MHD graphene-polydimethylsiloxane Maxwell nanofluid flow in a squeezing channel with thermal radiation effects

doi:10.1007/s10483-019-2517-9

摘要/Abstract

摘要： The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system via the Bejan number is studied extensively. The governing partial differential equations are converted by using the similarity transformations into a set of coupled ordinary differential equations. The set of these converted equations is solved by using the differential transform method (DTM). The entropy generation in terms of the Bejan number, the coefficient of skin-friction, and the heat transfer rate is furthermore investigated under the effects of various physical parameters of interest. The present study shows that the Bejan number, the velocity and thermal profiles, and the rate of heat transfer decrease with a rise in the Deborah number De while the skin-friction coefficient increases. It is also observed that the entropy generation due to frictional forces is higher than that due to thermal effects. Thus, the study bears the potential application in powder technology as well as in biomedical engineering.

关键词: graphene-polydimethylsiloxane (PDMS), Maxwell fluid, differential transform method (DTM), thermal radiation, Bejan number

Abstract: The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system via the Bejan number is studied extensively. The governing partial differential equations are converted by using the similarity transformations into a set of coupled ordinary differential equations. The set of these converted equations is solved by using the differential transform method (DTM). The entropy generation in terms of the Bejan number, the coefficient of skin-friction, and the heat transfer rate is furthermore investigated under the effects of various physical parameters of interest. The present study shows that the Bejan number, the velocity and thermal profiles, and the rate of heat transfer decrease with a rise in the Deborah number De while the skin-friction coefficient increases. It is also observed that the entropy generation due to frictional forces is higher than that due to thermal effects. Thus, the study bears the potential application in powder technology as well as in biomedical engineering.

Key words: graphene-polydimethylsiloxane (PDMS), Maxwell fluid, differential transform method (DTM), thermal radiation, Bejan number

中图分类号:

G. C. SHIT, S. MUKHERJEE. MHD graphene-polydimethylsiloxane Maxwell nanofluid flow in a squeezing channel with thermal radiation effects[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1269-1284.

参考文献

[1] BOLAND, C. S., KHAN, U., RYAN, G., BARWICH, S., CHARIFOU, R., HARVEY, A., BACKES, C., LI, Z., FERREIRA, M. S., MÖBIUS, M. E., YOUNG, R. J., and COLEMAN, J. N. Sensitive electromechanical sensors using viscoelastic graphene-polymer nanocomposites. Science, 354, 1257-1260(2016)
[2] CHOI, S. U. S. Enhancing thermal conductivity of fluids with nanoparticle. Developments and Applications of Non-Newtonian Flows, ASME, New York (1995)
[3] ANGAYARKANNI, S. A. and PHILIP, J. Review on thermal properties of nanofluids:recent developments. Advances in Colloid and Interface Science, 225, 146-176(2015)
[4] ARCHIBALD, F. R. Load capacity and time relations for squeeze films. Journal of Lubrication Technology, 78, A231-A245(1956)
[5] RASHIDI, M. M., SHAHMOHAMADI, H., and DINARVAND, S. Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Mathematical Problems in Engineering, 2008, 1-13(2008)
[6] MAHMOOD, M., ASGHAR, S., and HUSSAIN, M. A. Squeezed flow and heat transfer over a porous surface for viscous fluid. Heat and Mass Transfer, 44, 165-173(2007)
[7] MUSTAFA, M., HAYAT, T., and OBAIDAT, S. On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica, 47, 1581-1589(2012)
[8] HAYAT, T., MUHAMMAD, T., SHEHZAD, S. A., and ALSAEDI, A. Three-dimensional boundary layer flow of Maxwell nanofluid:mathematical model. Applied Mathematics and Mechanics (English Edition), 36(6), 747-762(2015) https://doi.org/10.1007/s10483-015-1948-6
[9] SIDDIQUI, A. A. and SHEIKHOLESLAMI, M. TiO₂-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity. Applied Mathematics and Mechanics (English Edition), 39(8), 1201-1216(2018) https://doi.org/10.1007/s10483-018-2359-6
[10] HUANG, W. B., XU, Y., LIAN, G. P., and LI, H. Y. Squeeze flow of a power-law fluid between two rigid spheres with wall slip. Applied Mathematics and Mechanics (English Edition), 23(7), 811-818(2002) https://doi.org/10.1007/BF02456977
[11] SETH, G. S. and MISHRA, M. K. Analysis of transient flow of MHD nanofluid past a non-linear stretching sheet considering Naviers slip boundary condition. Advanced Powder Technology, 28, 375-384(2017)
[12] IMTIAZ, M., HAYAT, T., and ALSAEDI, A. Flow of magneto nanofluid by a radiative exponentially stretching surface with dissipation effect. Advanced Powder Technology, 27, 2214-2222(2016)
[13] JAMIL, M., KHAN, N. A., and NAZISH, S. Fractional MHD Oldroyd-B fluid over an oscillating plate. Thermal Science, 17, 997-1011(2013)
[14] HAYAT, T., SHEHZAD, S. A., QASIM, M., and OBAIDAT, S. Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source. Nuclear Engineering Design, 243, 15-19(2012)
[15] RASHIDI, M. M., MOMONIAT, E., and ROSTAMI, B. Analytic approximate solutions for MHD boundary-layer viscoelastic fluid flow over a continuously moving stretching surface by homotopy analysis method with two auxiliary parameters. Journal of Applied Mathematics, 2012, 1-19(2012)
[16] HAYAT, T. and SHEHZAD, A. MHD three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. International Journal for Numerical Methods in Fluids, 24, 1073-1085(2014)
[17] RAHBARI, A., ABBASI, M., RAHIMIPETROUDI, I., SUNDEN, B., GANJI, D. D., and GHOLAMI, M. Maxwell fluid through a parallel plate channel:analytical and numerical solution. Mechanical Sciences, 9, 61-70(2018)
[18] IMRAN, M. A., RIAZ, M. B., SHAH, N. A., and ZAFAR, A. A. Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary. Results in Physics, 8, 1061-1067(2018)
[19] SAJID, T., SAGHEER, M., HUSSAIN, S., and BILAL, M. Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy. AIP Advances, 8, 035102(2018)
[20] MUSHTAQ, A., MUSTAFA, M., HAYAT, T., ALSAEDI, A. Buoyancy effects in stagnation-point flow of Maxwell fluid utilizing non-Fourier heat flux approach. PLoS One, 13(7), e0200325(2018)
[21] BILAL, M., SAGHEER, M., and HUSSAIN, S. Three dimensional MHD upper-convected Maxwell nanofluid flow with nonlinear radiative heat flux. Alexandria Engineering Journal, 57(3), 1917-1925(2018)
[22] BHATTI, M. M. and RASHIDI, M. M. Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet. Journal of Molecular Liquids, 221, 567-573(2016)
[23] PERALTA, M., BAUTISTA, O., MENDEZ, F., and BAUTISTA, E. Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials. Applied Mathematics and Mechanics (English Edition), 39(5), 667-684(2018) https://doi.org/10.1007/s10483-018-2328-6
[24] LIU, Y. and GUO, B. Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform. Applied Mathematics and Mechanics (English Edition), 37(2), 137-150(2016) https://doi.org/10.1007/s10483-016-2021-8
[25] ZHOU, J. K. Differential Transformation and Its Applications for Eelectrical Circuits, Huazhong University Press, Wuhan (1986)
[26] CHEN, C. K. and HO, S. H. Solving partial differential equations by two dimensional differential transform method. Applied Mathematics and Computation, 106, 171-179(1999)
[27] ABDEL-HALIM HASSAN, I. H. Comparison differential transformation technique with Adomain decomposition method for linear and nonlinear initial value problems. Chaos, Solitons and Fractals, 36, 53-65(2008)
[28] ACHARYA, N., DAS, K., and KUNDU, P. K. The squeezing flow of Cu-water and Cu-kerosene nanofluids between two parallel plates. Alexandria Engineering Journal, 55, 1177-1186(2016)
[29] BEJAN, A. Entropy Generation through Heat and Fluid Flow, Wiley, New York (1982)
[30] BEJAN, A. Study of entropy generation in fundamental convective heat transfer. Journal of Heat Transfer, 101, 718-725(1979)
[31] RASHIDI, M. M., BHATTI, M. M., ABBAS, M. A., and EL-SAYED ALI, M. Entropy generation of MHD blood flow of nanofluid due to peristaltic waves. Entropy, 4, 18-117(2016)
[32] TING, T. W., HUNG, Y. M., and GUO, N. Entropy generation of viscous dissipative nanofluid convection in asymmetrically heated porous microchannels with solid-phase heat generation. Energy Conversion and Management, 105, 731-745(2015)
[33] TING, T. W., HUNG, Y. M., and GUO, N. Entropy generation of viscous dissipative nanofluid flow in thermal non-equilibrium porous media embedded in microchannels. International Journal of Heat and Mass Transfer, 81, 862-877(2015)
[34] MKWIZU, M. H. and MAKINDE, O. D. Entropy generation in a variable viscosity channel flow of nanofluids with convective cooling. Comptes Rendus Mecanique, 343, 38-56(2015)
[35] NEZHAD, A. H. and SHAHRI, M. F. Entropy generation case studies of two-immiscible fluids under the influence of a uniform magnetic field in an inclined channel. Journal of Mechanics, 32, 749-757(2016)
[36] BHATTI, M. M., ABBAS, T., RASHIDI, M. M., ALI, M. E. S., and YANG, Z. Entropy generation on MHD Eyring-Powell nanofluid through a permeable stretching surface. Entropy, 18(6), 224(2016)
[37] MAHIAN, O., KIANIFAR, A., KLEINSTREUER, C., AL-NIMR, M. A., POP, I., SAHIN, A. Z., and WONGWISES, S. A review of entropy generation in nanofluid flow. International Journal of Heat and Mass Transfer, 65, 514-532(2013)
[38] HAYAT, T., MUHAMMAD, T., SHEHZAD, S. A., and ALSAEDI, A. Three dimensional rotating flow of Maxwell nanofluid. Journal of Molecular Liquids, 229, 495-500(2017)
[39] SHIT, G. C. and MUKHERJEE, S. Differential transform method for unsteady magnetohydrodynamic nanofluid flow in the presence of thermal radiation. Journal of Nanofluids, 8(5), 998-1009(2019)
[40] MAXWELL, J. C. A Treatise on Electricity and Magnetism Vol. (Ⅱ), Oxford University Press, Cambridge (1873)
[41] BRINKMAN, H. C. The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 20, 571-581(1952)
[42] SHEIKHOLESLAMI, M. and GANJI, D. D. Heat transfer of Cu-water nanofluid flow between parallel plates. Powder Technology, 235, 873-879(2013)
[43] SHEIKHOLESLAMI, M., GANJI, D. D., and ASHORYNEJAD, H. R. Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technology, 239, 259-265(2013)
[44] MUSTAFA, M., HAYAT, T., and OBAIDAT, S. On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica, 47, 1581-1589(2012)
[45] POURMEHRAN, O., RAHIMI-GORJI, M., GORJI-BANDPY, M., and GANJI, D. D. Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM. Alexandria Engineering Journal, 54, 17-26(2005)
[46] MARK, J. E. Polymer Data Handbook, Oxford University Press, Oxford (1998)
[47] POTENZA, M., CATALDO, A., BOVESECCHI, G., CORASANITI, S., COPPA, P., and BELLUCCI, S. Graphene nanoplatelets:thermal diffusivity and thermal conductivity by the flash method. AIP Advances, 7, 075214(2017)
[48] POP, E., VARSHNEY, V., and ROY, A. K. Thermal properties of graphene:fundamentals and applications. MRS Bulletin, 37(12), 1273-1281(2012)
[49] ROBERTS, C., GRAHAM, A., PHINNEY, L., NEMER, M., GARCIA, R., and STIRRUP, E. Physical Properties of Low-Molecular Weight Polydimethylsiloxane Fluids, Sandia national laboratories, 1242, California (2017)
[50] KAMINSKI, E. and JAUPART, C. Laminar starting plumes in high-Prandtl-number fluids. Journal of Fluid Mechanics, 478, 287-298(2003)
[51] KONG, K. T. S., MARIATTI, M., RASHID, A. A., and BUSFIELD, J. J. C. Enhanced conductivity behavior of polydimethylsiloxane (PDMS) hybrid composites containing exfoliated graphite nanoplatelets and carbon nanotubes. Composites:Part B, 58, 457-462(2014)