Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T05:36:41.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Bivariate Pseudo-Spectral Local Linearisation Method for Mixed Convective Flow Over the Vertical Frustum of a Cone in a Nanofluid with Soret and Viscous Dissipation Effects

Published online by Cambridge University Press:  18 August 2017

Ch. RamReddy  and
Ch. Venkata Rao
Ch. RamReddy*
Affiliation:
Department of MathematicsNational Institute of TechnologyWarangal, India
Ch. Venkata Rao
Affiliation:
Department of MathematicsNational Institute of TechnologyWarangal, India
*
*Corresponding author (chramreddy@nitw.ac.in; chittetiram@gmail.com)
Get access

Abstract

In this investigation, we intend to present the influence of the prominent viscous dissipation and Soret effects on mixed convection heat and mass transfer over the vertical frustum of a cone in a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition, the uniform wall nanoparticle condition at the surface is replaced with the zero nanoparticle mass flux condition to execute physically applicable results. The governing equations of a nanofluid flow in the dimensional form are reduced to a system of partial differential equations in the non-dimensional form by using suitable non-similarity variables and then solved by using a recently introduced spectral method named as Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM). The convergence and error analysis tests are conducted to examine the accuracy of the spectral method. To validate the method, the present numerical results are compared with the existing results in some special cases and the outcomes are observed to be in very good agreement. The effects of Brownian motion, thermophoresis, Eckert number, Soret number, nanoparticle and regular buoyancy parameters on the dimensionless surface drag, heat, nanoparticle mass and regular mass transfer rates over the vertical frustum of a cone are discussed and illustrated graphically.

Keywords

NanofluidSoret effectViscous dissipationBivariate Pseudo-Spectral Local Linearisation Method (BPSLLM)
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 5 , October 2017 , pp. 687 - 702
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Choi, S. U. S., “Enhancing Thermal Conductivity of Fluids with Nanoparticles: Developments and Applications of Non-Newtonian Flows,” ASME: Fluids Engineering Division, 231, pp. 99–105 (1995).Google Scholar
2. Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E. and Grulke, E. A. “Anomalously Thermal Conductivity Enhancement in Nanotube Suspension,” Applied Physics Letters, 79, pp. 2252–2254 (2001).CrossRefGoogle Scholar
3. Das, S. K., Choi, S. U. S., Yu, W. and Pradeep, T., Nanofluids: Science and Technology, Wiley-Interscience, New Jersey (2007).CrossRefGoogle Scholar
4. Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240–250 (2006).CrossRefGoogle Scholar
5. Das, S. K. and Stephen, U. S., “A Review of Heat Transfer in Nanofluids,” Advances in Heat Transfer, 41, pp. 81–197 (2009).Google Scholar
6. Kakac, S. and Pramuanjaroenkij, A., “Review of Convective Heat Transfer Enhancement with Nanofluids,” International Journal of Heat and Mass Transfer, 52, pp. 3187–3196 (2009).Google Scholar
7. Ali Agha, H., Bouaziz, M. N. and Hanini, S., “Magnetohydrodynamic, Thermal Radiation and Convective Boundary Effects of Free Convection Flow Past a Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid,” Journal of Mechanics, 31, pp. 607–616 (2015).Google Scholar
8. Malvandi, A. and Ganji, D. D., “Effects of Nanoparticle Migration on Water/Alumina Nanofluid Flow inside a Horizontal Annulus with a Moving Core,” Journal of Mechanics, 31, pp. 291–305 (2015).Google Scholar
9. Merk, H. J. and Prins, J. A., “Thermal Convection in Laminar Boundary Layers I,” Applied Scientific Research, Section A, 4, pp. 11–24 (1953).CrossRefGoogle Scholar
10. Hering, R. G. and Grosh, R. J., “Laminar Free Convection from a Non-Isothermal Cone,” International Journal of Heat and Mass Transfer, 5, pp. 1059–1068 (1962).Google Scholar
11. Kumari, M., Pop, I. and Nath, G., “Mixed Convection along a Vertical Cone,” International Communications in Heat and Mass Transfer, 16, pp. 247–255 (1989).CrossRefGoogle Scholar
12. Cheng, C. Y. “Natural Convection Boundary Layer Flow over a Truncated Cone in a Porous Medium Saturated by a Nanofluid,” International Communications in Heat and Mass Transfer, 39, pp. 231–235 (2012).CrossRefGoogle Scholar
13. Patrulescu, F. O., Groşan, T. and Pop, I., “Mixed Convection Boundary Layer Flow from a Vertical Truncated Cone in a Nanofluid,” International Journal of Numerical Methods for Heat and Fluid Flow, 24, pp. 1175–1190 (2014).Google Scholar
14. Noghrehabadi, A., Behseresht, A. and Ghalambaz, M., “Natural Convection Flow of Nanofluids over Vertical Cone Embedded in Non-Darcy Porous Media,” Journal of Thermophysics and Heat Transfer, 27, pp. 334–341 (2013).Google Scholar
15. Na, T. Y. and Chiou, J. P., “Laminar Natural Convection over a Frustum of a Cone,” Applied Scientific Research, 35, pp. 409–421 (1979).Google Scholar
16. Singh, P., Radhakrishnan, V. and Narayan, K. A., “Natural Convection Flow over a Vertical Frustum of a Cone for Constant Wall Heat Flux,” Applied Scientific Research, 46, pp. 335–345 (1989).Google Scholar
17. Ahmed, S. E. and Mahdy, A., “Natural Convection Flow and Heat Transfer Enhancement of a Nanofluid past a Truncated Cone with Magnetic Field Effect,” World Journal of Mechanics, 2, pp. 272–279 (2012).Google Scholar
18. Eckert, E. R. G. and Drake, R. M., Analysis of Heat and Mass Transfer, McGraw-Hill, New York (1972).Google Scholar
19. Dursunkaya, Z. and Worek, W. M., “Diffusion-Thermo and Thermal Diffusion Effects in Transient and Steady Natural Convection from a Vertical Surface,” International Journal of Heat Mass Transfer, 35, pp. 2060–2065 (1972).Google Scholar
20. Awad, F. G., Sibanda, P., Motsa, S. S. and Makinde, O. D., “Convection from an Inverted Cone in a Porous Medium with Cross-Diffusion Effects,” Computers and Mathematics with Applications, 61, pp. 1431–1441 (2011).Google Scholar
21. Cheng, C. Y., “Soret and Dufour Effects on Double Diffusive Free Convection over a Vertical Truncated Cone in Porous Media with Variable Wall Heat and Mass Fluxes,” Transport in Porous Media, 91, pp. 877–888 (2012).Google Scholar
22. Hady, F. M., Eid, M. R., Abd-Elsalam, M. R. and Ahmed, M. A., “Soret Effect on Natural Convection Boundary-layer Flow of a Non-Newtonian Nanofluid over a Vertical Cone Embedded in a Porous Medium,” IOSR Journal of Mathematics, 8, pp. 51–61 (2013).Google Scholar
23. RamReddy, Ch., Murthy, P. V. S. N., Chamkha, A. J. and Rashad, A. M., “Soret Effect on Mixed Convection Flow in a Nanofluid under Convective Boundary Condition,” International Journal of Heat and Mass Transfer, 64, pp. 384–392 (2013).CrossRefGoogle Scholar
24. Gebhart, B., “Effects of Viscous Dissipation in Natural Convection,” Journal of Fluid Mechanics, 14, pp. 225–232 (1962).Google Scholar
25. Gebhart, B. and Mollendorf, J., “Viscous Dissipation in External Natural Convection Flows,” Journal of Fluid Mechanics, 38, pp. 97–107 (1969).Google Scholar
26. Murthy, P. V. S. N. and Singh, P., “Effect of Viscous Dissipation on a Non-Darcy Natural Convection Regime,” International Journal of Heat and Mass Transfer, 40, pp. 1251–1260 (1997).CrossRefGoogle Scholar
27. Rashad, A. M., Chamkha, A. J., RamReddy, C. and Murthy, P. V. S. N., “Effect of Viscous Dissipation on Mixed Convection in a Nanofluid Saturated Non-Darcy Porous Medium under Convective Boundary Condition,” Journal of Nanofluids, 4, pp. 548–559 (2015).CrossRefGoogle Scholar
28. Kuznetsov, A. V. and Nield, D. A., “Natural Convective Boundary Layer Flow of a Nanofluid past a Vertical Plate-A Revised Model,” International Journal of Thermal Sciences, 77, pp. 126–129 (2014).Google Scholar
29. Motsa, S. S., “A New Spectral Local Linearization Method for Non-Linear Boundary Layer Flow Problems,” Journal of Applied Mathematics, ID 423628 (2013).CrossRefGoogle Scholar
30. Motsa, S. S. and Animasaun, I. L., “A New Numerical Investigation of Some Thermo Physical Properties on Unsteady MHD Non-Darcian Flow past an Impulsively Started Vertical Surface,” Thermal Science, 19, pp. 249–258 (2015).Google Scholar
31. Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin (1988).Google Scholar
32. Trefethen, L. N., Spectral Methods in MATLAB, SIAM (2000).Google Scholar
33. Weideman, J. A. and Reddy, S. C., “A MATLAB Differentiation Matrix Suite,” ACM Transactions on Mathematical Software (TOMS), 26, pp. 465–519 (2000).CrossRefGoogle Scholar
34. Lloyd, J. R. and Sparrow, E. M., “Combined Forced and Free Convection Flow on Vertical Surfaces,” International Journal of Heat and Mass Transfer, 13, pp. 434–438 (1970).Google Scholar
35. Kafoussias, N. G., “Local Similarity Solution for Combined Free-Forced Convective and Mass Transfer Flow past a Semi-Infinite Vertical Plate,” International Journal of Energy Research, 14, pp. 305–309 (1990).Google Scholar
36. Srinivasacharya, D. and Vijay Kumar, P., “Thermal Stratification on Natural Convection over an Inclined Wavy Surface in a Nanofluid Saturated Porous Medium,” Computational Thermal Sciences: An International Journal, 7, pp. 405–415 (2015).Google Scholar