## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Thermo diffusion aspects in Jeffrey nanofluid over periodically moving surface with time dependent thermal conductivity

**ABSTRACT**

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of nonlinear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

**KEYWORDS**

PAPER SUBMITTED: 2019-04-28

PAPER REVISED: 2019-07-02

PAPER ACCEPTED: 2019-07-11

PUBLISHED ONLINE: 2019-08-10

- Ahmed ,J., Shehzad, A., Khan, M. and Ali, R., A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet, AIP Advances 5, 117117 (2015); doi.org/10.1063/1.4935571.
- Hayat, T., Zahid, T., Meraj M. and Ahmed, A., Unsteady flow and heat transfer of Jeffrey fluid over a stretching sheet, Thermal Science, 18(4), .(2014), pp. 1069-1078. 10p.
- Das, K., Acharya, N., Kundu, P. K., Radiative flow of MHD Jeffrey fluid past a stretching sheet with surface slip and melting heat transfer, Alexandria Engineering Journal, 54 (2015), pp. 815-821
- Ahmad, K., Ishak, A., Magnetohydrodynamic (MHD) Jeffrey fluid over a stretching vertical surface in a porous medium, Propulsion and Power Research, 6(4) (2017) pp. 269-276.
- Zin, NAM.,, Khan, K., Shafie, S., Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature, Mathematical Problems in Engineering, (2016), Article ID 6257071, pp. 12.
- . Ramesh, G. K, Numerical Study of the Influence of Heat Source on Stagnation Point Flow towards a Stretching Surface of a Jeffrey Nanoliquid, Journal of Engineering 2015, Article ID 382061, (2015) pp. 10 dx.doi.org/10.1155/2015/382061.
- Saleem, S., Al-Qarni, M. M., Nadeem, S. and Sandeep, N., Convective Heat and Mass Transfer in Magneto Jeffrey Fluid Flow on a Rotating Cone with Heat Source and Chemical Reaction, Communications in Theoretical Physics, 70 (5) (2018) pp. 534.
- Narayan, P.V.S., Babu, D. H., Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation, Journal of the Taiwan Institute of Chemical Engineers, 59, (2016), pp. 18-25.
- Hussain, Q., Asghar, S., Hayat, T., Alsaedi, A., Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity, Applied Mathematics and Computations (English Edition) 36 (2015) 499. doi.org/10.1007/s10483-015-1926-9.
- Babu, D. H., and Narayana, P.V. S., Melting heat transfer and radiation effects on Jeffrey fluid flow over a continuously moving surface with parallel free stream, Journal of Applied and Computational Mechanics, 5(2), (2019) pp. 468-476.
- Narayana, P. V. S., Babu, D. H and Babu, M. S., Numerical Study of a Jeffrey Fluid over a Porous Stretching Sheet with Heat Source/Sink, International Journal of Fluid Mechanics Research, 46 (2), (2019) pp. 187-197.
- Choi, S.U.S. and Estman J, Enhancing thermal conductivity of fluids with nanoparticles. ASME- Publications-Fed, 231, (1995) pp. 99-106.
- Buongiorno, J. Convective transport in nanofluids, Journal of Heat Transfer 128 (2006) pp. 240-250.
- Liu, T., Liu, L. and Zheng, L., Unsteady flow and heat transfer of Maxwell nanofluid in a finite thin film with internal heat generation and thermophoresis, Thermal Science, 22(6B) (2018) pp. 2803-2813.
- Lin,Y., Zheng, L., Zhang, X.X., Lianxi M, Goong Chen, MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation, International Journal of Heat and Mass Transfer, 84, (2015), pp. 903-911.
- Sheikholeslami, M., Hatami, M. Ganji, D.D., Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, Journal of Molecular Liquids 190, (2014), pp. 112-120.
- Sheikholeslami, M., Numerical investigation for CuO-H2O nanofluid flow in a porous channel with magnetic field using mesoscopic method, Journal of Molecular Liquids, 249, (2018), pp. 739-746.
- Malik, M.Y., Khan, I., Hussain, A., and Salahuddin, T., Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: A numerical, AIP Advances 5, 117118 (2015); doi.org/10.1063/1.4935639study.
- Hayat, T., Imtiaz, M., and Alsaedi, A., Magnetohydrodynamic flow of nanofluid over permeable stretching sheet with convective boundary conditions, Thermal science, 20(6), (2016) pp. 1835-1845.
- Sheikholeslami M and Bhatti M.M,. Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles, International Journal of Heat and Mass Transfer 111, (2017) pp. 1039-1049.
- Abbasi F M, Shanakhat I and Shehzad S.A. Analysis of entropy generation in peristaltic nanofluid flow with Ohmic heating and Hall current, Physica. Scripta 94(2) (2019) pp. 025001.
- Reddy,K.V., Reddy M.G., and Makinde O. D ,Thermophoresis and Brownian Motion Effects on Magnetohydrodynamics Electro-Osmotic Jeffrey Nanofluid Peristaltic Flow in Asymmetric Rotating Microchannel, Journal of Nanofluids 8, pp. (2019) 349-358.
- Mahantesh M. Nandeppanavar, M. C. Kemparaju, and J. M. Shilpa J., Heat and Mass Transfer Analysis of Carreau Nanofluid Over an Exponentially Stretching Sheet in a Saturated Porous Medium , Nanofluids 8, (2019) pp. 990-997.
- Gireesha, B. J., Krishnamurthy, M. R , and Ganeshkumar, K., Nonlinear Radiative Heat Transfer and Boundary Layer Flow of Maxwell Nanofluid Past Stretching Sheet, Journal of Nanofluids 8, (2019) pp. 1093-1102.
- Babu, D. H., Ajmath, K. A., Venkateswarlu, B. and P. V. Satya Narayana, Thermal Radiation and Heat Source effects in MHD Non-Newtonian Nanofluid Flow over a Stretching Sheet, Journal of Nanofluids, 8(5), (2019), pp. 1085-1092.
- Latif, N. A. A., Uddin, M. J. and Ismail, A. I. MD, Unsteady MHD bio-nanoconvective anistropic slip flow past a vertical rotating cone, Thermal Science, 23(2A), (2019), pp. 427-441.
- Abro, K. A., Khan, I., Nisar, K. S. and Alsagri, A. S., effects of carbon nanotubes on magnetohydrodynamic flow of methanol based nanofluids via Atangana-Baleanu and Caputo-fabrizio fractional derivatives, Thermal Science, 23(2b) (2019), pp. 883-898.
- Goyal, M and Bhargava, R. Numerical study of thermodiffusion effects on boundary layer flow of nanofluids over a power law stretching sheet, Microfluid Nanofluid, 17 (3), (2014), pp. 591-604.
- Liao SJ. Advance in the Homotopy Analysis Method. 5 Toh Tuck Link, Singapore: World Scientific Publishing; (2014).
- Turkyilmazoglu M, Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection, International Journal of Mechanical Sciences 52 (2010) pp. 1735-1744.
- Turkyilmazoglu M, Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian decomposition method Mediterr Journal of Mathematics, 13 (2016) pp. 4019-4037.
- Turkyilmazoglu, M., Some issues on HPM and HAM methods: A convergence scheme, Mathematical and Computer Modelling 53, (2011) pp. 1929-1936
- Dinarvand, S., Abbassi, A., Hosseini, R. and Pop, I., Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder, Thermal Science, 19(2), (2015), pp. 549-561
- Turkyilmazoglu M, The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface, International Journal Mechanical Sciences 77 (2013) pp. 263-268.
- Zheng, L. C., Jin, X., Zhang, X.X. and Zhang, J.H., Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects, Acta Mechica Sinica, 29(5) (2013) pp. 667-675.
- Abbas, Z., Wang, Y., Hayat, T. and Oberlack, M., Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface, International Journal of Nonlinear Mechanics 43, (2008), pp. 783-797.