Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid

doi:10.1007/s10483-017-2250-6

Abstract

Abstract:

This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo-Christov theory of heat and mass diffusion.

Key words: circular cylindrical shell, non-circular cutout, Stress concentration, complex variable method and conformal mapping technique, Maxwell liquid, temperature-dependent conductivity, chemical reactive flow, Cattaneo-Christov theory

2010 MSC Number:

75A10

S. A. SHEHZAD, T. HAYAT, A. ALSAEDI, M. A. MERAJ. Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1347-1356.

TrendMD

References

[1] Fourier, J. B. J. Théorie Analytique de la Chaleur, Didot, Paris (1822)
[2] Fick, R. On liquid diffusion. Journal of Membrane Science, 100, 33-38(1995)
[3] Cattaneo, C. Sulla conduzione del calore. Atti Semin Mat Fis University Modena Reggio Emilia, 3, 83-101(1948)
[4] Christov, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communications, 36, 481-486(2009)
[5] Ciarletta, M. and Straughan, B. Uniqueness and structural stability for the Cattaneo-Christov equations. Mechanics Research Communications, 37, 445-447(2010)
[6] Straughan, B. Thermal convection with the Cattaneo-Christov model. International Journal of Heat and Mass Transfer, 53, 95-98(2010)
[7] Li, J., Zheng, L., and Liu, L. MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects. Journal of Molecular Liquids, 221, 19-25(2016)
[8] Abbasi, F. M., Shehzad, S. A., Hayat, T., Alsaedi, A., and Hegazy, A. Influence of Cattaneo- Christov heat flux in flow of an Oldroyd-B fluid with variable thermal conductivity. International Journal of Numerical Methods for Heat & Fluid Flow, 26, 2271-2282(2016)
[9] Waqas, M., Hayat, T., Farooq, M., Shehzad, S. A., and Alsaedi, A. Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. Journal of Molecular Liquids, 220, 642-648(2016)
[10] Sui, J., Zheng, L., and Zhang, X. Boundary layer heat and mass transfer with Cattaneo-Christov double-diffusion in upper-convected Maxwell nanofluid past a stretching sheet with slip velocity. International Journal of Thermal Sciences, 104, 461-468(2016)
[11] Swati, M. M. Golam, A. M., and Wazed, A. P. Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction. Chinese Physics B, 22, 124701(2013)
[12] Shehzad, S. A., Alsaedi, A., and Hayat, T. Hydromagnetic steady flow of Maxwell fluid over a bidirectional stretching surface with prescribed surface temperature and prescribed surface heat flux. PLoS One, 8, e68139(2013)
[13] Ramesh, G. K. and Gireesha, B. J. Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Engineering Journal, 5, 991-998(2014)
[14] Hsiao, K. L. Conjugate heat transfer for mixed convection and Maxwell fluid on a stagnation point. Arabian Journal of Science and Engineering, 39, 4325-4332(2014)
[15] Hayat, T., Shehzad, S. A., and Alsaedi, A. MHD three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. International Journal of Numerical Methods for Heat & Fluid Flow, 24, 1073-1085(2014)
[16] Liu, Y. and Guo, B. Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform. Applied Mathematics and Mechanics (English Edition), 37(2), 137- 150(2016) DOI 10.1007/s10483-016-2021-8
[17] Cao, L., Si, X., and Zheng, L. Convection of Maxwell fluid over stretching porous surface with heat source/sink in presence of nanoparticles:Lie group analysis. Applied Mathematics and Mechanics (English Edition), 37(4), 433-442(2016) DOI 10.1007/s10483-016-2052-9
[18] Zhao, J., Zheng, L., Zhang, X., and Liu, F. Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects. International Journal of Heat and Mass Transfer, 103, 203-210(2016)
[19] Zhao, J., Zheng, L., Zhang, X., and Liu, F. 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(2016)
[20] Hsiao, K. L. Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects. Applied Thermal Engineering, 112, 1281-1288(2017)
[21] Chiam, T. C. Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mechanica, 129, 63-72(1998)
[22] Liao, S. J. Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press, Beijing (2012)
[23] Turkyilmazoglu, M. Solution of the Thomas-Fermi equation with a convergent approach. Com- munications in Nonlinear Science and Numerical Simulations, 17, 4097-4103(2012)
[24] Han, S., Zheng, L., Li, C., and Zhang, X. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Applied Mathematics Letters, 38, 87-93(2014)
[25] Abbasbandy, S., Hayat, T., Alsaedi, A., and Rashidi, M. M. Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat & Fluid Flow, 24, 390-401(2014)
[26] Shehzad, S. A., Hayat, T., Alsaedi, A., and Ahmad, B. Effects of thermophoresis and thermal radiation in mixed convection three-dimensional flow of Jeffrey fluid. Applied Mathematics and Mechanics (English Edition), 36(5), 655-668(2015) DOI 10.1007/s10483-015-1935-7
[27] Hayat, T., Muhammad, T., Shehzad, S. A., and Alsaedi, A. Three-dimensional boundary layer flow of Maxwell nanofluid:mathematical model. Applied Mathematics and Mechanics (English Edition), 36(6), 747-762(2015) DOI 10.1007/s10483-015-1948-6
[28] Shehzad, S. A., Abbasi, F. M., Hayat, T., and Ahmad, B. Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet. Applied Mathematics and Mechanics (English Edition), 37(6), 761-768(2016) DOI 10.1007/s10483-016-2088-6
[29] Hayat, T., Shafiq, A., Alsaedi, A., and Shahzad, S. A. Unsteady MHD flow over exponentially stretching sheet with slip conditions. Applied Mathematics and Mechanics (English Edition), 37(2), 193-208(2016) DOI 10.1007/s10483-016-2024-8
[30] Hayat, T., Imtiaz, M., and Alsaedi, A. Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet. Applied Mathematics and Mechanics (English Edition), 37(5), 573-582(2016) DOI 10.1007/s10483-016-2072-8
[31] Hayat, T., Muhammad, T., Shehzad, S. A., and Alsaedi, A. Three dimensional rotating flow of Maxwell nanofluid. Journal of Molecular Liquids, 229, 495-500(2017)
[32] Meraj, M. A., Shehzad, S. A., Hayat, T., Abbasi, F. M., and Alsaedi, A. Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory. Applied Mathematics and Mechanics (English Edition), 38(4), 557-566(2017) DOI 10.1007/s10483-017-2188-6