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Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection

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  • 1. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;
    2. Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
    3. Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan

Received date: 2019-03-30

  Revised date: 2019-06-13

  Online published: 2019-11-20

Abstract

The nonlinear convective flow of an Oldroyd-B fluid due to a nonlinear stretching sheet with varying thickness is examined. The salient features of the random movement and thermophoresis are described. Formulation is made with the nonlinear thermal radiation and heat generation/absorption. Further, the convective conditions and double stratification are taken into account. The resulting flow problems are tackled by the optimal homotopy analysis method (OHAM). The resulting nonlinear problems are solved for the velocity, temperature, and concentration fields. The temperature and concentration gradients are numerically discussed. The total residual error is calculated. The Nusselt number is an increasing function of the radiation parameter. The Sherwood number increases with the increase in the solutal stratification or the Schmidt number. The main outcomes are presented in conclusions. This study has a wide range of applications such as thermal stratification of oceans, reservoirs, and rivers, density stratification of atmosphere, hydraulic lifts, and polymer processing.

Cite this article

T. HAYAT, M. Z. KIYANI, I. AHMAD, A. ALSAEDI . Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection[J]. Applied Mathematics and Mechanics, 2019 , 40(12) : 1861 -1878 . DOI: 10.1007/s10483-019-2251-6

References

[1] MASUDA, H., EBATA, A., and TERAMAE, K. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei, 7, 227-233(1993)
[2] CHOI, S. U. S. and EASTMAN, J. Enhancing thermal conductivity of fluids with nanoparticle. Developments and Applications of Non-Newtonian Flows, ASME, New York (1995)
[3] XUAN, Y., LI, Q., and HU, W. Aggregation structure and thermal conductivity of nanofluids. AIChE Journal, 49, 1038-1043(2003)
[4] BUONGIORNO, J. Convective transport in nanofluids. Journal of Heat Transfer, 128, 240-250(2006)
[5] ZERRADI, H., OUASKIT, S., DEZAIRI, A., LOULIJAT, H., and MIZANI, S. New Nusselt number correlations to predict the thermal conductivity of nanofluids. Advanced Powder Technology, 25, 1124-1131(2014)
[6] KAKAC, S. and PRAMUANJAROENKIJ, A. Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52, 3187-3196(2009)
[7] XUAN, Y. and LI, Q. Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Flow, 21, 58-64(2000)
[8] HAYAT, T., KHAN, M. I., WAQAS, M., and ALSAEDI, A. Newtonian heating effect in nanofluid flow by a permeable cylinder. Results in Physics, 7, 256-262(2017)
[9] BILAL, M., SAGHEER, M., and HUSSAIN, S. Numerical study of magnetohydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity. Alexandria Engineering Journal, 57, 3281-3289(2018)
[10] CRANE, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik ZAMP, 21, 645-647(1970)
[11] ABBAS, Z., NAVEED, M., and SAJID, M. Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. Journal of Molecular Liquids, 215, 756-762(2016)
[12] JAMALUDIN, A., NAZAR, R., and POP, I. Three-dimensional mixed convection stagnationpoint flow over a permeable vertical stretching/shrinking surface with a velocity slip. Chinese Journal of Physics, 55, 1865-1882(2017)
[13] HAYAT, T., KHAN, M. I., QAYYUM, S., ALSAEDI, A., and KHAN, M. I. New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials. Physics Letters A, 382, 749-760(2018)
[14] MUKHOPADHYAY, S. and VAJRAVELU, K. Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface. Journal of Hydrodynamics, 25, 591-598(2013)
[15] QAYYUM, S., KHAN, M. I., HAYAT, T., and ALSAEDI, A. Comparative investigation of five nanoparticles in flow of viscous fluid with Joule heating and slip due to rotating disk. Physica B:Condensed Matter, 534, 173-183(2018)
[16] KHAN, M., SHAHID, A., MALIK, M. Y., and SALAHUDDIN, T. Thermal and concentration diffusion in Jeffery nanofluid flow over an inclined stretching sheet:a generalized Fourier's and Fick's perspective. Journal of Molecular Liquids, 251, 7-14(2018)
[17] KHAN, M. I., HAYAT, T., and ALSAEDI, A. Numerical investigation for entropy generation in hydromagnetic flow of fluid with variable properties and slip. Physics of Fluids, 30, 023601(2018)
[18] JUSOH, R., NAZAR, R., and POP, I. Flow and heat transfer of magnetohydrodynamic threedimensional Maxwell nanofluid over a permeable stretching/shrinking surface with convective boundary conditions. International Journal of Mechanical Sciences, 124, 166-173(2017)
[19] ZEESHAN, A. and MAJEED, A. Heat transfer analysis of Jeffery fluid flow over a stretching sheet with suction/injection and magnetic dipole effect. Alexandria Engineering Journal, 55, 2171-2181(2016)
[20] KHAN, M. I., KIYANI, M. Z., MALIK, M. Y., YASMEEN, T., KHAN, M. W. A., and ABBAS, T. Numerical investigation of magnetohydrodynamic stagnation point flow with variable properties. Alexandria Engineering Journal, 55, 2367-2373(2016)
[21] AHMAD, I., ZAFAR, H., KIYANI, M. Z., and FAROOQ, S. Zero mass flux characteristics in Jeffery nanoliquid flow by a nonlinear stretchable surface with variable thickness. International Journal of Heat and Mass Transfer, 132, 1166-1175(2019)
[22] HAYAT, T., KIYANI, M. Z., ALSAEDI, A., KHAN, M. I., and AHMAD, I. Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction. International Journal of Heat and Mass Transfer, 127, 422-429(2018)
[23] HAYAT, T., KIYANI, M. Z., AHMAD, I., KHAN, M. I., and ALSAEDI, A. Stagnation point flow of viscoelastic nanomaterial over a stretched surface. Results in Physics, 9, 518-526(2018)
[24] LU, D., MOHAMMAD, M., RAMZAN, M., BILAL, M., HOWARI, F., and SULEMAN, M. MHD boundary layer flow of Carreau fluid over a convectively heated bidirectional sheet with non-Fourier heat flux and variable thermal conductivity. Symmetry, 11, 618(2019)
[25] HAYAT, T., WAQAS, M., ALSAEDI, A., BASHIR, G., and ALZAHRANI, F. Magnetohydrodynamic (MHD) stretched flow of tangent hyperbolic nanoliquid with variable thickness. Journal of Molecular Liquids, 229, 178-184(2017)
[26] HAYAT, T., BASHIR, G., WAQAS, M., and ALSAEDI, A. MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer. Journal of Molecular Liquids, 223, 836-844(2016)
[27] LIU, L. and LIU, F. Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness. Applied Mathematics Letters, 79, 92-99(2018)
[28] FANG, T., ZHANG, J., and ZHONG, Y. Boundary layer flow over a stretching sheet with variable thickness. Applied Mathematics and Computation, 218, 7241-7252(2012)
[29] HAYAT, T., KIYANI, M. Z., AHMAD, I., and AHMAD, B. On analysis of magneto Maxwell nano-material by surface with variable thickness. International Journal of Mechanical Sciences, 131, 1016-1025(2017)
[30] DANIEL, Y. S., AZIZ, Z. A., ISMAIL, Z., and SALAH, F. Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness. Journal of Computational Design and Engineering, 5, 232-242(2018)
[31] SHAH, S., HUSSAIN, S., and SAGHEER, M. Impacts of variable thermal conductivity on stagnation point boundary layer flow past a Riga plate with variable thickness using generalized Fourier's law. Results in Physics, 9, 303-312(2018)
[32] MUTUKU, W. N. and MAKINDE, O. D. Double stratification effects on heat and mass transfer in unsteady MHD nanofluid flow over a flat surface. Asia Pacific Journal on Computational Engineering, 4, 2(2017)
[33] OLDROYD, J. G. On the formulation of rheological equations of state. Proceedings of the Royal Society of London, Series A:Mathematical and Physical Sciences, 200, 523-541(1950)
[34] BERGMAN, T. L., INCROPERA, F. P., DEWITT, D. P., and LAVINE, A. S. Fundamentals of Heat and Mass Transfer, John Wiley and Sons, Hoboken, New Jersey (2011)
[35] LIAO, S. Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press, Beijing, 153-165(2012)
[36] LIAO, S. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15, 2003-2016(2010)
[37] HAYAT, T., MUHAMMAD, T., MUSTAFA, M., and ALSAEDI, A. An optimal study for threedimensional flow of Maxwell nanofluid subject to rotating frame. Journal of Molecular Liquids, 229, 541-547(2017)
[38] AWAIS, M., AWAN, S. E., IQBAL, K., KHAN, Z. A., and RAJA, M. A. Z. Hydromagnetic mixed convective flow over a wall with variable thickness and Cattaneo-Christov heat flux model:OHAM analysis. Results in Physics, 8, 621-627(2018)
[39] MEHMOOD, R., RANA, S., and NADEEM, S. Transverse thermopherotic MHD Oldroyd-B fluid with Newtonian heating. Results in Physics, 8, 686-693(2018)
[40] FANG, T., ZHANG, J., and ZHONG, Y. Boundary layer flow over a stretching sheet with variable thickness. Applied Mathematics and Computation, 2187241-7252(2012)
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