# HPM ANALYSIS TO MHD FLOW OF A RADIATIVE NANOFLUID WITH VISCOUS DISSIPATION AND OHMIC HEATING OVER A STRETCHING POROUS PLATE

## Main Article Content

## Abstract

An analytical study is performed to explore the flow and heat transfer characteristics of nano fluid (Al2O3-water and TiO3-water) over a linearly stretching porous sheet in the presence of radiation, ohmic heating and viscous dissipation. Homotopy perturbed method is used and complete solution is presented, the results for the nanofluids velocity and temperature are obtained. The effects of various thermophysical parameters on the boundary layer flow characteristics are displayed graphically and discussed quantitatively. The effect of viscous dissipation on the thermal boundary layer is seen to be reverse after a fixed distance from the wall, which is very strange in nature and is the result of a reverse flow. The finding of this paper are unique and may be useful for future research on nanofluid.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2195>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI150731209K.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

[2] Wong, K.F.V., Leon, O.D. , Applications of nanofluids: current and future, Adv. Mech. Eng. Article ID: 519659 (2010).

[3] Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two- dimensional enclosure utilizing nanofluids, J. Heat Mass Transfer,46 (2003), pp. 3639-3653.

[4] Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G., Galanis, N., Heat transfer enhancement by using nanofluids in forced convection flows, Int. J. Heat Fluid Flow, 26 (2005), pp. 530-546.

[5] Jou, R.Y., Tzeng, S.C., Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, Int. Commun. Heat Transfer, 33 (2006), pp. 727-736.

[6] Tiwari, R.K., Das, M.K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer, 50 (2007), pp. 2002–2018.

[7] Hwang, K.S., Lee, Ji-H., Jang, S.P., Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity, Int. J. Heat Mass Transfer, 50 (2007), pp. 4003-4010.

[8] Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29 (2008), pp. 1326–1336.

[9] Muthtamilselvan, M., Kandaswamy, P., Lee, J., Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure, Communications in Nonlinear Science and Numerical Simulation, 15 (2010), pp. 1501–1510.

[10] Buongiorno, J., Convective Transport in Nanofluids, ASME J. Heat Transfer, 128 (2006), pp. 240-250.

[11] Kuznetsov, A.V., Nield, D.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 49 (2010), pp. 243-247.

[12] Abu-Nada, E., Oztop, H.F., Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid, International Journal of Heat Fluid Flow, 30 (2009), pp. 669 – 678.

[13] Gebhart. B., Effects of viscous dissipation in natural convection, J. Fluid Mech., 14 (1962), pp. 225-232.

[14] Pantokratoras. A., Effect of viscous dissipation in natural convection along a heated vertical plate, Appl. Math. Model., 29 (2004), pp. 553-564.

[15] Makinde. O.D., Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating, Appl. Math. Mech., 33 (2012), pp. 1442-1450.

[16] Aminossadati. S.M., Ghasemi. B., Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, European Journal of Mechanics B/Fluids, 28 (2009), pp. 630–640.

[17] Kumar. H., Radiative heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface in the presence of variable heat flux, Therm. Sci., 13 (2009), 163-169.

[18] He. J.H., Non-perturbative methods for strongly nonlinear problems, Ph.D. thesis, de-Verlag im Internet GmbH, Berlin, Germany, (2006).

[19] He. J.H., Some asymptoticmethods for strongly nonlinear equations, International Journal of Modern Physics B, 20 (2006), pp. 1141–1199.

[20] He. J.H., Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350 (2006), pp. 87–88.

[21] He. J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons & Fractals, 26 (2005), pp. 695–700.

[22] He. J.H., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167 (1998), pp. 57–68.

[23] He. J.H., Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167 (1998), pp. 69– 73.

[24] He. J.H., Variational iteration method—a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics, 34 (1999), pp. 699–708.

[25] He. J.H., Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999), pp. 257–262.

[26] He. J.H., A coupling method of a homotopy technique and a perturbation technique for non- linear problems, International Journal of Non-Linear Mechanics, 35 (2000), pp. 37–43.