Nanofluids flow over a permeable unsteady stretching surface with non-uniform heat source/sink in the presence of inclined magnetic field
Tóm tắt
This work analyzes the unsteady two-dimensional nanofluid flow over a vertical stretching permeable surface in the presence of an inclined magnetic field and non-uniform heat source/sink. Four different types of nanoparticles, namely silver Ag, copper Cu, alumina Al2O3, and titania TiO2, are considered by using water as a base fluid with the Prandtl number Pr = 6.785. The governing partial differential equations are transformed to coupled non-linear ordinary differential equations by appropriate similarity transformation. Furthermore, the similarity equations are solved numerically by using the fourth-order Runge-Kutta integration scheme with Newton Raphson shooting method. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. Numerical results for velocity and temperature profiles as well as skin friction coefficient and local Nusselt number are discussed for various values of physical parameters. It tends to be discovered that, the magnetic field inclination angle γ has the capability to strengthens the magnetic field and reduce the velocity profile of the flow. Also, it can be found that, by using various types of nanofluids, velocity and temperature distributions change, which means that the nanofluids are important in the cooling and heating processes. The thermal boundary layer thickness is related to the increased thermal conductivity of different types of nanofluids, i.e., the minimum (maximum) value of the temperature is obtained by adding titanium oxide (silver) to the fluid as the nanoparticles.
Tài liệu tham khảo
Sakiadis, B.C.: Boundary layer behavior on continuous solid surfaces. AICHE J. 7, 26–28 (1961)
Erickson, L.E., Fan, L.T., Fox, V.G.: Heat and mass transfer on a continuous flat plate with suction/injection. Ind. Eng. Chem. Fundam. 5, 19–25 (1966)
Tsou, F.K., Sparrow, E.M., Goldstein, R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transf. 10, 219–235 (1967)
Crane, L.J.: Flow past a stretching plate. Z. Angew. Math. Phys. 21, 645–647 (1970)
Hayat, T., Saif, S., Abbas, Z.: The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet. Phys. Letters A. 372, 5037–5045 (2008)
Prasad, K.V., Vajravelu, K.: Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. Int. J. Heat Mass Transf. 52, 4956–4965 (2009)
Kumaran, V., Vanav Kumar, A., Pop, I.: Transition of MHD boundary layer flow past a stretching sheet. Commun. Nonlinear Sci. Nume. Simul. 15, 300–311 (2010)
Mukhopadhyay, S.: Heat transfer analysis for unsteady MHD flow past a non-isothermal stretching surface. Nucl. Eng. Des. 241, 4835–4839 (2011)
Wolfgang, C.W., Ostwald, W.: An Introduction to Theoretical and Applied Colloid Chemistry, the World of Neglected Dimensions, 1st edn. Stanpobe Press, Boston (1917)
Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., Thompson, L.J.: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Phys. Letters. 78, 718–720 (2001)
Liu, M.S., Lin, M.C.C., Huang, I.T., Wang, C.C.: Enhancement of thermal conductivity with CuO for nanofluids. Chem. Eng. Technol. 29, 72–77 (2006)
Garg, J., Poudel, B., Chiesa, M., Gordon, J.B., Ma, J.J., Wang, J.B., Ren, Z.F., Kang, Y.T., Ohtani, H., Nanda, J., McKinley, G.H., Chen, G.: Enhanced thermal conductivity and viscosity of copper nanoparticles in ethylene glycol nanofluid. J. Appl. Phys. 103, 074301–074306 (2008)
S.U.S. Choi, Enhancing Thermal Conductivity of Fluids with Nanoparticles, in: The Proceedings of the 1995 ASME Int. Mech. Eng. Congress and Exposition, San Francisco, ASME, FED 231/MD 66 (1995) 99–105
Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E., Grulke, E.A.: Anomalously thermal conductivity enhancement in nanotube suspensions. Applied Phys. Letters. 79, 2252–2254 (2001)
Yu, W.H., France, D.M., Routbort, J.L., Choi, S.U.S.: Review and comparison of nanofluid thermal conductivity and heat transfer enhancements. Heat Transfer Engineering. 29, 432–460 (2008)
Kakaç, S., Pramuanjaroenkij, A.: Review of convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transf. 52, 3187–3196 (2009)
Godson, L., Raja, B., Mohan Lal, D., Wongwises, S.: Enhancement of heat transfer using nanofluids - an overview. Renew. Sustain. Energy Rev. 14(2), 629–641 (2009)
Heris, S., Etemad, S.G., Esfahany, M.: Experimental investigation of oxide nanofluids laminar flow convective heat transfer. Int. Commun. Heat Mass Transfer. 33(4), 529–535 (2006)
Minsta, H.A., Roy, G., Nguyen, C.T., Doucet, D.: New temperature dependent thermal conductivity data for water based nanofluids. Int. J. Thermal Sci. 48, 363–371 (2009)
Daniel, Y.S., Abdul Aziz, Z., Ismail, Z., Salah, F.: Double stratification effects on unsteady electrical MHD mixed convection flow of nanofluid with viscous dissipation and Joule heating. J. Applied Research and Tech. 15(5), 464–476 (2017)
Reddy, P.S., Chamkha, A.J., Al-Mudhaf, A.: MHD heat and mass transfer flow of a nanofluid over an inclined vertical porous plate with radiation and heat generation/absorption. Adv. Powder Technol. 28(3), 1008–1017 (2017)
Prabhavathi, B., Reddy, P.S., Vijaya, R.B., Chamkha, A.J.: MHD boundary layer heat and mass transfer flow over a vertical cone embedded in porous media filled with Al2O3-water and Cu-water nanofluid. J. Nanofluids. 6, 883–891 (2017)
Sreedevi, P., Reddy, P.S., Rao, K.V.S.N., Chamkha, A.J.: Heat and mass transfer flow over a vertical cone through nanofluid saturated porous medium under convective boundary condition with suction/injection. J. Nanofluids. 6, 478–486 (2017)
Hayat, T., Ijaz Khan, M., Waqas, M., Alsaedi, A., Farooq, M.: Numerical simulation for melting heat transfer and radiation effects in stagnation point flow of carbon-water nanofluid. Comput. Methods Appl. Mech. Eng. 315, 1011–1024 (2017)
Madhu, M., Kishan, N., Chamkha, A.J.: Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects. Propulsion Power Res. 6(1), 31–40 (2017)
Hayat, T., Muhammad, T., Shehzad, S.A., Alsaedi, A.: An analytical solution for magnetohydrodynamic Oldroyd-B nanofluid flow induced by a stretching sheet with heat generation/absorption. Int. J. Thermal Sciences. 111, 274–288 (2017)
Hsiao, K.-L.: Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature. Int. J. Heat and Mass Transfer. 112, 983–990 (2017)
Eldabe, N.T., Abou-zeid, M.Y.: Homotopy perturbation method for MHD pulsatile non-Newtonian nanofluid flow with heat transfer through a non-Darcy porous medium. J. Egyptian Math. Soc. 25, 375–381 (2017)
Sreedevi, P., Reddy, P.S., Chamkha, A.J.: Heat and mass transfer analysis of nanofluid over linear and non- linear stretching surface with thermal radiation and chemical reaction. Powder Technol. 315, 194–204 (2017)
Sreedevi, P., Reddy, P.S., Chamkha, A.J.: Magneto-hydrodynamics heat and mass transfer analysis of single and multi-wall carbon nanotubes over vertical cone with convective boundary condition. Int. J. Mech. Sci. 135, 646–655 (2018)
Jyothi, K., Reddy, P.S., Reddy, M.S.: Influence of magnetic field and thermal radiation on convective flow of SWCNTs-water and MWCNTs-water nanofluid between rotating stretchable disks with convective boundary conditions. Powder Technol. 331, 326–337 (2018)
Zeeshan, A., Shehzad, N., Ellahi, R.: Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results in Phys. 8, 502–512 (2018)
Tiwari, R.K., Das, M.K.: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50, 2002–2018 (2007)
Abu-Nada, E.: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat Fluid Flow. 29, 242–249 (2008)
Oztop, H.F., Abu-Nada, E.: Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow. 29, 1326–1336 (2008)
Hady, F.M., Ibrahim, F.S., Abdel-Gaied, S.M., Eid, M.R.: Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid. Int. Commun. Heat Mass Transfer. 38, 1414–1420 (2011)
Ishak, A., Nazar, R., Pop, I.: Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica. 44, 369–375 (2009)
Grubka, L.J., Bobba, K.M.: Heat transfer characteristics of a continuous, stretching surface with variable temperature. ASME J Heat Transfer. 107, 248–250 (1985)
Ali, M.E.: Heat transfer characteristics of a continuous stretching surface. Heat Mass Transf. 29, 227–234 (1994)
Raju, C.S.K., Sandeep,N., Sulochana, C, Sugunamma, V., Babu, M.J.: Radiation, inclined magnetic field and cross-diffusion effects on flow over a stretching surface. J. Nigerian Math. Soc. 34, 169–180 (2015)
Brinkman, H.C.: The viscosity of concentrated suspensions and solution. J. Chem. Phys. 20, 571–581 (1952)
Maxwell, J.: A Treatise on Electricity and Magnetism, 2nd edn. Clarendon Press, Oxford (1881)
Mahmoud, M.A.A., Megahed, A.M.: Non-uniform heat generation effect on heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching sheet. Meccanica. 47, 1131–1139 (2012)
Das, K.: Slip flow and convective heat transfer of nanofluids over a permeable stretching surface. Comput. Fluids. 64, 34–42 (2012)