×

Axisymmetric squeezing flow of third grade fluid in presence of convective conditions. (English) Zbl 1539.76269

Summary: This article examines unsteady axisymmetric flow of third grade fluid between two disks. Upper disk is being squeezed towards the lower porous disk. Electrically conducting fluid and convective boundary conditions are used. Heat transfer analysis is carried out in the presence of Joule heating, viscous dissipation and thermal radiation effects. Partial differential equations are reduced into ordinary differential equations by using suitable transformations. Convergent series solutions of velocity and temperature are obtained. Effects of various dimensionless parameters are observed on the velocity and temperature. Numerical values of skin friction coefficient and Nusselt number are also computed and examined.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
80A19 Diffusive and convective heat and mass transfer, heat flow
80A21 Radiative heat transfer
Full Text: DOI

References:

[1] Fetecau, C.; Hayat, T.; Zierep, J.; Sajid, M., Energetic balance for the rayleigh-stokes problem of an Oldroyd-B fluid, Nonlinear Anal. Real World Appl., 12, 1, 1-13, (2011) · Zbl 1205.35223
[2] Hayat, T.; Imtiaz, M.; Alsaedi, A.; Almezal, S., On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions, J. Magn. Magn. Mater., 401, 296-303, (2016)
[3] Abbasbandy, S.; Naz, R.; Hayat, T.; Alsaedi, A., Numerical and analytical solutions for Falkner-Skan flow of MHD maxwell fluid, Appl. Math. Comput., 242, 569-575, (2014) · Zbl 1334.76165
[4] Rashidi, M. M.; Pour, S. A.M.; Abbasbandy, S., Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation, Commun. Nonlinear Sci. Numer.Simul., 16, 4, 1874-1889, (2011)
[5] Hayat, T.; Hussain, Z.; Farooq, M.; Alsaedi, A., Effects of homogeneous and heterogeneous reactions and melting heat in the viscoelastic fluid flow, J. Mol. Liq., 215, 749-755, (2016)
[6] Makinde, O. D.; Chinyoka, T., Numerical study of unsteady hydromagnetic generalized couette flow of a reactive third-grade fluid with asymmetric convective cooling, Comput. Math. Appl., 61, 4, 1167-1179, (2011) · Zbl 1217.76087
[7] Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, S. J., Heat and mass transfer of two-layer flows of third-grade nanofluids in a vertical channel, Appl. Math. Comput., 242, 528-540, (2014) · Zbl 1334.80004
[8] Ellahi, R.; Hayat, T.; Mahomed, F. M.; Asghar, S., Effects of slip on the non-linear flows of a third grade fluid, Nonlinear Anal. Real World Appl., 11, 1, 139-146, (2010) · Zbl 1287.76035
[9] Fosdick, R. L.; Rajagopal, K. R., Thermodynamics and stability of fluids of third grade, Proc. R. Soc. A, 369, 1738, 351-377, (1980) · Zbl 0441.76002
[10] Abbasbandy, S.; Hayat, T., On series solution for unsteady boundary layer equations in a special third grade fluid, Commun. Nonlinear Sci. Numer. Simul., 16, 8, 3140-3146, (2011) · Zbl 1419.76151
[11] Fakhar, K.; Kara, A. H.; Khan, I.; Sajid, M., On the computation of analytical solutions of an unsteady magnetohydrodynamics flow of a third grade fluid with hall effects, Comput. Math. Appl., 61, 4, 980-987, (2011) · Zbl 1217.76085
[12] Hayat, T.; Shafiq, A.; Alsaedi, A., MHD axisymmetric flow of third grade fluid by a stretching cylinder, Alexandria Eng. J., 54, 2, 205-212, (2015)
[13] Stefan, M. J., Versuch ber die sheinbare adhesion Akad Wissensch Wein Math Natur, 69, 713, (1874)
[14] Khan, U.; Khan, S. I.; Ahmed, N.; Bano, S.; Mohyud-Din, S. T., Heat transfer analysis for squeezing flow of a Casson fluid between parallel plates, Ain Shams Eng. J., 7, 1, 497-504, (2016)
[15] Hayat, T.; Muhammad, K.; Farooq, M.; Alsaedi, A., Squeezed flow subject to Cattaneo-Christov heat flux and rotating frame, J. Mol. Liq., 220, 216-222, (2016)
[16] Domairry, G.; Hatami, M., Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Padé method, J. Mol. Liq., 193, 37-44, (2014)
[17] Sheikholeslami, M.; Ganji, D. D.; Ashorynejad, H. R., Investigation of squeezing unsteady nanofluid flow using ADM, Powder Technol., 239, 259-265, (2013)
[18] Mustafa, M.; Khan, J. A.; Hayat, T.; Alsaedi, A., On bodewadt flow and heat transfer of nanofluids over a stretching stationary disk, J. Mol. Liq., 211, 119-125, (2015)
[19] Khan, N.; Mahmood, T., Thermophoresis particle deposition and internal heat generation on MHD flow of an Oldroyd-B nanofluid between radiative stretching disks, J. Mol. Liq., 216, 571-582, (2016)
[20] Hayat, T.; Qayyum, S.; Imtiaz, M.; Alzahrani, F.; Alsaedi, A., Partial slip effect in flow of magnetite-Fe_3O_4 nanoparticles between rotating stretchable disks, J. Magn. Magn. Mater., 413, 39-48, (2016)
[21] Mustafa, I.; Javed, T.; Ghaffari, A., Heat transfer in MHD stagnation point flow of a ferrofluid over a stretchable rotating disk, J. Mol. Liq., 219, 526-532, (2016)
[22] Turkyilmazoglu, M., Three dimensional MHD stagnation flow due to a stretchable rotating disk, Int. J. Heat Mass Transf., 55, 23-24, 6959-6965, (2012)
[23] Sheikholeslami, M.; Hayat, T.; Alsaedi, A., MHD free convection of Al_2O_3-water nanofluid considering thermal radiation: a numerical study, Int. J. Heat Mass Transf., 96, 513-524, (2016)
[24] Cortell, R., Fluid flow and radiative nonlinear heat transfer over a stretching sheet, J. King Saud Univ.- Sci., 26, 2, 161-167, (2014)
[25] Sheikholeslami, M.; Ganji, D. D..; Javed, M. Y.; Ellahi, R., Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model, J. Magn. Magn. Mater., 374, 36-43, (2015)
[26] Lin, Q.; Xuan, Y.; Han, Y., The effects of randomly distributed droplets on thermal radiation of surfaces, Int. J. Heat Mass Transf., 96, 231-241, (2016)
[27] Hayat, T.; Imtiaz, M.; Alsaedi, A.; Kutbi, M. A., MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation, J. Magn. Magn. Mater., 396, 31-37, (2015)
[28] Hatami, M.; Nouri, R.; Gangi, D. D., Forced convection analysis for MHD Al_2O_3-water nannofluid flow over a horizontal plate, J. Mol. Liq., 187, 294-301, (2013)
[29] Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, S. J., Effective computation of exact and analytic approximate solutions to singular nonlinear equations of Lane-Emden-Fowler type, Numer. Algorithms, 70, 43-59, (2015) · Zbl 1329.76256
[30] Turkyilmazoglu, M., Effective computation of exact and analytic approximate solutions to singular nonlinear equations of Lane-Emden-Fowler type, Appl. Math. Model, 37, 14-15, 7539-7548, (2013) · Zbl 1449.65171
[31] Han, S.; Zheng, L.; Li, C.; Zhang, X., Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model, Appl. Math. Lett., 38, 87-93, (2014) · Zbl 1314.76009
[32] Sui, J.; Zheng, L.; Zhang, X.; Chen, G., Mixed convection heat transfer in power law, fluids over a moving conveyor along an inclined plate, Int. J. Heat Mass Transf., 85, 1023-1033, (2015)
[33] Hayat, T.; Jabeen, S.; Shafiq, A.; Alsaedi, A., Radiative squeezing flow of second grade fluid with convective boundary conditions, PLoS ONE, 11, 4, (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.