ANALYTICAL STUDY OF VARIABLE FLUID PROPERTIES AND MAGNETIC FIELD IN THIN-FILM FLOW OVER A STRETCHING STEADY SURFACE
DOI:
https://doi.org/10.46754/jmsi.2024.12.003Keywords:
Water based GO-EG nanofluid, Water based GO-W nanofluid, OHAM, MHD, Steady stretching surfaceAbstract
This research paper explains the effect of dynamic viscosity on steady thin film flow of water based nanofluid GO-EG and GO-W in the presence of magnetic field, variable thermal conductivity and convective boundary condition over a stretching surface. By using the similarity transformation, the partial differential equation is converted to nonlinear third order ordinary differential equations. The analytical method (OHAM) is used to find the analytical solution of the nonlinear problem which analyze the problem. The result of important parameters for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergence of the problem up to 25 iterations. The skin friction coefficient and Nusselt number is explained in table form.
References
Sandeep, N., & Malvandi, A. (2016). Enhanced heat transfer in liquid thin film flow of non-Newtonian nanofluids embedded with graphene nanoparticles. Advanced Powder Technology, 27(6), 2448-2456. https://doi.org/10.1016/j.apt.2016.08.023
Wang, C. Y. (1990). Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics, 48(4), 601-610. http://www.jstor.org/stable/43637666
Usha, R., & Sridharan, R. (1993). On the motion of a liquid film on an unsteady stretching surface. Open Journal of Fluid Dynamics, 150(1993), 43-48.
Liu, I., & Andersson, H. I. (2007). Heat transfer in a liquid film on an unsteady stretching sheet. Journal of Thermal Sciences, 47(6), 766-772.
Aziz, R.C., Hashim, I. & Alomari, A.K. (2011). Thin film flow and heat transfer on an unsteady stretching sheet with internal heating, Meccanica, 46, 349-357.
Tawade, J., Abel, M. S., Metri, P. G., & Koti, A. (2016). Thin film flow and heat transfer over an unsteady stretching sheet with thermal radiation, internal heating in presence of external magnetic field. International Journal Advances in Applied Mathematics and Mechanics,
(4), 29-40. http://www.ijaamm.com/uploads/2/1/4/8/21481830/v3n4p5_29-40.pdf
Andersson, H. I., Aarseth, J. B., & Dandapat, B. S. (2000). Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer, 43(1), 69-74. https://doi.org/10.1016/s0017-9310(99)00123-4
Chen, C. H. (2003). Heat transfer in a power-law fluid film over an unsteady stretching sheet, International Journal of Heat and Mass Transfer, 39(8), 791-796. https://doi.org/10.1007/s00231-002-0363-2
Chen, C. H. (2006). Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Journal of Non-Newtonian Fluid Mechanics, 135(2-3), 128-135. https://doi.org/10.1016/j.jnnfm.2006.01.009
Wang, C., & Pop, I. (2006). Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method, Journal of Non-Newtonian Fluid Mechanics, 138(3) (2006), 161-172. https://doi.org/10.1016/j.jnnfm.2006.05.011
Abdelmotalib, H. M., Youssef, M. A., Hassan, A. A., Youn, S. B., & Im, I. (2015). Heat transfer process in gas–solid fluidized bed combustors. International Journal of Heat and Mass Transfer, 89, 567-575. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.085
Megahed, A. M. (2015). Effect of slip velocity on casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation. Applied Mathematics and Mechanics, 36(10), 1273-1284. https://doi.org/10.1007/s10483-015-1983-9
Khan, N. S., Gul, T., Islam, S., Khan, A., & Shah, Z. (2017). Brownian motion and thermophoresis effects on MHD mixed convective thin film second-grade nanofluid flow with Hall effect and heat transfer past a stretching sheet. Journal of Nanofluids, 6(5), 812-829. https://doi.org/10.1166/jon.2017.1383
Tahir, F., Gul, T., Islam, S., Shah, Z., Khan, A., Khan, W., Ali, L., & Muradullah, N. (2017). Flow of a nano-liquid film of Maxwell fluid with thermal radiation and magneto hydrodynamic properties on an unstable stretching sheet, Journal of Nanofluids, 6(6) (2017), 1021-1030. https://doi.org/10.1166/jon.2017.1400
Abolbashari, M. H., Freidoonimehr, N., Nazari, F., & Rashidi, M. M. (2015). Analytical modeling of entropy generation for Cassonnano-fluid flow induced by a stretching surface. Advanced Powder Technology, 26(2), 542-552. https://doi.org/10.1016/j.apt.2015.01.003
Hayat, T., Muhammad, T., Shehzad, S. A., & Alsaedi, A. (2015). Three-dimensional boundary layer flow of Maxwell nanofluids: mathematical model. Applied Mathematics and Mechanics, 36(6), 747-762. https://doi.org/10.1007/s10483-015-1948-6
Malik, M. Y., Khan, I., Hussain, A., & Salahuddin, T. (2015). Mixed convection flow of MHD Eyring–powell nanofluid over a stretching sheet: A numerical study. AIP Advances, 5(11), 117-118. https://doi.org/10.1063/1.4935639
Nadeem, S., Haq, R. U., & Khan, Z. (2014). Numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nanoparticles, Journal of the Taiwan Institute of Chemical Engineers, 45(11), 121-126. https://doi.org/10.1016/j.jtice.2013.04.006
Raju, C. S. K., Sanjeevi, P., Raju, M. C., Ibrahim, S. M., Lorenzini, G., & Lorenzini, E. (2017). The flow of magnetohydrodynamic Maxwell nanofluid over a cylinder with Cattaneo-Christov heat flux model. Continuum Mechanics and Thermodynamics, 29(6), 1347-1363. https://doi.org/10.1007/s00161-017-0580-z
Rokni, H. B., Alsaad, D. M., & Valipour, P. (2016). Electrohydrodynamic nanofluid flow and heat transfer between two plates. Journal of Molecular Liquids, 216, 583-589. https://doi.org/10.1016/j.molliq.2016.01.073
Nadeem, S., Haq, R. U., & Khan, Z. H. (2014). Numerical solution of non-Newtonian nanofluid flow over a stretching sheet. Applied Nanoscience, 4(5), 625-631. https://doi.org/10.1007/s13204-013-0235-8
Shehzad, S. A., Hayat, T., & Alsaedi, A. (2015). MHD flow of Jeffrey nanofluid with convective boundary conditions. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37(3), 873-883. https://doi.org/10.1007/s40430-014-0222-3
Sheikholeslami, M., Hatami, M., & Ganji, D. (2014). Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. Journal of Molecular Liquids, 190, 112-120. https://doi.org/10.1016/j.molliq.2013.11.002
Mahmoodi, M., & Kandelousi, S. (2016). Kerosene−alumina nanofluid flow and heat transfer for cooling application. Journal of Central South University, 23(4), 983-990. https://doi.org/10.1007/s11771-016-3146-5
Shah, Z., Islam, S., Gul, T., Bonyah, E., & Khan, M. A. (2018). The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates. Results in Physics, 9, 1201-1214. https://doi.org/10.1016/j.rinp.2018.01.064
Shah, Z., Gul, T., Islam, S., Khan, M. A., Bonyah, E., Hussain, F., Mukhtar, S., & Ullah, M. (2018b). Three dimensional third grade nanofluid flow in a rotating system between parallel plates with Brownian motion and thermophoresis effects. Results in Physics, 10, 36-45. https://doi.org/10.1016/j.rinp.2018.05.020
Shah, Z., Gul, T., Khan, M. A., Ali, I., & Islam, S. (2017). Effects of hall current on steady three dimensional non-Newtonian nanofluid in a rotating frame with Brownian motion and thermophoresis effects, Journal of Engineering Technology, 6(SP), 280-296.
Sheikholeslami, M., Shamlooei, M., & Moradi, R. (2017). Fe3O4-ethylene glycol nanofluids forced convection inside a porous enclosure in existence of Coulomb force. Journal of Molecular Liquids, 249, 429-437. https://doi.org/10.1016/j.molliq.2017.11.048
Sheikholeslami, M. (2017). Numerical investigation of nanofluid free convection under the influence of electric field in a porous enclosure. Journal of Molecular Liquids, 249, 1212–1221. https://doi.org/10.1016/j.molliq.2017.11.141
Sheikholeslami, M., & Rokni, H. B. (2017). Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation. International Journal of Heat and Mass Transfer, 118, 823-831. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.041
Shah, Z., Bonyah, E., Islam, S., Khan, W., & Ishaq, M. (2018). Radiative MHD thin film flow of Williamson fluid over an unsteady permeable stretching sheet. Heliyon, 4(10), 825-830. https://doi.org/10.1016/j.heliyon.2018.e00825
Towers, S., Afzal, S., Bernal, G., Bliss, N., Brown, S., Espinoza, B., Jackson, J., Judson-Garcia, J., Khan, M., Lin, M., Mamada, R., Moreno, V. M., Nazari, F., Okuneye, K., Ross, M. L., Rodriguez, C., Medlock, J., Ebert, D., & Castillo-Chavez, C. (2015). Mass media and the contagion of fear: The case of Ebola in America. PLOS ONE, 10(6), 1-13. https://doi.org/10.1371/journal.pone.0129179
Rehman, A., Salleh, Z., Gul, T., & Zaheer, Z. (2019). The impact of viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids, Mathematics, 7(7), Article 653. https://doi.org/10.3390/math7070653
Balandin, A. A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F., & Lau, C. N. (2008). Superior thermal conductivity of single-layer graphene. Nano Letters, 8(3), 902-907. https://doi.org/10.1021/nl0731872
Yu, W., Xie, H., & Bao, D. (2010). Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets. Nanotechnology, 21(5), Article 055705. https://doi.org/10.1088/0957-4484/21/5/055705
Gul, T., & Firdous, K. (2018). The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO-H2O nanofluid flow between two rotating disks. Applied Nanoscience, 8(7), 1711-1727. https://doi.org/10.1007/s13204-018-0851-4
Gul, T., Noman, W., Sohail, M., & Khan, M. A. (2019) Impact of the Marangoni and thermal radiation convection on the graphene-oxide-water-based and ethylene-glycol-based nanofluids. Advances in Mechanical Engineering, 11(6), 1-9. https://doi.org/10.1177/1687814019856773
Rehman, A., Gul, T., Salleh, Z., Mukhtar, S., Hussain, F., Nisar, K. S., & Kumam, P. (2019). Effect of the marangoni convection in the unsteady thin film spray of CNT nanofluids. Processes, 7(6), Article 392. https://doi.org/10.3390/pr7060392
Khan, D., Kumam, P., Kumam, W., Suttiarporn, P., & Rehman, A. (2023). Relative magnetic field and slipping effect on Casson dusty fluid of two phase fluctuating flow over inclined parallel plate. South African Journal of Chemical Engineering, 44, 135-146. https://doi.org/10.1016/j.sajce.2023.01.010
Rehman, A., Khan, W., Bonyah, E., Karim, S. A. A., Alshehri, A., & Galal, A. M. (2022). Steady three-dimensional MHD mixed convection couple stress flow of hybrid nanofluids with hall and ion slip effect. Advances in Civil Engineering, 2022(1), 1-11. https://doi.org/10.1155/2022/9193875
Rehman, A., Alhefthi, R. K., Inc, M., & Jan, R. (2024). Analytical investigation of MgO–CuOH2O, hybrid nanofluid MHD stagnation point flow with the influence of viscous dissipation for enhancement of heat transfer ratio. Modern Physics Letters B, 38(15), 1-16. https://doi.org/10.1142/s0217984924501082
Rehman, A., Inc, M., Salah, B., & Hussain, S. (2023). Analytical analysis of silverwater, silver-blood base nanofluid flow over fluctuating disk with the influence of viscous dissipation over fluctuating disk. Modern Physics Letters B, 37(32), Article 2350113. https://doi.org/10.1142/s0217984923501130
Rehman, A., Salleh, Z., & Gul, T. (2019). Influence of dynamics viscosity on the water base graphene oxide–ethylene glycol/graphene oxide–water nanofluid flow over a stretching cylinder. Journal of Nanofluids, 8(8), 1661-1667.
Rehman, A., Salleh, Z., & Gul, T. (2019b). The impact of the magnetic field and viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids. Journal of Physics Conference Series, 1366(1), 012031. https://doi.org/10.1088/1742-6596/1366/1/012031.
Rehman, A., Salleh, Z., & Gul, T. (2019c). The impact of Marangoni convection, magnetic field and viscous dissipation on the thin film unsteady flow of go-eg/go-w nanofluids over an extending sheet. JP Journal of Heat and Mass Transfer, 18(2), 477-496. https://doi.org/10.17654/hm018020477
Rehman, A., Saeed, A., Salleh, Z., Jan, R., & Kumam, P. (2022). Analytical investigation of the time-dependent stagnation point flow of a CNT nanofluid over a stretching surface. Nanomaterials, 12(7), Article 1108. https://doi.org/10.3390/nano12071108
Rehman, A., Khan, W., Abdelrahman, A., Jan, R., Khan, M. S., & Galal, A. M. (2022). Influence of Marangoni convection, solar radiation, and viscous dissipation on the bioconvection couple stress flow of the hybrid nanofluid over a shrinking surface. Frontiers in Materials, 9,
Article 964543. https://doi.org/10.3389/fmats.2022.964543
Srivastava, H. M., Khan, Z., Mohammed, P. O., Al-Sarairah, E., Jawad, M., & Jan, R. (2022). Heat transfer of buoyancy and radiation on the free convection boundary layer MHD flow across a stretchable porous sheet. Energies, 16(1), Article 58. https://doi.org/10.3390/en16010058
Zubair, M., Jawad, M., Bonyah, E., & Jan, R. (2021). MHD analysis of couple stress hybrid nanofluid free stream over a spinning darcy-forchheimer porous disc under the effect of thermal radiation. Journal of Applied Mathematics, 2021(2), 1-18. http://dx.doi.org/10.1155/2021/2522155
Chakraborty, T., Das, K., & Kundu, P. K. (2018). Framing the impact of external magnetic field on bioconvection of a nanofluid flow containing gyrotactic microorganisms with convective boundary conditions. Alexandria Engineering Journal, 57(1), 61–71. https://doi.org/10.1016/j.aej.2016.11.011
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