## THERMAL SCIENCE

International Scientific Journal

### IMPACT OF WAVY TEXTURE AND HYBRIDITY OF NANOFLUID ON HEAT TRANSFER AUGMENTATION OVER THE FRUSTUM OF CONE GEOMETRY

**ABSTRACT**

In this article, the impact of water-based hybrid nanofluid on heat transfer characteristics along the wavy frustum of the cone is examined. We considered hybrid nanofluid containing Cu and TiO2 nanoparticles. Non-similar form of the constitutive equations is obtained by using an appropriate set of transformations and results are achieved by employing transformed into compact non-similar form and are solved by the famous numerically implicit finite difference scheme known as Keller-box technique. The influence of the hybrid nanoparticles’ volume fraction, frustum of cone half-angle, and the wavy texture parameters on the Nusselt number and skin friction are scrutinized and comparison is made between the wavy frustum of the cone and flat frustum of the cone through numerical data. It is observed that the rise in the truncated cone half-angle leads to an increase in skin friction and Nusselt number. The TiO2-water nanofluid has lower heat transfer rates as compared to Cu-TiO2 hybrid nanofluid. The increasing of the truncated cone half-angle enhances the heat transfer rates. Generally, the results established from this analysis can be used as a benchmark for improving the natural convection heat transfer performance along the frustum of cone wavy texture.

**KEYWORDS**

PAPER SUBMITTED: 2020-08-22

PAPER REVISED: 2020-10-07

PAPER ACCEPTED: 2020-10-10

PUBLISHED ONLINE: 2020-11-07

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 4**, PAGES [2691 - 2700]

- Na, T.Y. and Chiou, J.P., 1979. Laminar natural convection over a frustum of a cone. Applied Scientific Research, 35(5-6), pp.409-421.
- Na, T.Y. and Chiou, J.P., 1979. Laminar natural convection over a slender vertical frustum of a cone. Wärme-und Stoffübertragung, 12(2), pp.83-87.
- Singh, P., Radhakrishnan, V. and Narayan, K.A., 1989. Natural convection flow over a vertical frustum of a cone for constant wall heat flux. Applied scientific research, 46(4), pp.335-345.
- Singh, P., Radhakrishnan, V. and Narayan, K.A., 1989. Non-similar solutions of free convection flow over a vertical frustum of a cone for constant wall temperature. Ingenieur-Archiv, 59(5), pp.382-389.
- Pop, I. and Na, T.Y., 1999. Natural convection over a vertical wavy frustum of a cone. International journal of non-linear mechanics, 34(5), pp.925-934.
- Yih, K.A., 1999. Effect of radiation on natural convection about a truncated cone. International Journal of Heat and Mass Transfer, 42(23), pp.4299-4305.
- Chamkha, A.J., 2001. Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects. Numerical Heat Transfer: Part A: Applications, 39(5), pp.511-530.
- Hossain, M.A., Munir, M.S. and Takhar, H.S., 2000. Natural convection flow of a viscous fluid about a truncated cone with temperature dependent viscosity. Acta Mechanica, 140(3-4), pp.171-181.
- Postelnicu, A., 2006. Free convection about a vertical frustum of a cone in a micropolar fluid. International journal of engineering science, 44(10), pp.672-682.
- Cheng, C.Y., 2008. Natural convection of a micropolar fluid from a vertical truncated cone with power-law variation in surface temperature. International communications in heat and mass transfer, 35(1), pp.39-46.
- Cheng, C.Y., 2009. Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity. Applied mathematics and computation, 212(1), pp.185-193.
- Cheng, C.Y., 2011. Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature. International Communications in Heat and Mass Transfer, 38(4), pp.429-433.
- Srinivasa, A.H. and Eswara, A.T., 2016. Effect of internal heat generation or absorption on MHD free convection from an isothermal truncated cone. Alexandria engineering journal, 55(2), pp.1367-1373.
- Cheng, C.Y., 2013. Free convective boundary-layer flow over a vertical truncated cone in a bidisperse porous medium. In Proceedings of the World Congress on Engineering (Vol. 3).
- Pătrulescu, F.O., Groşan, T. and Pop, I., 2014. Mixed convection boundary layer flow from a vertical truncated cone in a nanofluid. International Journal of Numerical Methods for Heat & Fluid Flow.
- Siddiqa, S.; Begum, N.; Hossain, M.A.; Mustafa, N.: Two-phase dusty fluid flow along a cone with variable properties. Heat Mass Transf. 53, 1517-1525 (2017)
- Amanulla, C.H., Nagendra, N. and Suryanarayana Reddy, M., 2017. Thermal and momentum slip effects on hydromagnetic convection flow of a Williamson fluid past a vertical truncated cone. Frontiers in Heat and Mass Transfer (FHMT), 9(1).
- Ahmed, S.E. and Mahdy, A., 2012. Natural convection flow and heat transfer enhancement of a nanofluid past a truncated cone with magnetic field effect. World Journal of Mechanics, 2(05), p.272.
- Siddiqa, S., Begum, N., Iftikhar, T., Rafiq, M., Hossain, M.A. and Gorla, R.S.R., 2019. Thermal Radiation Effects on Casson Dusty Boundary-Layer Fluid Flow Along an Isothermal Truncated Vertical Cone. Arabian Journal for Science and Engineering, 44(9), pp.7833-7842.
- Siddiqa, S., Begum, N., Hossain, M.A., Shoaib, M. and Reddy Gorla, R.S., 2018. Radiative heat transfer analysis of non-Newtonian dusty Casson fluid flow along a complex wavy surface. Numerical Heat Transfer, Part A: Applications, 73(4), pp.209-221.
- Siddiqa, S., Begum, N., Hossain, M.A. and Massarotti, N., 2016. Influence of thermal radiation on contaminated air and water flow past a vertical wavy frustum of a cone. International Communications in Heat and Mass Transfer, 76, pp.63-68.
- Mahdy, A. and Elshehabey, H.M., 2018. Gyrotactic microorganisms free convection boundary layer flow about a vertical truncated cone in nanofluid porous media. Latin American Applied Research-An international journal, 48(1), pp.57-62.
- Ram Reddy, C. and Rao, C.V., 2017. Non-similarity Solutions for Natural Convective Flow of a Nanofluid Over Vertical Frustum of a Cone Embedded in a Doubly Stratified Non-Darcy Porous Medium. International Journal of Applied and Computational Mathematics, 3(1), pp.99-113.
- Siddiqa, S., Begum, N., Hossain, M.A. and Gorla, R.S.R., 2017. Numerical solutions of natural convection flow of a dusty nanofluid about a vertical wavy truncated cone. Journal of Heat Transfer, 139(2).
- Ghaffari, A., Mustafa, I., & Javed, T. (2019). Influence of nonlinear radiation on natural convection flow of carbon nanotubes suspended in water-based fluid along a vertical wavy surface. Physica Scripta, 94(11), 115214.
- Iqbal, M. S., Mustafa, I., & Ghaffari, A. (2019). Analysis of Heat Transfer Enrichment in Hydromagnetic Flow of Hybrid Nanofluid Along Vertical Wavy Surface. Journal of Magnetics, 24(2), 271-280.
- Ghaffari, A., Javed, T., Mustafa, I., & Labropulu, F. (2018). Modeling and simulation of natural convection flow along a rough surface of sinusoidal nature with variable heat flux: Using Keller box scheme. Thermal Science, (00), 106-106.
- Mustafa, I., Javed, T., & Ghaffari, A. (2017). Hydromagnetic natural convection flow of water-based nanofluid along a vertical wavy surface with heat generation. Journal of Molecular Liquids, 229, 246-254.
- Javed, T., Ahmad, H., & Ghaffari, A. (2016). Influence of radiation on vertical wavy surface with constant heat flux: Using Keller box scheme. Alexandria Engineering Journal, 55(3), 2221-2228.
- Siddiqa, S., Begum, N. and Hossain, M.A., 2016. Radiation effects from an isothermal vertical wavy cone with variable fluid properties. Applied Mathematics and Computation, 289, pp.149-158.
- Tiwari, R. K., and Das, M. K. (2007). Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. International Journal of heat and Mass transfer, 50(9-10), 2002-2018.
- Na, T.Y. ed., 1980. Computational methods in engineering boundary value problems. Academic Press.
- Cebeci, T. and Bradshaw, P., 2012. Physical and computational aspects of convective heat transfer. Springer Science & Business Media.
- Alim M.A., Karim M.R. and Akand M.M. (2012) Heat generation effects on magnetohydrodynamic (MHD) natural convection flow along a vertical wavy surface with variable thermal conductivity. A. J. of Comput. Math., 2 , 42-50.
- Hossain, M. A., Kabir, S., & Rees, D. A. S. (2002). Natural convection of fluid with variable viscosity from a heated vertical wavy surface ZAMP, 53(1), 48-57.