# Free Convection Boundary Layer Flow from a Vertical Truncated Cone in a Hybrid Nanofluid

## Authors

• Muhammad Khairul Anuar Mohamed Centre for Mathematical Sciences,College of Computing & Applied Sciences,Universiti Malaysia Pahang,26300 Gambang,Kuantan, Pahang Darul Makmur,Malaysia
• Anuar Mohd Ishak School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi,Selangor, MALAYSIA
• Ioan Pop Department of Mathematics, Babeṣ-Bolyai University, 400084 Cluj-Napoca, Romania
• Nurul Farahain Mohammad Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University Malaysia, Bandar Indera Mahkota, 25200 Kuantan, Pahang, Malaysia
• Siti Khuzaimah Soid Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 UiTM Shah Alam, Selangor, Malaysia

## Keywords:

Free convection, full-cone, hybrid nanofluid, truncated cone,

## Abstract

The present study investigates the mathematical model of free convection boundary layer flow from a vertical truncated cone immersed in Cu/water nanofluid and Al2O3-Cu/water hybrid nanofluid. The governing non-linear equations are first transformed to a more convenient set of partial differential equations before being solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number and the reduced skin friction coefficient are obtained and illustrated graphically as well as temperature profiles and velocity profiles. Effects of the alumina Al2O3 and copper Cu nanoparticle volume fraction for hybrid nanofluid are analyzed and discussed. It is found that the high-density and highly thermal conductivity nanoparticles like copper contributed more in skin friction and convective heat transfer capabilities. The appropriate nanoparticles combination in hybrid nanofluid may reduce the friction between fluid and surface but yet still gave the heat transfer capabilities comparable to metal nanofluid.

## References

Wong, K. V. and De Leon, O. (2010). Applications of Nanofluids: Current and Future Advances in Mechanical Engineering, 2010 1-11.

Eastman, J., Choi, U., Li, S., Thompson, L. and Lee, S. 1997. Enhanced thermal conductivity through the development of nanofluids. Materials Research Society proceedings, Pittsburgh. Cambridge Univ Press.

Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E. and Grulke, E. A. (2001). Anomalously thermal conductivity enhancement in nanotube suspensions Applied Physics Letters, 79 2252-2254.

Kakaç, S. and Pramuanjaroenkij, A. (2009). Review of convective heat transfer enhancement with nanofluids International Journal of Heat and Mass Transfer, 52(13–14), 3187-3196.

Devi, S. S. U. and Devi, S. P. A. (2017). Heat transfer enhancement of Cu - Al2O3/water hybrid nanofluid flow over a stretching sheet Journal of the Nigerian Mathematical Society, 36(2), 419-433.

Na, T.-Y. and Chiou, J. (1979). Laminar natural convection over a frustum of a cone Applied Scientific Research, 35(5-6), 409-421.

Na, T. and Chiou, J. (1979). Laminar natural convection over a slender vertical frustum of a cone Wärme-und Stoffübertragung, 12(2), 83-87.

Kumari, M., Pop, I. and Nath, G. (1989). Mixed convection along a vertical cone International Communications in Heat and Mass Transfer, 16(2), 247-255.

Pop, I. and Na (1999). Natural convection over a vertical wavy frustum of a cone International Journal of Non-Linear Mechanics, 34 925-934.

Yih, K. (1999). Effect of radiation on natural convection about a truncated cone International Journal of Heat and Mass Transfer, 42(23), 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), 511-530.

Alim, M., Alam, M. M. and Chowdhury, M. M. (2006). Pressure work effect on natural convection flow from a vertical circular cone with suction and non-uniform surface temperature Journal of Mechanical Engineering, 36 6-11.

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), 272-279.

Chamkha, A., Abbasbandy, S., Rashad, A. M. and Vajravelu, K. (2013). Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid Meccanica, 48(2), 275-285.

Pătrulescu, F., 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, 24 1175-1190.

Mahdy, A. (2016). Natural convection boundary layer flow due to gyrotactic microorganisms about a vertical cone in porous media saturated by a nanofluid Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(1), 67-76.

Khan, W. A., Rashad, A., Abdou, M. and Tlili, I. (2019). Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone European Journal of Mechanics-B/Fluids, 75 133-142.

Khan, W. A., Rashad, A., EL-Kabeir, S. and EL-Hakiem, A. (2020). Framing the MHD Micropolar-Nanofluid Flow in Natural Convection Heat Transfer over a Radiative Truncated Cone Processes, 8(4), 379.

Ellahi, R., Zeeshan, A., Waheed, A., Shehzad, N. and Sait, S. M. (2021). Natural convection nanofluid flow with heat transfer analysis of carbon nanotubes–water nanofluid inside a vertical truncated wavy cone Mathematical Methods in the Applied Sciences, 202 11-19.

Rao, M. V. S., Gangadhar, K., Chamkha, A. J. and Surekha, P. (2021). Bioconvection in a Convectional Nanofluid Flow Containing Gyrotactic Microorganisms over an Isothermal Vertical Cone Embedded in a Porous Surface with Chemical Reactive Species Arabian Journal for Science and Engineering, 46(3), 2493-2503.

Keller, H. B. (1970). A New Difference Scheme for Parabolic Problems. Dalam: Bramble, Numerical Solutions of Partial Differential Equations. New York: Academic Press 1970.

Na, T. Y. (1979). Computational methods in engineering boundary value problems. New York: Academic Press 1979.

Cebeci, T. and Cousteix, J. (2005). Modeling and computation of boundary layer flows. Springer 2005.

Mohamed, M. K. A. (2018). Keller-box method: Partial differential equations in boundary layer flow of nanofluid. Pekan: DRB-HICOM University Publisher 2018.