Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

doi:10.1007/s10483-019-2464-8

Abstract

Abstract:

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations (ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.

Key words: general solution, noncommutative ring, construction of solution, conjugate operator, Brownian motion, shooting method, nanofluid, thermophoresis, thermal radiation

2010 MSC Number:

K. RAMESH, O. OJJELA. Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 481-498.

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References

[1] RIVLIN, R. S. and ERICKSEN, J. L. Stress deformation relations for isotropic materials. Journal of Rational Mechanics and Analysis, 4, 323-425(1955)
[2] RAJAGOPAL, K. R. On the creeping flow of the second-order fluid. Journal of Non-Newtonian Fluid Mechanics, 15(2), 239-246(1984)
[3] MASSOUDI, M. and PHUOC, T. X. Fully developed flow of a modified second grade fluid with temperature dependent viscosity. Acta Mechanica, 150(1), 23-37(2001)
[4] DONALD-ARIEL, P. On exact solutions of flow problems of a second grade fluid through two parallel porous walls. International Journal of Engineering Science, 40(8), 913-941(2002)
[5] EMIN-ERDO?AN, M. and ERDEM-IMRAK, C. On some unsteady flows of a non-Newtonian fluid. Applied Mathematical Modelling, 31(2), 170-180(2007)
[6] HAYAT, T., IQBAL, Z., and MUSTAFA, M. Flow of a second grade fluid over a stretching surface with Newtonian heating. Journal of Mechanics, 28(1), 209-216(2012)
[7] SHRESTHA, G. M. Singular perturbation problems of laminar flow in a uniformly porous channel in the presence of a transverse magnetic field. The Quarterly Journal of Mechanics and Applied Mathematics, 20(2), 233-246(1967)
[8] RAFTARI, B., PARVANEH, F., and VAJRAVELU, K. Homotopy analysis of the magneto hydrodynamic flow and heat transfer of a second grade fluid in a porous channel. Energy, 59, 625-632(2013)
[9] RAMZAN, M. and BILAL, M. Time dependent MHD nano-second grade fluid flow induced by permeable vertical sheet with mixed convection and thermal radiation. PLoS One, 10(5), e0124929(2015)
[10] LABROPULU, F., XU, X., and CHINICHIAN, M. Unsteady stagnation point flow of a nonNewtonian second-grade fluid. International Journal of Mathematics and Mathematical Sciences, 60, 3797-3807(2003)
[11] HAYAT, T., KHAN, M. W. A., ALSAEDI, A., and KHAN, M. I. Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption. Colloid and Polymer Science, 295(6), 967-975(2017)
[12] CHENG, C. Y. Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. International Communications in Heat and Mass Transfer, 33(5), 627-635(2006)
[13] ABDULAZIZ, O. and HASHIM, I. Fully developed free convection heat and mass transfer of a micropolar fluid between porous vertical plates. Numerical Heat Transfer, 55(3), 270-288(2009)
[14] CHAMKHA, A. J., MOHAMED, R. A., and AHMED, S. E. Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects. Meccanica, 46(2), 399-411(2011)
[15] SINGH, A. K. and GORLA, R. S. R. Free convection heat and mass transfer with Hall current, Joule heating and thermal diffusion. Heat and Mass Transfer, 45(11), 1341-1349(2009)
[16] HAYAT, T., MUHAMMAD, T., ALSAEDI, A., and ALHUTHALI, M. S. Magneto hydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials, 385, 222-229(2015)
[17] HAYAT, T., WAQAS, M., SHEHZAD, S. A., and ALSAEDI, A. Chemically reactive flow of third grade fluid by an exponentially convected stretching sheet. Journal of Molecular Liquids, 223, 853-860(2016)
[18] AHMED, N., KHAN, U., and MOHYUD-DIN, S. T. Influence of nonlinear thermal radiation on the viscous flow through a deformable asymmetric porous channel:a numerical study. Journal of Molecular Liquids, 225, 167-173(2017)
[19] SUDARSANA-REDDY, P., CHAMKHA, A. J., and AL-MUDHAF, A. MHD heat and mass transfer flow of a nanofluid over an inclined vertical porous plate with radiation and heat generation/absorption. Advanced Powder Technology, 28(3), 1008-1017(2017)
[20] DOGONCHI, A. S., ALIZADEH, M., and GANJI, D. D. Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect. Advanced Powder Technology, 28(7), 1815-1825(2017)
[21] EEGUNJOBI, A. S., MAKINDE, O. D., and JANGILI, S. Unsteady MHD chemically reacting and radiating mixed convection slip flow past a stretching surface in a porous medium. Defect and Diffusion Forum, 377, 200-210(2017)
[22] BHATTI, M. M., ABBAS, M. A., and RASHIDI, M. M. A robust numerical method for solving stagnation point flow over a permeable shrinking sheet under the influence of MHD. Applied Mathematics and Computation, 316, 381-389(2018)
[23] 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
[24] ABOLBASHARI, M. H., FREIDOONIMEHR, N., NAZARI, F., and RASHIDI, M. M. Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid. Powder Technology, 267, 256-267(2014)
[25] RASHIDI, M. M., MAHMUD, S., FREIDOONIMEHR, N., and ROSTAMI, B. Analysis of entropy generation in an MHD flow over a rotating porous disk with variable physical properties. International Journal of Exergy, 16(4), 481-503(2015)
[26] MAHMOODI, M. and KANDELOUSI, S. Effects of thermophoresis and Brownian motion on nanofluid heat transfer and entropy generation. Journal of Molecular Liquids, 211, 15-24(2015)
[27] SRINIVAS, J., RAMANA-MURTHY, J. V., and ANWAR-BÉG, O. Entropy generation analysis of radiative heat transfer effects on channel flow of two immiscible couple stress fluids. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 9(6), 2191-2202(2017)
[28] MAKINDE, O. D. Entropy analysis for MHD boundary layer flow and heat transfer over a flat plate with a convective surface boundary condition. International Journal of Exergy, 10(2), 142-154(2012)
[29] NOGHREHABADI, A., SAFFARIAN, M., POURRAJAB, R., and GHALAMBAZ, M. Entropy analysis for nanofluid flows over a stretching sheet in the presence of heat generation/absorption and partial slip. Journal of Mechanical Science and Technology, 27(3), 927-937(2013)
[30] SHIT, G. C., HALDAR, R., and MANDAL, S. Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids. Advanced Powder Technology, 28(6), 1519-1530(2017)
[31] ABOLBASHARI, M. H., FREIDOONIMEHR, N., NAZARI, F., and RASHIDI, M. M. Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface. Advanced Powder Technology, 26(2), 542-552(2015)
[32] JBARA, A., SLIMI, K., and MHIMID, A. Entropy generation for unsteady natural convection and thermal radiation inside a porous enclosure. International Journal of Exergy, 12(4), 522-551(2013)
[33] DAS, S., CHAKRABORTY, S., JANA, R. N., and MAKINDE, O. D. Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition. Applied Mathematics and Mechanics (English Edition), 36(12), 1593-1610(2015) https://doi.org/10.1007/s10483-015-2003-6
[34] BHATTI, M. M., ABBAS, T., RASHIDI, M. M., and ALI, M. E. S. Numerical simulation of entropy generation with thermal radiation on MHD Carreau nanofluid towards a shrinking sheet. Entropy, 18(6), 200(2016)
[35] 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)
[36] BHATTI, M. M. and RASHIDI, M. M. Numerical simulation of entropy generation on MHD nanofluid towards a stagnation point flow over a stretching surface. International Journal of Applied and Computational Mathematics, 3(3), 2275-2289(2017)
[37] ABBAS, M. A., BAI, Y., RASHIDI, M. M., and BHATTI, M. M. Analysis of entropy generation in the flow of peristaltic nanofluids in channels with compliant walls. Entropy, 18(3), 90(2016)
[38] BHATTI, M. M., ABBAS, T., and RASHIDI, M. M. Entropy generation as a practical tool of optimisation for non-Newtonian nanofluid flow through a permeable stretching surface using SLM. Journal of Computational Design and Engineering, 4(1), 21-28(2017)
[39] BHATTI, M. M., RASHIDI, M. M., and POP, I. Entropy generation with nonlinear heat and mass transfer on MHD boundary layer over a moving surface using SLM. Nonlinear Engineering, 6(1), 43-52(2017)
[40] BHATTI, M. M., SHEIKHOLESLAMI, M., and ZEESHAN, A. Entropy analysis on electrokinetically modulated peristaltic propulsion of magnetized nanofluid flow through a microchannel. Entropy, 19(9), 481(2017)
[41] AFRIDI, M. I., QASIM, M., and MAKINDE, O. D. Second law analysis of boundary layer flow with variable fluid properties. Journal of Heat Transfer, 39(10), 104505(2017)
[42] EEGUNJOBI, A. S. and MAKINDE, O. D. Irreversibility analysis of hydromagnetic flow of couple stress fluid with radiative heat in a channel filled with a porous medium. Results in Physics, 7, 459-469(2017)
[43] DAS, S., JANA, R. N., and MAKINDE, O. D. MHD flow of Cu-Al₂O₃/water hybrid nanofluid in porous channel:analysis of entropy generation. Defect and Diffusion Forum, 377, 42-61(2017)
[44] EEGUNJOBI, A. S. and MAKINDE, O. D. MHD mixed convection slip flow of radiating Casson fluid with entropy generation in a channel filled with porous media. Defect and Diffusion Forum, 374, 47-66(2017)
[45] ALAM, M., KHAN, M., HAKIM, A., and MAKINDE, O. D. Magneto-nanofluid dynamics in convergent-divergent channel and its inherent irreversibility. Defect and Diffusion Forum, 377, 95-110(2017)
[46] EEGUNJOBI, A. S. and MAKINDE, O. D. Inherent irreversibility in a variable viscosity Hartmann flow through a rotating permeable channel with Hall effects. Defect and Diffusion Forum, 377, 180-188(2017)
[47] CHOI, S. U. S. and ESTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, 231, 99-106(1995)
[48] BUONGIORNO, J. Convective transport in nanofluids. Journal of Heat Transfer, 128(3), 240-250(2006)
[49] SHEIKHOLESLAMI, M., RASHIDI, M. M., AL-SAAD, D. M., FIROUZI, F., ROKNI, H. B., and DOMAIRRY, G. Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects. Journal of King Saud University-Science, 28(4), 380-389(2016)
[50] HAYAT, T., MUHAMMAD, T., QAYYUM, A., ALSAEDI, A., and MUSTAFA, M. On squeezing flow of nanofluid in the presence of magnetic field effects. Journal of Molecular Liquids, 213, 179-185(2016)
[51] RAMANA-REDDY, J. V., SUGUNAMMA, V., and SANDEEP, N. Thermophoresis and Brownian motion effects on unsteady MHD nano fluid flow over a slendering stretching surface with slip effects. Alexandria Engineering Journal, 57, 2465-2473(2017)
[52] GUHA, A. and SAMANTA, S. Effect of thermophoresis on the motion of aerosol particles in natural convective flow on horizontal plates. International Journal of Heat and Mass Transfer, 68, 42-50(2014)
[53] AWAD, F. G., AHAMED, S. M. S., SIBANDA, P., and KHUMALO, M. The effect of thermophoresis on unsteady Oldroyd-B nanofluid flow over stretching surface. PLoS One, 10(8), e0135914(2015)
[54] QAYYUM, S., HAYAT, T., ALSAEDI, A., and AHMAD, B. Magnetohydrodynamic (MHD) nonlinear convective flow of Jeffrey nanofluid over a nonlinear stretching surface with variable thickness and chemical reaction. International Journal of Mechanical Sciences, 134, 306-314(2017)
[55] KIUSALAAS, J. Numerical Methods in Engineering with MATLAB, Cambridge University Press, New York (2005)