Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink. (English) Zbl 1457.76029
Summary: Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.
MSC:
| 76A10 | Viscoelastic fluids |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 76V05 | Reaction effects in flows |
Keywords:
viscoelastic fluid; three dimensional flow; mixed convection flow; exponentially stretching surface; chemical reaction; heat source/sinkReferences:
| [1] | L. J. Crane, “Flow past a stretching plate,” Z. Angew. Math. Phys. 21, 645-647 (1970). · doi:10.1007/BF01587695 |
| [2] | M. M. Rashidi, A. J. Chamkha, and M. Keimanesh, “Application of multi-step differential transform method on flow of a second-grade fluid over a stretching or shrinking sheet,” Am. J. Comput. Math. 6, 119-128 (2011). · doi:10.4236/ajcm.2011.12012 |
| [3] | A. Ahmad and S. Asghar, “Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field,” Appl. Math. Lett. 24, 1905-1909 (2011). · Zbl 1408.76008 · doi:10.1016/j.aml.2011.05.016 |
| [4] | T. Hayat, S. A. Shehzad, M. Qasim, and S. Obaidat, “Flow of a second grade fluid with convective boundary conditions,” Thermal Sci. S 15, 253-261 (2011). · doi:10.2298/TSCI101014058H |
| [5] | M. Nazar, C. Fetecau, D. Vieru, and C. Fetecau, “New exact solutions corresponding to the second problem of Stokes for second grade fluids,” Nonlinear Anal. Real World Appl. 11, 584-591 (2010). · Zbl 1287.76040 · doi:10.1016/j.nonrwa.2008.10.055 |
| [6] | R. Nazar and N. A. Latip, “Numerical investigation of three-dimensional boundary layer flow due to a stretching surface in a viscoelastic fluid,” Eur. J. Sci. Res. 29, 509-517 (2009). |
| [7] | K. Bhattacharyya, M. S. Uddin, G. C. Layek, and M. A. Malek, “Effect of chemically reactive solute diffusion on boundary layer flow past a stretching surface with suction or blowing,” J. Math. Math. Sci. 25, 41-48 (2010). |
| [8] | R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl. Math. Comput. 184, 864-873 (2007). · Zbl 1112.76022 |
| [9] | Abbasbandy, S.; Ghehsareh, H. R.; Hashim, I., An approximate solution of the MHD flow over a nonlinearly stretching sheet by rational Chebyshev collocation method (2012) · Zbl 1299.76175 |
| [10] | S. Mukhopadhyay, “Casson fluid flow and heat transfer over a nonlinearly stretching surface,” Chin. Phys. B 22, 074701 (2013). · doi:10.1088/1674-1056/22/7/074701 |
| [11] | M. Turkyilmazoglu and I. Pop, “Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid,” Int. J. Heat Mass Transf. 57, 82-88 (2013). · doi:10.1016/j.ijheatmasstransfer.2012.10.006 |
| [12] | M. Q. Al-Odat, R. A. Damesh, and T. A. Al-Azab, “Thermal boundary layer on an exponentially stretching continuous surface in the presence of magnetic field,” Int. J. Appl. Mech. Eng. 11, 289-299 (2006). · Zbl 1195.76425 |
| [13] | M. Sajid and T. Hayat, “Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet,” Int. Commun. Heat Mass Transfer 35, 347-356 (2008). · doi:10.1016/j.icheatmasstransfer.2007.08.006 |
| [14] | S. Nadeem and C. Lee, “Boundary layer flow of nanofluid over an exponentially stretching surface,” Nanoscale Res. Lett. 7, 94 (2012). · doi:10.1186/1556-276X-7-94 |
| [15] | K. Bhattacharyya, “Boundary layer flow and heat transfer over an exponentially shrinking sheet,” Chin. Phys. Lett. 28, 074701 (2011). · doi:10.1088/0256-307X/28/7/074701 |
| [16] | S. Mukhopadhyay, K. Vajravelu, and R. A. V. Gorder, “Casson fluid flow and heat transfer at an exponentially stretching permeable surface,” J. Appl. Mech. 80, 054502 (2013). · doi:10.1115/1.4023618 |
| [17] | M. Mustafa, T. Hayat, and S. Obaidat, “Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions,” Int. J. Numer. Meth. Heat Fluid Flow 23, 945-959 (2013). · Zbl 1356.76086 · doi:10.1108/HFF-09-2011-0179 |
| [18] | I. C. Liu, H. H. Wang, and Y. F. Peng, “Flow and heat transfer for three dimensional flow over an exponentially stretching surface,” Chem. Eng. Commun. 200, 253-268 (2013). · doi:10.1080/00986445.2012.703148 |
| [19] | S. Mukhopadhyay, G. C. Layek, and S. K. A. Samad, “Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity,” Int. J. Heat Mass Transf. 48, 4460-4466 (2005). · Zbl 1189.76787 · doi:10.1016/j.ijheatmasstransfer.2005.05.027 |
| [20] | Motsa, S. S.; Hayat, T.; Aldossary, O. M., MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method, 975-990 (2012) · Zbl 1266.76007 |
| [21] | M. M. Rashidi and E. Erfani, “A new analytical study of MHD stagnation-point flow in porous media with heat transfer,” Comput. Fluids 40, 172-178 (2011). · Zbl 1245.76160 · doi:10.1016/j.compfluid.2010.08.021 |
| [22] | S. Mukhopadhyay, “Effects of slip on unsteady mixed convective flow and heat transfer past a stretching surface,” Chin. Phys. Lett. 27, 124401 (2010). · doi:10.1088/0256-307X/27/12/124401 |
| [23] | T. Hayat, Z. Abbas, I. Pop, and S. Asghar, “Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium,” Int. J. Heat Mass Transf. 53, 466-474 (2010). · Zbl 1180.80022 · doi:10.1016/j.ijheatmasstransfer.2009.09.010 |
| [24] | M. Turkyilmazoglu, “The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface,” Int. J. Mech. Sci. 77, 263-268 (2013). · doi:10.1016/j.ijmecsci.2013.10.011 |
| [25] | E. M. A. Elbashbeshy and D. A. Aldawody, “Heat transfer over an unsteady stretching surface with variable heat flux in the presence of a heat source or sink,” Comput. Math. Appl. 60, 2806-2811 (2010). · Zbl 1207.76054 · doi:10.1016/j.camwa.2010.09.035 |
| [26] | R. Kandasamy, T. Hayat, and S. Obaidat, “Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink,” Nuclear Eng. Design 241, 2155-2161 (2011). · doi:10.1016/j.nucengdes.2011.03.002 |
| [27] | A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Commun. Nonlinear Sci. Numer. Simul. 14, 1064-1068 (2009). · doi:10.1016/j.cnsns.2008.05.003 |
| [28] | O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition,” Int. J. Therm. Sci. 50, 1326-1332 (2011). · doi:10.1016/j.ijthermalsci.2011.02.019 |
| [29] | S. A. Shehzad, T. Hayat, and A. Alsaedi, “Three-dimensional flow of Jeffery fluid with convective surface boundary conditions,” Int. J. Heat Mass Transf. 55, 3971-3976 (2012). · doi:10.1016/j.ijheatmasstransfer.2012.03.027 |
| [30] | M. M. Rashidi, N. F. Mehr, A. Hosseini, O. A. Bég, and T. K. Hung, “Homotopy simulation of nanofluid dynamics from a nonlinearly stretching isothermal permeable sheet with transpiration,” Meccanica. doi 10.1007/s11012-013-9805-9 · Zbl 1361.76024 |
| [31] | Y.P. Liu, S. J. Liao, and Z. B. Li, “Symbolic computation of strongly nonlinear periodic oscillations,” J. Symb. Comput. 55, 72-95 (2013). · Zbl 1325.68292 · doi:10.1016/j.jsc.2013.03.006 |
| [32] | S. Abbasbandy, M. S. Hashemi, and I. Hashim, “On convergence of homotopy analysis method and its application to fractional integro-differential equations,” Quaestiones Math. 36, 93-105 (2013). · Zbl 1274.65229 · doi:10.2989/16073606.2013.780336 |
| [33] | L. Zheng, J. Niu, X. Zhang, and Y. Gao, “MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump,” Math. Comput. Model. 56, 133-144 (2012). · Zbl 1255.76154 · doi:10.1016/j.mcm.2011.11.080 |
| [34] | M. M. Rashidi, S.C. Rajvanshi, and M. Keimanesh, “Study of Pulsatile flow in a porous annulus with the homotopy analysis method,” Int. J. Numer. Methods Heat Fluid Flow 22, 971-989 (2012). · Zbl 1356.76254 · doi:10.1108/09615531211271817 |
| [35] | M. Turkyilmazoglu, “Solution of Thomas-Fermi equation with a convergent approach,” Commun. Nonlinear Sci. Numer. Simul. 17, 4097-4103 (2012). · Zbl 1316.34020 · doi:10.1016/j.cnsns.2012.01.030 |
| [36] | T. Hayat, M. B. Ashraf, H. H. Alsulami, and M. S. Alhuthali, “Three dimensional mixed convection flow of viscoelastic fluid with thermal radiation and convective conditions,” Plos One 9, e90038 (2014). · doi:10.1371/journal.pone.0090038 |
| [37] | H. N. Hassan and M. M. Rashidi, “An analytic solution of micropolar flow in a porous channel with mass injection using homotopy analysis method,” Int. J. Numer. Methods Heat Fluid Flow 24 (2), 419-437 (2014). · Zbl 1356.76231 · doi:10.1108/HFF-08-2011-0158 |
| [38] | T. Hayat, S. A. Shehzad, M. B. Ashraf, and A. Alsaedi, “Magnetohydrodynamic mixed convection flow of thixotropic fluid with thermophoresis and Joule heating,” J. Thermophys. Heat Transf. 27, 733-740 (2013). · doi:10.2514/1.T4039 |
| [39] | T. Hayat, M. B. Ashraf, and A. Alsaedi, “Small-time solutions for the thin-film flow of a Casson fluid due to a suddenly moved plate,” J. Aerosp. Eng. 27, 04014034 (2014). · doi:10.1061/(ASCE)AS.1943-5525.0000330 |
| [40] | T. Hayat, M. Farooq, and A. Alsaedi, “Melting heat transfer in the stagnation point flow of Maxwell fluid with double-diffusive convection,” Int. J. Numer. Methods Heat Fluid Flow 24, 760-774 (2014). · Zbl 1356.76321 · doi:10.1108/HFF-09-2012-0219 |
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.
