Numerical Study of MHD Viscoelastic Fluid Flow with Binary Chemical Reaction and Arrhenius Activation Energy
-
M. Mustafa
,
A. Mushtaq
Abstract
Here we address the influence of heat/mass transfer on MHD axisymmetric viscoelastic fluid flow developed by an elastic sheet stretching linearly in the radial direction. Constitutive relations of Maxwell fluid model are utilized in mathematical formulation of the problem. Non-linear radiation heat flux is factored in the model which accounts for both small and large temperature differences. Chemical reaction effects with modified Arrhenius energy function are analyzed which are not yet explored for viscoelastic fluid flows. Highly accurate numerical computations are performed. Our computations show S-shaped profiles of temperature function in case of sufficiently large temperature differences. Species concentration increases when activation energy for chemical reaction is increased. However, both chemical reaction rate and temperature gradient tend to reduce the solute concentration.
Nomenclature
Cylindrical coordinate system
radial and axial velocity components
magnetic field strength
velocity of the stretching sheet
dimensionless radial component of velocity
Hartman number
concentration
wall concentration
ambient concentration
fluid temperature
wall temperature
ambient fluid temperature
heat source/sink parameter
specific heat
Prandtl number
wall and Rosseland radiative heat flux respectively
local Nusselt number
mean absorption coefficient
Reynolds number
non-dimensional activation energy
solutal diffusivity
Deborah number
Schmidt number
radiation parameter
- Greek symbols
similarity variable
dimensionless nanoparticle concentration
dimensionless chemical reaction rate constant
fluid relaxation time
density
dynamic viscosity
kinematic viscosity
thermal diffusivity
Stefan-Boltzman constant
dimensionless temperature
1st order derivative with respect to
2nd order derivative with respect to
3rd order derivative with respect to
References
1. Abbas, Z., Sheikh, M., Motsa, S.S., 2016. Numerical solution of binary chemical reaction on stagnation-point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation. Energy 95, 12–20.10.1016/j.energy.2015.11.039Suche in Google Scholar
2. Abbasi, F.M., Shehzad, S.A., Hayat, T., Ahmad, B., 2016. Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption. Journal of Magnetism and Magnetic Materials 404, 159–165.10.1016/j.jmmm.2015.11.090Suche in Google Scholar
3. Abel, M.S., Tawade, J.V., Nandeppanavar, M.M., 2012. MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet. Meccanica 47, 385–393.10.1007/s11012-011-9448-7Suche in Google Scholar
4. Ariel, P.D., 2001. Axisymmetric flow of a second grade fluid past a stretching sheet. International Journal of Engineering Science 39, 529–553.10.1016/S0020-7225(00)00052-5Suche in Google Scholar
5. Ariel, P.D., 2007. Axisymmetric flow due to a stretching sheet with partial slip. Computers & Mathematics with Applications 54, 1169–1183.10.1016/j.camwa.2006.12.063Suche in Google Scholar
6. Ariel, P.D., Hayat, T., Asghar, S., 2006. Homotopy perturbation method and axisymmetric flow over a stretching sheet. International Journal of Nonlinear Sciences and Numerical Simulation 7, 399–406.10.1515/IJNSNS.2006.7.4.399Suche in Google Scholar
7. Awad, F.G., Motsa, S., Khumalo, M., 2014. Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy. PLoS ONE 9. doi:10.1371/journal.pone.0107622.Suche in Google Scholar PubMed PubMed Central
8. Cortell, R., 2014a. Fluid flow and radiative nonlinear heat transfer overa stretching sheet. Journal of King Saud University-Science 26, 161-167. doi.org/10.1016/j jksus.2013.08.004.doi.org/10.1016/j jksus.2013.08.004Suche in Google Scholar
9. Cortell, R., 2014b. MHD (magneto-hydrodynamic) flow and radiative nonlinear heat transfer of a viscoelastic fluid over a stretching sheet with heat generation/absorption. Energy 74, 896–905.10.1016/j.energy.2014.07.069Suche in Google Scholar
10. Crane, L.J., 1970. Flow past a stretching plate. Journal of Applied Mathematics and Physics. (ZAMP) 21, 645–647.10.1007/BF01587695Suche in Google Scholar
11. Han, S., Zheng, L., Li, C., Zhang, X., 2014. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Applied Mathematics Letters 38, 87–93.10.1016/j.aml.2014.07.013Suche in Google Scholar
12. Hayat, T., Imtiaz, M., Alsaedi, A., Almezal, S., 2016. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous/heterogeneous reactions. Journal of Magnetism and Magnetic Materials 401, 296–303.10.1016/j.jmmm.2015.10.039Suche in Google Scholar
13. Hayat, T., Imtiaz, M., Alsaedi, A., Kutbi, M.A., 2015. MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials 396, 31–37.10.1016/j.jmmm.2015.07.091Suche in Google Scholar
14. Hayat, T., Muhammad, T., Alsaedi, A., Alhuthali, M.S., 2015. Magneto hydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials 385, 222–229.10.1016/j.jmmm.2015.02.046Suche in Google Scholar
15. Hayat, T., Mustafa, M., Shehzad, S.A., Obaidat, S., 2012. Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet. International Journal for Numerical Methods in Fluids 68, 233–243.10.1002/fld.2503Suche in Google Scholar
16. Hsiao, K.L., 2011. MHD mixed convection for viscoelastic fluid past a porous wedge. International Journal of Non-Linear Mechanics 46, 1–8.10.1016/j.ijnonlinmec.2010.06.005Suche in Google Scholar
17. Hsiao, K.L., 2015. Corrigendum to ‘‘Heat and mass mixed convection for MHD viscoelastic fluid past a stretching sheet with Ohmic dissipation’’ [Commun Nonlinear Sci Numer Simulat 15 (2010) 1803–1812)]. Communications in Nonlinear Science and Numerical Simulation 28, 232. doi:10.1016/j.cnsns.2015.04.004.Suche in Google Scholar
18. Hsiao, K.L., 2016. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering 98, 850–861.10.1016/j.applthermaleng.2015.12.138Suche in Google Scholar
19. Hsiao, K.L.. Numerical solution for Ohmic Soret-Dufour Heat and Mass Mixed Convection of Viscoelastic Fluid over a Stretching Sheet with Multimedia Physical Features. Journal of Aerospace Engineering. doi:10.1061/(ASCE)AS.1943–5525.0000681.Suche in Google Scholar
20. Khan, N., Mahmood, T., Sajid, M., Hashmi, M.S., 2016. Heat and mass transfer on MHD mixed convection axisymmetric chemically reactive flow of Maxwell fluid driven by exothermal and isothermal stretching disks. International Journal of Heat and Mass Transfer 92, 1090–1105.10.1016/j.ijheatmasstransfer.2015.09.001Suche in Google Scholar
21. Khan, J.A., Mustafa, M., Hayat, T., Alsaedi, A., 2015. Numerical study of Cattaneo-Christov heat flux model for viscoelastic flow due to an exponentially stretching surface. PLoS ONE 9. doi:10.1371/journal.pone.0137363.Suche in Google Scholar
22. Li, C., Zheng, L., Zhang, X., Chen, G., 2016. Flow and heat transfer of a generalized Maxwell fluid with modified fractional Fourier’s law and Darcy’s law. Computers & Fluids 125, 25–38.10.1016/j.compfluid.2015.10.021Suche in Google Scholar
23. Magyari, E., Pantokratoras, A., 2011. Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows. International Communications in Heat and Mass Transfer 38, 554–556.10.1016/j.icheatmasstransfer.2011.03.006Suche in Google Scholar
24. Makinde, O.D., Olanrewaju, P.O., Charles, W.M., 2011. Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture. Afrika Matematika 21, 1–17.10.1007/s13370-011-0008-zSuche in Google Scholar
25. Maleque, K.A., 2013. Unsteady natural convection boundary layer heat and mass transfer flow with exothermic chemical reactions. Indian Journal of Pure and Applied Mathematics 9, 17–41.Suche in Google Scholar
26. Mushtaq, A., Abbasbandy, M.,S., Mustafa, M., Hayat, T., Alsaedi, A., 2016. Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model. AIP Advances 6. doi: org/10.1063/1.4940133.Suche in Google Scholar
27. Mushtaq, A., Mustafa, M., Hayat, T., Alsaedi, A., 2014. About thermal radiation effects on the stagnation-point flow of upper-convected Maxwell (UCM) fluid over a stretching sheet. Journal of Aerospace Engineering 27. doi: 10.1061/(ASCE)AS.1943-5525.0000361.Suche in Google Scholar
28. Mustafa, M., 2015. Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid, AIP Advances 5. doi: 10.1063/1.4917306.Suche in Google Scholar
29. Mustafa, M., Hayat, T., Alsaedi, A., 2012. Axisymmetric flow of a nanofluid over a radially stretching sheet with convective boundary conditions. Current Nanoscience 8, 328–334.10.2174/157341312800620241Suche in Google Scholar
30. Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A., 2015. Simulations for Maxwell fluid flow past a convectively heated exponentially stretching sheet with nanoparticles. AIP Advances 5. doi: org/10.1063/1.4916364.Suche in Google Scholar
31. Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A., 2015. Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet. International Journal of Non-Linear Mechanics 71, 22–29.10.1016/j.ijnonlinmec.2015.01.005Suche in Google Scholar
32. Mustafa, M., Mushtaq, A., Hayat, T., Ahmad, B., 2014. Nonlinear radiation heat transfer effects in the natural convective boundary layer flow of nanofluid past a vertical plate: A numerical study. PLoS ONE 9. doi: 10.1371/journal.pone.0103946.Suche in Google Scholar PubMed PubMed Central
33. Mustafa, A., Mustafa, M., Hayat, T., Alsaedi, A., 2014. Nonlinear radiative heat transfer in the flow of nanofluid due to solar energy: A numerical study. Journal of the Taiwan Institute of Chemical Engineers 45, 1176–1183.10.1016/j.jtice.2013.11.008Suche in Google Scholar
34. Mustafa, A.,Mustafa, M., Hayat, T., Alsaedi, A., 2016. A numerical study for three-dimensional viscoelastic flow inspired by non-linear radiative heat flux. International Journal of Non-Linear Mechanics 79, 83–87.10.1016/j.ijnonlinmec.2015.11.006Suche in Google Scholar
35. Nandy, S.K., 2015. Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip. Journal of the Taiwan Institute of Chemical Engineers 52, 22–30.10.1016/j.jtice.2015.01.025Suche in Google Scholar
36. Pantokratoras, A., Fang, T., 2013. Sakiadis flow with nonlinear Rosseland thermal radiation. Physica Scripta 87, 015703(5 pages).10.1088/0031-8949/87/01/015703Suche in Google Scholar
37. Pantokratoras, A., Fang, T., 2014. Blasius flow with non-linear Rosseland thermal radiation. Meccan 49, 1539–1545.10.1007/s11012-014-9911-3Suche in Google Scholar
38. Rahman, M.M., Eltayeb, I.A., 2013. Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition. Meccan 48, 601–615.10.1007/s11012-012-9618-2Suche in Google Scholar
39. Sajid, M., Hayat, T., Asghar, S., Vajravelu, K., 2008. Analytic solution for axisymmetric flow over a nonlinearly stretching sheet. Archive of Applied Mechanics 78, 127–134.10.1007/s00419-007-0146-9Suche in Google Scholar
40. Sakiadis, C., 1961. Boundary-layer behaviour on continuous solid surfaces. I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal 7, 26–28.10.1002/aic.690070108Suche in Google Scholar
41. Shahzad, A., Ali, R., Khan, M., 2012. On the exact solution for axisymmetric flow and heat transfer over a non-linear radially stretching sheet. Chinese Physics Letters 29, 084705.10.1088/0256-307X/29/8/084705Suche in Google Scholar
42. Shehzad, S.A., Abdullah, Z., Abbasi, F.M., Hayat, T., Alsaedi, A., 2016. Magnetic field effect in three-dimensional flow of an Oldroyd-B nanofluid over a radiative surface. Journal of Magnetism and Magnetic Materials 399, 97–108.10.1016/j.jmmm.2015.09.001Suche in Google Scholar
43. Turkyilmazoglu, M., 2011. Multiple solutions of hydromagnetic permeable flow and heat for viscoelastic fluid. Journal of Thermophysics and Heat Transfer 25, 595–605.10.2514/1.T3749Suche in Google Scholar
44. Turkyilmazoglu, M., 2016. Equivalences and correspondences between the deforming body induced flow and heat in two-three dimensions. Physics of Fluids 28, Article ID 043102.10.1063/1.4945650Suche in Google Scholar
45. Wahab, A., Rasheed, A., Nawaz, R., Javaid, N., 2015. Numerical study of two dimensional unsteady flow of an anomalous Maxwell fluid. International Journal of Numerical Methods for Heat and Fluid Flow 25, 1120–1137.10.1108/HFF-07-2014-0199Suche in Google Scholar
46. Zhao, J., Zheng, L., Zhang, X., Liu, F., 2016. Unsteady natural convection boundary layer heat transfer of fractional Maxwell viscoelastic fluid over a vertical plate. International Journal of Heat and Mass Transfer 97, 760–766.10.1016/j.ijheatmasstransfer.2016.02.059Suche in Google Scholar
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