Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

doi:10.1007/s10483-018-2374-8

摘要/Abstract

摘要： The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

关键词: variational inequations, elasto-plasticity, linear complementaryequations, Lemke algorithm, nonlinear mixed convection, thermal radiation, Maxwell nanomaterial, double stratification, convective condition

Abstract: The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Key words: Maxwell nanomaterial, nonlinear mixed convection, variational inequations, elasto-plasticity, linear complementaryequations, Lemke algorithm, double stratification, convective condition, thermal radiation

中图分类号:

76A05

T. HAYAT, S. NAZ, M. WAQAS, A. ALSAEDI. Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(10): 1373-1384.

参考文献

[1] CHOI, S. U. S. and EASTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, 66, 99-105(1995)
[2] KUZNETSOV, A. V. and NIELD, D. A. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 49, 243-247(2010)
[3] KANDASAMY, R., MUHAIMIN, I., and MOHAMAD, R. Thermophoresis and Brownian motion effects on MHD boundary-layer flow of a nanofluid in the presence of thermal stratification due to solar radiation. International Journal of Mechanical Sciences, 70, 146-154(2013)
[4] SANDEEP, N., KUMAR, B. R., and KUMAR, M. S. J. A comparative study of convective heat and mass transfer in non-Newtonian nanofluid flow past a permeable stretching sheet. Journal of Molecular Liquids, 212, 585-591(2015)
[5] MAHANTHESH, B., GIREESHA, B. J., PRASANNAKUMARA, B. C., and KUMAR, P. B. S. Magneto-thermo-Marangoni convective flow of Cu-H₂O nanoliquid past an infinite disk with particle shape and exponential space based heat source effects. Results in Physics, 7, 2990-2996(2017)
[6] AHMED, S. E. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Applied Mathematics and Mechanics (English Edition), 38, 1171-1180(2017) https://doi.org/10.1007/s10483-017-2231-9
[7] NAGENDRAMMA, V., RAJU, C. S. K., MALLIKARJUNA, B., SHEHZAD, S. A., and LEELARATHNAM, A. 3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux. Applied Mathematics and Mechanics (English Edition), 39, 623-638(2018) https://doi.org/10.1007/s10483-018-2331-6
[8] GIREESHA, B. J., MAHANTHESH, B., and KRUPALAKSHMI, K. L. Hall effect on two-phase radiated flow of magneto-dusty-nanoliquid with irregular heat generation/consumption. Results in Physics, 7, 4340-4348(2017)
[9] HAYAT, T., KHALID, H., WAQAS, M., and ALSAEDI, A. Homotopic solutions for stagnation point flow of third-grade nanoliquid subject to magnetohydrodynamics. Results in Physics, 7, 4310-4317(2017)
[10] IRFAN, M., KHAN, M., and KHAN, W. A. Numerical analysis of unsteady 3D flow of Carreau nanofluid with variable thermal conductivity and heat source/sink. Results in Physics, 7, 3315-3324(2017)
[11] MAHANTHESH, B., GIREESHA, B. J., and RAJU, C. S. K. Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source. Informatics in Medicine Unlocked, 9, 26-34(2017)
[12] WAQAS, M., HAYAT, T., SHEHZAD, S. A., and ALSAEDI, A. Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Physica B:Condensed Matter, 529, 33-40(2018)
[13] HAMID, A., HASHIM., and KHAN, M. Numerical simulation for heat transfer performance in unsteady flow of Williamson fluid driven by a wedge-geometry. Results in Physics, 9, 479-485(2018)
[14] GIREESHA, B. J., MAHANTHESH, B., THAMMANNA, G. T., and SAMPATHKUMAR, P. B. Hall effects on dusty nanofluid two-phase transient flow past a stretching sheet using KVL model. Journal of Molecular Liquids, 256, 139-147(2018)
[15] HAMID, H. A. and KHAN, M. Unsteady mixed convective flow of Williamson nanofluid with heat transfer in the presence of variable thermal conductivity and magnetic field. Journal of Molecular Liquids, 260, 436-446(2018)
[16] DARCY, H. Les Fontaines Publiques de la Ville de Dijon, Hachette Livre Bnf, Paris (1856)
[17] FORCHHEIMER, P. H. Wasserbewegung Durch Boden, Spielhagen & Schurich, Wien (1901)
[18] SEDDEEK, M. A. Effects of magnetic field and variable viscosity on forced non-Darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing. Journal of Applied Mechanics and Technical Physics, 43, 13-17(2002)
[19] SINGH, A. K., KUMAR, R., SINGH, U., SINGH, N. P., and SINGH, A. K. Unsteady hydromagnetic convective flow in a vertical channel using Darcy-Brinkman-Forchheimer extended model with heat generation/absorption:analysis with asymmetric heating/cooling of the channel walls. International Journal of Heat and Mass Transfer, 54, 5633-5642(2011)
[20] GIREESHA, B. J., MAHANTHESH, B., MANJUNATHA, P. T., and GORLA, R. S. R. Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension. Journal of the Nigerian Mathematical Society, 34, 267-285(2015)
[21] KHAN, M. I., WAQAS, M., HAYAT, T., KHAN, M. I., and ALSAEDI, A. Numerical simulation of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface. Journal of Molecular Liquids, 246, 259-267(2017)
[22] SADIQ, M. A., WAQAS, M., and HAYAT, T. Importance of Darcy-Forchheimer relation in chemically reactive radiating flow towards convectively heated surface. Journal of Molecular Liquids, 248, 1071-1077(2017)
[23] HAYAT, T., SHAH, F., ALSAEDI, A., and WAQAS, M. Numerical simulation for magneto nanofluid flow through a porous space with melting heat transfer. Microgravity Science and Technology, 30, 265-275(2018)
[24] WANG, S. and TAN, W. C. Stability analysis of Soret-driven double-diffusive convection of Maxwell fluid in a porous medium. International Journal of Heat and Fluid Flow, 32, 88-94(2011)
[25] HAYAT, T., WAQAS, M., SHEHZAD, S. A., and ALSAEDI, A. Mixed convection radiative flow of Maxwell fluid near a stagnation point with convective condition. Journal of Mechanics, 29, 403-409(2013)
[26] HAYAT, T., WAQAS, M., SHEHZAD, S. A., and ALSAEDI, A. Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions. Scientia Iranica Transaction B, Mechanical Engineering, 21, 682-692(2014)
[27] KHAN, M. I., KHAN, M. I., WAQAS, M., HAYAT, T., and ALSAEDI, A. Chemically reactive flow of Maxwell liquid due to variable thicked surface. International Communications in Heat and Mass Transfer, 86, 231-238(2017)
[28] LIU, Y. and GUO, B. Effects of second-order slip on the flow of a fractional Maxwell MHD fluid. Journal of the Association of Arab Universities for Basic and Applied Sciences, 24, 232-241(2017)
[29] KHAN, M., IRFAN, M., and KHAN, W. A. Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition. Results in Physics, 9, 851-857(2018)
[30] CHRISTENSEN, R. M. Theory of Viscoelasticity, Academic Press, London (1971)
[31] LIAO, S. J. An optimal homotopy-analysis approach for strongly nonlinear dixoerential equations. Communications in Nonlinear Science and Numerical Simulation, 15, 2003-2016(2010)
[32] TURKYILMAZOGLU, M. Series solution of nonlinear two-point singularly perturbed boundary layer problems. Journal of Computational and Applied Mathematics, 60, 2109-2114(2010)
[33] HAYAT, T., ALI, S., AWAIS, M., and ALHUTHALI, M. S. Newtonian heating in stagnation point flow of Burgers fluid. Applied Mathematics and Mechanics (English Edition), 36, 61-68(2015) https://doi.org/10.1007/s10483-015-1895-9
[34] HAYAT, T., ALI, S., FAROOQ, M. A., and ALSAEDI, A. On comparison of series and numerical solutions for flow of Eyring-Powell fluid with Newtonian heating and internal heat generation/absorption. PLoS One, 10, e0129613(2015)
[35] WAQAS, M., FAROOQ, M., KHAN, M. I., HAYAT, T., ALSAEDI, A., and YASMEEN, T. Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. International Journal of Heat and Mass Transfer, 102, 766-772(2016)
[36] HAYAT, T., ALI, S., ALSAEDI, A., and ALSULAMI, H. H. Influence of thermal radiation and Joule heating in the Eyring-Powell fluid flow with the Soret and Dufour effects. Journal of Applied Mechanics and Technical Physics, 57, 1051-1060(2016)
[37] KHAN, M., IRFAN, M., and KHAN, W. A. Impact of nonlinear thermal radiation and gyrotactic microorganisms on the Magneto-Burgers nanofluid. International Journal of Mechanical Sciences, 130, 375-382(2017)
[38] MUHAMMAD, T., ALSAEDI, A., SHEHZAD, S. A., and HAYAT, T. A revised model for DarcyForchheimer flow of Maxwell nanofluid subject to convective boundary condition. Chinese Journal of Physics, 55, 963-976(2017)