Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

doi:10.1007/s10483-019-2518-9

摘要/Abstract

摘要： This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤ σ_m ≤ 2.5, 0 ≤ K₁ ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤ σ ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ N_b ≤ 0.8, and 0.2 ≤ N_t ≤ 0.8.

关键词: viscoelasticity-based micropolar nanofluid, porous medium, slip effect, numerical method

Abstract: This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤ σ_m ≤ 2.5, 0 ≤ K₁ ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤ σ ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ N_b ≤ 0.8, and 0.2 ≤ N_t ≤ 0.8.

Key words: viscoelasticity-based micropolar nanofluid, porous medium, slip effect, numerical method

中图分类号:

76Bxx
76Sxx

H. WAQAS, M. IMRAN, S. U. KHAN, S. A. SHEHZAD, M. A. MERAJ. Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1255-1268.

参考文献

[1] ERINGEN, A. C. Microcontinuum Field Theories, Vols. I, Ⅱ, Springer, New York (2001)
[2] ERINGEN, A. C. Simple micro fluids. International Journal of Engineering Science, 2, 205-217(1964)
[3] ERINGEN, A. C. Theory of micropolar fluid. Journal of Mathematics and Mechanics, 16, 1-18(1966)
[4] ERINGEN, A. C. Theory of thermomicro fluids. Journal of Mathematical Analysis and Applications, 38, 480-496(1972)
[5] ZUBAIR, M., WAQAS, M., HAYAT, T., AYUB, M., and ALSAEDI, A. The onset of modified Fourier and Fick's theories in temperature dependent conductivity flow of micropolar liquid. Results in Physics, 7, 3145-3152(2017)
[6] ASHRAF, M. and WEHGAL, A. R. MHD flow and heat transfer of a micropolar fluid between two porous disks. Applied Mathematics and Mechanics (English Edition), 33(1), 51-64(2012) https://doi.org/10.1007/s10483-012-1533-6
[7] HAYAT, T., FAROOQ, S., AHMAD, B., and ALSAEDI, A. Homogeneous-heterogeneous reactions and heat source/sink effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel. Journal of Molecular Liquids, 223, 469-488(2016)
[8] WAQAS, M., FAROOQ, M., KHAN, M. I., ALSEDI, A., HAYAT, T., 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)
[9] SHEHZAD, S. A., WAQAS, M., ALSAEDI, A., and HAYAT, T. Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid with convective boundary condition. Journal of Applied Fluid Mechanics, 9, 1437-1445(2016)
[10] SUI, J. Z., ZHAO, P., CHENG, Z. D., ZHENG, L. C., and ZHANG, X. A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer. Physics of Fluids, 29, 023105(2017)
[11] TURKYILMAZOGLU, M. Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate:exact solutions. International Journal of Heat and Mass Transfer, 106, 127-134(2017)
[12] TURKYILMAZOGLU, M. Flow of a micropolar fluid due to a porous stretching sheet and heat transfer. International Journal of Non-Linear Mechanics, 83, 59-64(2016)
[13] SALEEM, M., HOSSAIN, M. A., and SAHA, S. C. Mixed convection flow of micropolar fluid in an open ended arc-shape cavity. Journal of Fluids Engineering-Transactions of ASME, 134, 091101(2012)
[14] SUI, J., ZHAO, P., CHENG, Z., and DOI, M. Influence of particulate thermophoresis on convection heat and mass transfer in a slip flow of a viscoelasticity-based micropolar fluid. International Journal of Heat and Mass Transfer, 119, 40-51(2018)
[15] DING, Z., JIAN, Y., and YANG, L. Time periodic electroosmotic flow of micropolar fluids through microparallel channel. Applied Mathematics and Mechanics (English Edition), 37(6), 769-786(2016) https://doi.org/10.1007/s10483-016-2081-6
[16] CAO, L., SI, X., and ZHENG, L. The flow of a micropolar fluid through a porous expanding channel:a Lie group analysis. Applied Mathematics and Computation, 270, 242-250(2015)
[17] ANWAR, M. I., SHAFIE, S., HAYAT, T., SHEHZAD, S. A., and SALLEH, M. Z. Numerical study for MHD stagnation-point flow of a micropolar nanofluid towards a stretching sheet. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 89-100(2107)
[18] ALI, N., KHAN, S. U., ABBAS, Z., and SAJID, M. Slip effects in the hydromagnetic flow of a viscoelastic fluid through porous medium over a porous oscillatory stretching sheet. Journal of Porous Media, 20, 249-262(2017)
[19] REDDY, G. J., RAJU, R. S., and RAO, J. A. Thermal diffusion and diffusion thermo impact on chemical reacted MHD free convection from an impulsively started infinite vertical plate embedded in a porous medium using FEM. Journal of Porous Media, 20, 1097-1117(2018)
[20] KHAN, A., KHAN, I., KHAN, A., and SHAFIE, S. Heat transfer analysis in MHD flow of Casson fluid over a vertical plate embedded in a porous medium with arbitrary wall shear stress. Journal of Porous Media, 21, 739-748(2018)
[21] SHEIKHOLESLAMI, M. and SHEHZAD, S. A. CVFEM simulation for nanofluid migration in a porous medium using Darcy model. International Journal of Heat and Mass Transfer, 122, 1264-1271(2018)
[22] SINGH, V. and AGARWAL, S. MHD flow and heat transfer for Maxwell fluid over an exponentially stretching sheet with variable thermal conductivity in porous medium. Thermal Science, 18, S599-S615(2014)
[23] RAUF, A., ABBAS, Z., SHEHZAD, S. A., and MUSHTAQ, T. Thermally radiative viscous fluid flow over a curved stretching surface in non-Darcy porous medium. Communications in Theoretical Physics, 71, 259-266(2019)
[24] CHOI, S. Enhancing thermal conductivity of fluids with nanoparticle. Development and Applications of Non-Newtonian Flow, 66, 99-105(1995)
[25] ZHU, J., ZHENG, L., ZHENG, L., and ZHANG, X. Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction. Applied Mathematics and Mechanics (English Edition), 36(9), 1131-1146(2015) https://doi.org/10.1007/s10483-015-1977-6
[26] KHAN, S. U., SHEHZAD, S. A., and ALI, N. Interaction of magneto-nanoparticles in Williamson fluid flow over convective oscillatory moving surface. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 195(2018)
[27] KHAN, M., MALIK, R., MUNIR, A., and KHAN, W. A. Flow and heat transfer to Sisko nanofluid over a nonlinear stretching sheet. PLoS One, 10, e0125683(2015)
[28] SHEIKHOLESLAMI, M. Investigation of Coulomb force effects on ethylene glycol based nanofluid laminar flow in a porous enclosure. Applied Mathematics and Mechanics (English Edition), 39(9), 1341-1352(2018) https://doi.org/10.1007/s10483-018-2366-9
[29] USMAN, M., SOOMRO, F. A., HAQ, R. U., WANG, W., and DEFTERLI, O. Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method. International Journal of Heat and Mass Transfer, 122, 1255-1263(2018)
[30] ROUT, B. C. and MISHRA, S. R. Thermal energy transport on MHD nanofluid flow over a stretching surface:a comparative study. Engineering Science and Technology:An International Journal, 21, 60-69(2018)
[31] SHEIKHOLESLAMI, M. CuO-water nanofluid flow due to magnetic field inside a porous media considering Brownian motion. Journal of Molecular Liquids, 249, 921-929(2018)