Interpretation of Homotopy Perturbation Method. Int. J. Mod. Phys. B. 634-638.

He, J. H. 2008. An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering. Int. J. Mod. Phys. B. 22(21): 3487-3578.

Cai, X. , Wu,W. and Li, M. 2006. Approximate Period Solution for a Kind of Nonlinear Oscillator by He’s Perturbation Method. Int. J. Nonlinear Sci. 7(1): 109-112.

Cveticanin, L. 2006. Homotopy–perturbation Method For Pure Nonlinear Differential Equation. Chaos, Solitons & Fractals. 30: 1221-1230.

El-Shahed, M. 2005. Application of He’s Homotopy Perturbation Method to Volterra's Integro-differential Equation. Int. J. Nonlinear Sci. 6(2): 163-168.

Abbasbandy, S. 2006. Application of He’s Homotopy Perturbation Method for Laplace Transform. Chaos, Solitons & Fractals. 30: 1206-1212.

Beléndez, A. and Hernandez, A. 2007. Application of He’s Homotopy Perturbation Method to the Duffing-harmonic Oscillator. Int. J. Nonlinear Sci. Numer. Simul. 8(1): 79-88.

He, J. H. 1999. Homotopy Perturbation Technique. Comput. Methods Appl. Mech. Eng. 178(3-4): 257-262.

He, J. H. 1998. Approximate Solution of Nonlinear Differential Equations with Convolution Product Nonlinearities. Comput. Methods Appl. Mech. Engrg. 167: 69-73.

Mahmood, M. and Hossain, M. 2008. Application of homotopy Perturbation Method to Deformable Channel With Wall Suction and Injection in a Porous Medium. Int. J. Nonlinear Sci. Numer. Simul. 9(2): 195-206.

Ghori, Q., Ahmed, M. and Siddiqui, A. 2007. Application of Homotopy Perturbation Method to Squeezing Flow of a Newtonian Fluid. Int. J. Nonlinear Sci. Numer. Simulation. 8(2): 179-184.

Yulita Molliq, R., Noorani, M. S. M. and Hashim, I. 2009. Variational Iteration Method for Fractional Heat-and Wave-like Equations. Nonlinear Analysis: Real World Applications. 10(3): 1854-1869.

Cebeci, T. and Bradshaw, P. 1988. Physical and Computational Aspects of Convective Heat Transfer. New York: Springer-Verlag.

Kakaç, S. and Yener, Y. 1980. Convective Heat Transfer. Middle East Technical University: Faculty of Engineering.

Abbas, Z., Wang, Y., Hayat, T. and Oberlack, M. 2010. Mixed convection in the Stagnation-point Flow of a Maxwell Fluid Towards a Vertical Stretching Surface. Nonlinear Anal. Real World Appl. 11(4): 3218–3228.

Bird, B. R., Stewart, W. E. and Lightfood, E. N. 2002. Transfer Phenomena. 2nd ed. John Wiley & Sons.

Downloads

Published

2018-02-26

Issue

Section

Science and Engineering

How to Cite

AN APPLICATION OF ALGORITHMS OF ADAMS AND GEAR METHODS ON BOUNDARY LAYER CONVECTIVE HEAT TRANSFER WITH PRESSURE GRADIENT USING HOMOTOPY PERTURBATION METHOD (HPM) OVER A FLAT PLATE. (2018). Jurnal Teknologi, 80(3). https://doi.org/10.11113/jt.v80.10204