APPLICATION OF HOMOTOPY PERTURBATION METHOD TO HEAT TRANSFER IN NANOFLUIDS

Year 2018, , 73 - 78, 15.05.2018

Jonathan Oahimire Olusegun Adeokun

https://doi.org/10.31127/tuje.350418

Abstract

This paper investigates heat transfer in a nanofluid using the Homotopy Perturbation method. Similarity transformation variables and a stream function are used to transform the partial differential equations governing the fluid flow into ordinary differential equations. He’s Homotopy perturbation method is then used to solve the resulting dimensionless equations. It was discovered that an increase in the fraction number, magnetic parameter or Grashof number led to a corresponding increase in the rate of heat transfer regardless of the nanoparticles in the fluid. These results are in agreement with those found in existing literature.

Keywords

nanofluids, similarity transformation, homotopy perturbation method, heat transfer

References

• Ayati, Z. and Biazar, J. (2015). “On the Convergence of the Homotopy Perturbation Method.” Journal of the Egyptian Mathematical Society, Issue 23. pp. 424-428
• Do, k. h. and Jang S. (2010). “Effect of nanofluids on the thermal performance of a flat micro heat pipe with a rectangular grooved wick.” International Journal of Heat and Mass Transfer, 53 , pp 2183 – 2192
• Hamad M.A.A. (2011). “Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field.” International Communications in Heat and Mass Transfer, Vol. 38, Issue 4, pp 487 – 492.
• Oahimire J.I, Bazuaye F.E and Harry T. H ((2016). “Numerical method for the analysis of thermal radiation on heat transfer in nanofluid.” Journal of Nanoscience and Technology, Vol.3, Issue 1, pp 1-4
• Uddin M.J., Kahn W. A., and Ismail A.I. (2012) “MHD Free Convective Boundary Layer flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary condition.” PLoS ONE 7(11): e49499 doi:10.1371/journal.pone.49499
• Wang X., Xu X. and Choi S.U.S. (1999). “Thermal conductivity of nanoparticle - fluid mixture.” Journal of Thermophysics and Heat Transfer, Vol. 13, No. 4, pp 474 – 80.