Heat and Mass Transfer on MHD Jeffrey-Hamel Flow in Presence of Inclined Magnetic Field
Applied and Computational Mathematics
Volume 9, Issue 4, August 2020, Pages: 108-117
Received: May 11, 2020; Accepted: Jun. 3, 2020; Published: Jun. 17, 2020
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Authors
Edward Richard Onyango, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mathew Ngugi Kinyanjui, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mark Kimathi, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya; Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya
Surindar Mohan Uppal, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
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Abstract
In this study, a magnetohydrodynamic Jeffrey-Hamel flow of a viscous, fluid that conducts electricity and is incompressible through a divergent conduit in presence of inclined variable magnetic field with heat and mass transfer has been investigated. The solutions of the governing equations of the MHD flow are obtained numerically since they are non-linear. The numerical scheme used is implemented in a computer software program and the results presented in graphical form. The velocity profile, the temperature profiles, the effect of variable magnetic field and of varying various dimensionless numbers on the flow are analyzed. Jeffrey-Hamel flows are also applied in the diffuser development. Some of the systems include; the channel between the compressor and gas turbine engine burner, the canal at departure from a gas turbine linked to the jet pipe, the canal subsequent to the impellor of a centrifugal compressor, wind tunnels with closed circuits, and water turbine draft tubes among several others. The results provide significant information for the improvement of proficiency and performance of technologies in aerospace, chemical, civil, environmental, industrial and mechanical applications.
Keywords
Unsteadiness Parameter, Viscous Dissipation, Inclined Variable Magnetic Field
To cite this article
Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal, Heat and Mass Transfer on MHD Jeffrey-Hamel Flow in Presence of Inclined Magnetic Field, Applied and Computational Mathematics. Vol. 9, No. 4, 2020, pp. 108-117. doi: 10.11648/j.acm.20200904.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Jeffery, G. B. "L. The two-dimensional steady motion of a viscous fluid." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 29, no. 172 (1915): 455-465.
[2]
Hamel, Georg. "Spiralförmige Bewegungen zäher Flüssigkeiten." Jahresbericht der Deutschen mathematiker-Vereinigung 25 (1917): 34-60.
[3]
W. I. Axford, “The magnetohydrodynamic Jeffrey-Hamel problem for a weakly conducting fluid,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 14, pp. 335–351, 1961.
[4]
Imani, A. A., Rostamian, Y., Ganji, D. D., & Rokni, H. B. (2012). Analytical investigation of Jeffery-Hamel flows with high magnetic field and nanoparticle by rvim.
[5]
Koeltzsch, K., Dinkelacker, A., & Grundmann, R. (2002). Flow over convergent and divergent wall riblets. Experiments in fluids, 33(2), 346-350.
[6]
Makinde, O. D. and P. Y. Mhone (2006). Hermite- Pade’ Approximation approach to Hydromagnetic flows in convergent-divergent channels. Applied Mathematics and Computations 181(2), 966-972.
[7]
Esmaili, Q., A. Ramiar, E. Alizadeh and D. D. Ganji (2008). An approximation of the analytical Solution of the Jeffery–Hamel flow by decomposition method. Physics Letters A 372, 3434–3439.
[8]
T. Hayat, F. M. Abbasi, M. Al-Yami, S. Monaquel, Slip and Joule heating effects in mixed convection peristaltic transport of nanofluid with Soret and Dufour effects, J. Mol. Liq. 194 (2014) 93–99.
[9]
E. M. Abo-Eldahab, M. Abd El-Aziz, Blowing/suction effect on hydromagnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption, Int. J. Therm. Sci. 43 (2004) 709–719.
[10]
A. J. Chamkha, Double-diffusive convection in a porous enclosure with cooperating temperature and concentration gradients and heat generation or absorption effects, Numer. Heat Transfer, Part A: Appl. 41 (1) (2002) 65–87.
[11]
M. Umamaheswar, S. V. K. Varma and M. C. Raju, Unsteady MHD free convective visco-elastic fluid flow bounded by an infinite inclined porous plate in the presence of heat source, viscous dissipation, and Ohmic heating, International journal of advanced science and technology, 61 (2013) 39-52.
[12]
Vijayakumar, K., & Reddy, E. K. (2017). MHD Boundary Layer Flow of a VISCO-Elastic Fluid Past a Porous Plate with Varying Suction and Heat Source/Sink in the Presence of Thermal Radiation and Diffusion. Global Journal of Pure and Applied Mathematics, 13(6), 2717-2733
[13]
Zubair Akbar, M., Ashraf, M., Farooq Iqbal, M., & Ali, K. (2016). Heat and mass transfer analysis of unsteady MHD nanofluid flow through a channel with moving porous walls and medium. AIP Advances, 6(4), 045222.
[14]
Pourabdian, M., Qate, M., Morad, M. R., & Javareshkian, A. (2016). The Jeffery-Hamel flow and heat transfer of nanofluids by homotopy perturbation method and Comparison with Numerical Results. arXiv preprint arXiv:1601.05298.
[15]
Meher, R., & Patel, N. D. (2019). A study on magnetohydrodynamic Jeffery-Hamel flows with heat transfer problem in Eyring-Powell fluid using Differential Transform Method. Journal of Applied Mathematics and Computational Mechanics, 18(3).
[16]
Ara, A., Khan, N. A., Naz, F., Raja, M. A. Z., & Rubbab, Q. (2018). Numerical simulation for Jeffery-Hamel flow and heat transfer of micropolar fluid based on differential evolution algorithm. AIP Advances, 8(1), 015201.
[17]
Ochieng, F. O., Kinyanjui, M. N., & Kimathi, M. E. (2018). Hydromagnetic Jeffery-Hamel Unsteady Flow of a Dissipative Non-Newtonian Fluid with Nonlinear Viscosity and Skin Friction. Global Journal of Pure and Applied Mathematics, 14(8), 1101-1119.
[18]
Alam, M. S., Haque, M. M., & Uddin, M. J. (2016). The convective flow of nanofluid along with a permeable stretching/shrinking wedge with second-order slip using Buongiorno’s mathematical model. International Journal of Advanced in Applied Mathematics and Mechanics, 3(3), 79-91.
[19]
Sattar, M. A. (2013). Derivation of the similarity equation of the 2-D unsteady boundary layer equations and the corresponding similarity conditions. American Journal of Fluid Dynamics, 3(5), 135.
[20]
Nagler, J. (2017). Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction. Applied Mathematics and Mechanics, 38(6), 815-830.
[21]
Alam, M. S., & Huda, M. N. (2013). A new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface. International Journal of Advances in Applied Mathematics and Mechanics, 1(2), 39-52.
[22]
Alam, M. D. S., Khan, M. A. H., & Alim, M. A. (2016). Magnetohydrodynamic Stability of Jeffery-Hamel Flow using Different Nanoparticles. Journal of Applied Fluid Mechanics, 9(2).
[23]
Ojiambo, V., Kinyanjui, M., & Kimathi, M. (2018). A study of two-phase Jeffery Hamel flow in a geothermal pipe.
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