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Application of Response Surface Methodology in the Optimization of Magneto-Hydrodynamic Flow Around and Through a Porous Circular Cylinder

Published online by Cambridge University Press:  08 February 2018

S. M. Vahedi ,
A. Zare Ghadi  and
M. S. Valipour
S. M. Vahedi*
Affiliation:
Faculty of Mechanical EngineeringSemnan UniversitySemnan, Iran
A. Zare Ghadi
Affiliation:
Faculty of Mechanical EngineeringSemnan UniversitySemnan, Iran
M. S. Valipour
Affiliation:
Faculty of Mechanical EngineeringSemnan UniversitySemnan, Iran
*
*Corresponding author ([email protected])
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Abstract

In this study MHD flow around and through porous cylinder is numerically investigated. The governing equations are developed in polar coordinate arrangement in both porous and non-porous media on the basis of single-domain technique. The equations are solved numerically based on finite volume method over staggered grid structure. Nusselt number and drag coefficient are selected as two key parameters describing performance of this system. By applying response surface methodology the sensitivity of these parameters to main factors of the problem, including Stuart number, Darcy number and Reynolds number are quantified. RSM is also utilized to perform an optimization process to find the best condition in which the lowest drag force and highest heat transfer rate occur simultaneously. The CFD analysis is carried out for variant Reynolds numbers (10 ≤ Re ≤ 40), Darcy numbers (10-6 ≤ Da ≤ 10-2) and Stuart numbers (2 ≤ N ≤ 10). Streamlines and isotherms are presented to indicate the impacts of such parameters on heat and fluid flow. It can be seen that, Drag coefficient and Nusselt number increase by augmenting magnetic field strength. Beside, Darcy number and Reynolds numbers have a direct and inverse effect on Nuave and Cd, respectively. Results of optimization process show that Nuave and Cd are more sensitive to Reynolds and Stuart numbers, respectively, while they less sensitive to Darcy number. Moreover, it is revealed that the optimum condition occurs at Da = 10-2, Re = 38.1 and N = 4.49.

Keywords

MHD flowMulti-objective optimizationFinite volume methodPorous media
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 5 , October 2018 , pp. 695 - 710
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Farooq, M., Gull, N., Alsaedi, A. and Hayat, T., “MHD Flow of a Jeffrey Fluid with Newtonian Heating,” Journal of Mechanics, 31, pp. 319–329 (2015).Google Scholar
2. Seth, G. S., Tripathi, R., Sharma, R. and Chamkha, A. J., “MHD Double Diffusive Natural Convection Flow over Exponentially Accelerated Inclined Plate,” Journal of Mechanics, 33, pp. 87–99 (2017).Google Scholar
3. Bhattacharyya, S., Dhinakaran, S. and Khalili, A., “Fluid Motion around and through a Porous Cylinder,” Chemical Engineering Science, 61, pp. 4451–4461 (2006).Google Scholar
4. Zhu, Q., Chen, Y. and Yu, H., “Numerical Simulation of the Flow around and through a Hygroscopic Porous Circular Cylinder,” Computers & Fluids, 92, pp. 188–198 (2014).Google Scholar
5. Yu, P., Zeng, Y., Lee, T. S., Chen, X. B. and Low, H. T., “Steady Flow around and through a Permeable Circular Cylinder,” Computers & Fluids, 42, pp. 1–12 (2011).Google Scholar
6. Valipour, M. S. and Zare Ghadi, A., “Numerical Investigation of Forced Convective Heat Transfer around and through a Porous Circular Cylinder with Internal Heat Generation,” Journal of Heat Transfer, 134, 062601 (2012).Google Scholar
7. Valipour, M. S., Rashidi, S., Bovand, M. and Masoodi, R., “Numerical Modeling of Flow around and through a Porous Cylinder with Diamond Cross Section,” European Journal of Mechanics-B/Fluids, 46, pp. 74–81 (2014).Google Scholar
8. Yu, P., Zeng, Y., Lee, T. S., Bai, H. X. and Low, H. T., “Wake Structure for Flow past and through a Porous Square Cylinder,” International Journal of Heat and Fluid Flow, 31, pp. 141–153 (2010).Google Scholar
9. Dhinakaran, S. and Ponmozhi, J., “Heat Transfer from a Permeable Square Cylinder to a Flowing Fluid,” Energy Conversion and Management, 52, pp. 2170–2182 (2011).Google Scholar
10. Yu, P., Zeng, Y., Lee, T. S., Chen, X. B. and Low, H. T., “Numerical Simulation on Steady Flow around and through a Porous Sphere,” International Journal of Heat and Fluid Flow, 36, pp. 142–152 (2012).Google Scholar
11. Rashidi, M. M., Momoniat, E. and Rostami, B., “Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters,” Journal of Applied Mathematics (2012).Google Scholar
12. Freidoonimehr, N., Rashidi, M. M. and Mahmud, S., “Unsteady MHD Free Convective Flow past a Permeable Stretching Vertical Surface in a Nano-Fluid,” International Journal of Thermal Sciences, 87, pp. 136–145 (2015).Google Scholar
13. Rashidi, M. M., Ali, M., Freidoonimehr, N., Rostami, B. and Hossain, M. A., “Mixed Convective Heat Transfer for MHD Viscoelastic Fluid Flow over a Porous Wedge with Thermal Radiation,” Advances in Mechanical Engineering, 6, 735939 (2014).Google Scholar
14. Rashidi, M. M. and Erfani, E., “Analytical Method for Solving Steady MHD Convective and Slip Flow Due to a Rotating Disk with Viscous Dissipation and Ohmic Heating,” Engineering Computations, 29, pp. 562–579 (2012).Google Scholar
15. Yoon, H. S., Chun, H. H., Ha, M. Y. and Lee, H. G., “A Numerical Study on the Fluid Flow and Heat Transfer around a Circular Cylinder in an Aligned Magnetic Field,” International Journal of Heat and Mass Transfer, 47, pp. 4075–4087 (2004).Google Scholar
16. Grigoriadis, D. G. E., Sarris, I. E. and Kassinos, S. C., “MHD Flow past a Circular Cylinder Using the Immersed Boundary Method,” Computers & Fluids, 39, pp. 345–358 (2010).Google Scholar
17. Rashidi, S., Dehghan, M., Ellahi, R., Riaz, M. and Jamal-Abad, M. T., “Study of Stream Wise Transverse Magnetic Fluid Flow with Heat Transfer around an Obstacle Embedded in a Porous Medium,” Journal of Magnetism and Magnetic Materials, 378, pp. 128–137 (2015).Google Scholar
18. Bovand, M., Rashidi, S., Dehghan, M., Esfahani, J. A. and Valipour, M. S., “Control of Wake and Vortex Shedding behind a Porous Circular Obstacle by Exerting an External Magnetic Field,” Journal of Magnetism and Magnetic Materials, 385, pp. 198–206 (2015).Google Scholar
19. Valipour, M. S. and Zare Ghadi, A., “Numerical Investigation of Fluid Flow and Heat Transfer around a Solid Circular Cylinder Utilizing Nanofluid,” International Communications in Heat and Mass Transfer, 38, pp. 1296–1304 (2011).Google Scholar
20. Zare Ghadi, A., Goodarzian, H., Gorji-Bandpy, M. and Valipour, M. S., “Numerical Investigation of Magnetic Effect on Forced Convection around Two-Dimensional Circular Cylinder Embedded in Porous Media,” Engineering Applications of Computational Fluid Mechanics, 6, pp. 395–402 (2012).Google Scholar
21. Zare Ghadi, A., Noroozi, M. J. and Esfe, M. H., “Nanofluid Implementation for Heat Transfer Augmentation of Magneto Hydrodynamic Flows in a Lid-Driven Cavity Using Experimental-Based Correlations,” International Journal of Applied Electromagnetics and Mechanics, 42, pp. 589–602 (2013).Google Scholar
22. Derakhshan, S. and Yazdani, K., “3D Analysis of Magnetohydrodynamic (MHD) Micropump Performance Using Numerical Method,” Journal of Mechanics, 32, pp. 55–62 (2016).Google Scholar
23. Patankar, S. V. and Spalding, D. B., “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows,” International Journal of Heat and Mass Transfer, 15, pp. 1787–1806 (1972).Google Scholar
24. Versteeg, H. K. and Malalasekera, W., An Introduction to Computional Fluid Dynamics: The Finite Volume Method, 2nd Edition, Glasgow, Pearson Education Limited (2007).Google Scholar
25. Zare Ghadi, A., Haghighi Asl, A. and Valipour, M. S., “Numerical Modelling of Double-Diffusive Natural Convection within an Arc Shaped Enclosure Filled with a Porous Medium,” Journal of Heat and Mass Transfer Research, 1, pp. 83–91 (2007).Google Scholar
26. Bharti, R. P., Chhabra, R. P. and Eswaran, V., “A Numerical Study of the Steady Forced Convection Heat Transfer from an Unconfined Circular Cylinder,” Heat and Mass Transfer, 43, pp. 639–648 (2007).Google Scholar
27. Montgomery, D. C., Design and Analysis of Experiments, 7th Edition, John Wiley & Sons, Arizona (2008).Google Scholar
28. Khuri, A. I., Response Surface Methodology and Related topics, World Scientific, New Jersey (2006).Google Scholar
29. Grum, J. and Slabe, J. M., “The Use of Factorial Design and Response Surface Methodology for Fast Determination of Optimal Heat Treatment Conditions of Different Ni–Co–Mo Surfaced Layers,” Journal of Materials Processing Technology, 155, pp. 2026–2032 (2004).Google Scholar
30. Gilmour, S. G., “Response Surface Designs for Experiments in Bioprocessing,” Biometrics, 62, pp. 323–331 (2006).Google Scholar
31. Box, G. E. and Wilson, K. B., “On the Experimental Attainment of Optimum Conditions,” In Breakthroughs in Statistics, Springer New York, pp. 270–310 (1992).Google Scholar
32. Box, G. E. and Hunter, J. S., “Multi-Factor Experimental Designs for Exploring Response Surfaces,” The Annals of Mathematical Statistics, pp. 195–241 (1957).Google Scholar
33. Scheffe, H., The Analysis of Variance, John Wiley & Sons, New York (1999).Google Scholar
34. Diel, C. L. et al., “Optimization of Multiple-Effect Evaporation in the Pulp and Paper Industry Using Response Surface Methodology,” Applied Thermal Engineering, 95, pp. 18–23 (2016).Google Scholar
35. Rout, S. K., Choudhury, B. K., Sahoo, R. K. and Sarangi, S. K., “Multi-Objective Parametric Optimization of Inertance Type Pulse Tube Refrigerator Using Response Surface Methodology and Non-Dominated Sorting Genetic Algorithm,” Cryogenics, 62, pp. 71–83 (2014).Google Scholar
36. Ozcelik, B. and Erzurumlu, T., “Determination of Effecting Dimensional Parameters on Warpage of Thin Shell Plastic Parts Using Integrated Response Surface Method and Genetic Algorithm,” International Communications in Heat and Mass Transfer, 32, pp. 1085–1094 (2005).Google Scholar
37. Kansal, H. K., Singh, S. and Kumar, P., “Parametric Optimization of Powder Mixed Electrical Discharge Machining by Response Surface Methodology,” Journal of Materials Processing Technology, 169, pp. 427–436 (2005).Google Scholar