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Flow of Eyring-Powell liquid due to oscillatory stretchable curved sheet with modified Fourier and Fick's model

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  • 1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan;
    2. Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan

Received date: 2021-05-25

  Revised date: 2021-08-15

  Online published: 2021-09-23

Abstract

This study deals with the features of the mass and heat transport mechanism by adopting a modified version of Fourier and Fick's model known as the CattaneoChristov double diffusive theory. The time-dependent magnetohydrodynamic (MHD) flow of the Eyring-Powell liquid across an oscillatory stretchable curved sheet in the presence of Fourier and Fick's model is investigated. The acquired set of flow equations is transformed into the form of nonlinear partial differential equations (PDEs) by applying appropriate similarity variables. A convergent series solution to the developed nonlinear equations is accomplished with the help of an analytical approach, i.e., the homotopy analysis method (HAM). The consequences of diverse parameters, including the dimensionless EyringPowell liquid parameter, the radius of curvature, the Schmidt/Prandtl numbers, the ratio of the oscillatory frequency of the sheet to its stretchable rate constant, the mass and thermal relaxation variables involved in the flow, and the heat and mass properties, are displayed through graphs and tables. It is noted from this study that the amplitude of the pressure distribution rises for the high parametric values of the Eyring-Powell parameter.

Cite this article

M. IMRAN, Z. ABBAS, M. NAVEED . Flow of Eyring-Powell liquid due to oscillatory stretchable curved sheet with modified Fourier and Fick's model[J]. Applied Mathematics and Mechanics, 2021 , 42(10) : 1461 -1478 . DOI: 10.1007/s10483-021-2779-9

References

[1] CRANE, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 21(4), 645-647(1970)
[2] ALHARBI, S. M., BAZID, M. A., and EL GENDY, M. S. Heat and mass transfer in MHD viscoelastic fluid flow through a porous medium over a stretching sheet with chemical reaction. Applied Mathematics, 1(6), 446-455(2010)
[3] HAYAT, T., QASIM, M., and ABBAS, Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet. Zeitschrift für Naturforschung A, 65(3), 231-239(2010)
[4] HAYAT, T., SAIF, R. S., ELLAHI, R., MUHAMMAD, T., and AHMAD, B. Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions. Results in Physics, 7, 2601-2606(2017)
[5] YASMIN, A., ALI, K., and ASHRAF, M. Study of heat and mass transfer in MHD flow of micropolar fluid over a curved stretching sheet. Scientific Reports, 10, 4581(2020)
[6] WÖHLISCH, E. Adolf fick und die heutige physiologie. Naturwissenschaften, 26(36), 585-591(1938)
[7] FOURIER, J. B. J. Théorie Analytique de la Chaleur, Didot, Paris (1822)
[8] CATTANEO, C. Sulla conduzione del calore. Atti Semin. Mat. Fis. della Universit di Modena, 3, 83-101(1948)
[9] CHRISTOV, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communications, 36(4), 481-486(2009)
[10] HAYAT, T., FAROOQ, M., ALSAEDI, A., and AL-SOLAMY, F. Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness. AIP Advances, 5(8), 087159(2015)
[11] KHAN, A. A., BATOOL, R., and KOUSAR, N. Examining the behavior of MHD micropolar fluid over curved stretching surface based on the modified Fourier law. Scientia Iranica, 28, 223-230(2021)
[12] SUI, J., ZHENG, L., and ZHANG, X. Boundary layer heat and mass transfer with CattaneoChristov double-diffusion in upper-convected Maxwell nanofluid past a stretching sheet with slip velocity. International Journal of Thermal Sciences, 104, 461-468(2016)
[13] MALIK, R., KHAN, M., SHAFIQ, A., MUSHTAQ, M., and HUSSAIN, M. An analysis of Cattaneo-Christov double-diffusion model for Sisko fluid flow with velocity slip. Results in Physics, 7, 1232-1237(2017)
[14] HAYAT, T., QAYYUM, S., SHEHZAD, S. A., and ALSAEDI, A. Cattaneo-Christov doublediffusion theory for three-dimensional flow of viscoelastic nanofluid with the effect of heat generation/absorption. Results in Physics, 8, 489-495(2018)
[15] SRINIVAS REDDY, C. and ALI, F. Cattaneo-Christov double diffusion theory for MHD cross nanofluid flow towards a vertical stretching sheet with activation energy. International Journal of Ambient Energy (2020) https://doi.org/10.1080/01430750.2020.1852113
[16] MUHAMMAD, T., RAFIQUE, K., ASMA, M., and ALGHAMDI, M. Darcy-Forchheimer flow over an exponentially stretching curved surface with Cattaneo-Christov double diffusion. Physica A:Statistical Mechanics and Its Applications, 556, 123968(2020)
[17] WANG, C. Y. Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid. Acta Mechanica, 72(3), 261-268(1988)
[18] SIDDAPPA, B., ABEL, S., and HONGUNTI, V. Oscillatory motion of a viscoelastic fluid past a stretching sheet. Il Nuovo Cimento D, 17, 53-60(1995)
[19] ALI, N., KHAN, S. U., and ABBAS, Z. Hydromagnetic flow and heat transfer of a Jeffrey fluid over an oscillatory stretching surface. Zeitschrift für Naturforschung A, 70(7), 567-576(2015)
[20] KHAN, S. U. and SHEHZAD, S. A. Brownian movement and thermophoretic aspects in thirdgrade nanofluid over oscillatory moving sheet. Physica Scripta, 94(9), 095202(2019)
[21] ABBAS, Z., IMRAN, M., and NAVEED, M. Time-dependent flow of thermally developed viscous fluid over an oscillatory stretchable curved surface. Alexandria Engineering Journal, 59(6), 4377-4390(2020)
[22] IMRAN, M., ABBAS, Z., NAVEED, M., and SALAMAT, N. Impact of Joule heating and melting on time-dependent flow of nanoparticles due to an oscillatory stretchable curved wall. Alexandria Engineering Journal, 60(4), 4097-4113(2021)
[23] NAVEED, M., IMRAN, M., and ABBAS, Z. Curvilinear flow of micropolar fluid with CattaneoChristov heat flux model due to oscillation of curved stretchable sheet. Zeitschrift für Naturforschung A (2021) https://doi.org/10.1515/zna-2021-0006
[24] POWELL, R. E. and EYRING, H. Mechanisms for the relaxation theory of viscosity. nature, 154(3909), 427-428(1944)
[25] DAWAR, A., SHAH, Z., IDREES, M., KHAN, W., ISLAM, S., and GUL, T. Impact of thermal radiation and heat source/sink on Eyring-Powell fluid flow over an unsteady oscillatory porous stretching surface. Mathematical and Computational Applications, 23(2), 20(2018)
[26] ABBAS, Z., RAFIQ, M., and NAVEED, M. Analysis of Eyring-Powell liquid flow in curved channel with Cattaneo-Christov heat flux model. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 390(2018)
[27] ALHARBI, S. O., DAWAR, A., SHAH, Z., KHAN, W., IDREES, M., ISLAM, S., and KHAN, I. Entropy generation in MHD Eyring-Powell fluid flow over an unsteady oscillatory porous stretching surface under the impact of thermal radiation and heat source/sink. Applied Sciences, 8(12), 2588(2018)
[28] KHAN, S. U., VAIDYA, H., CHAMMAM, W., MUSMAR, S. E. A., PRASAD, K. V., and TLILI, I. Triple diffusive unsteady flow of Eyring-Powell nanofluid over a periodically accelerated surface with variable thermal features. Frontiers in Physics, 8, 246(2020)
[29] KHAN, S. U., SHEHZAD, S. A., RAUF, A., and ALI, N. Mixed convection flow of couple stress nanofluid over oscillatory stretching sheet with heat absorption/generation effects. Results in Physics, 8, 1223-1231(2018)
[30] NARLA, V. K., BISWAS, C., and RAO, G. A. Entropy analysis of MHD fluid flow over a curved stretching sheet. AIP Conference Proceedings, 2246, 020099(2020)
[31] MEGAHED, A. M., GHONEIM, N. I., REDDY, M. G., and EL-KHATIB, M. Magnetohydrodynamic fluid flow due to an unsteady stretching sheet with thermal radiation, porous medium, and variable heat flux. Advances in Astronomy, 2021, 6686883(2021)
[32] SHAFIQ, A., HAMMOUCH, Z., and SINDHU, T. N. Bioconvective MHD flow of tangent hyperbolic nanofluid with Newtonian heating. International Journal of Mechanical Sciences, 133, 759-766(2017)
[33] SHAFIQ, A. and SINDHU, T. N. Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface. Results in Physics, 7, 3059-3067(2017)
[34] SHAFIQ, A., SINDHU, T. N., and HAMMOUCH, Z. Characteristics of homogeneous heterogeneous reaction on flow of Walters' B liquid under the statistical paradigm. Applied Analysis and Computation, Springer, Singapore, 295-311(2018)
[35] SHAFIQ, A., HAMMOUCH, Z., and OZTOP, H. F. Radiative MHD flow of third-grade fluid towards a stretched cylinder. International Conference on Computational Mathematics and Engineering Sciences, Springer, Cham, 166-185(2019)
[36] RASOOL, G., ZHANG, T., CHAMKHA, A. J., SHAFIQ, A., TLILI, I., and SHAHZADI, G. Entropy generation and consequences of binary chemical reaction on MHD Darcy-Forchheimer Williamson nanofluid flow over non-linearly stretching surface. Entropy, 22, 18(2020)
[37] SHAFIQ, A., HAMMOUCH, Z., SINDHU, T. N., and BALEANU, D. Statistical approach of mixed convective flow of third-grade fluid towards an exponentially stretching surface with convective boundary condition. Special Functions and Analysis of Differential Equations, Chapman and Hall/CRC, Boca Raton, 307-319(2020)
[38] SHAFIQ, A., SINDHU, T. N., and AL-MDALLAL, Q. M. A sensitivity study on carbon nanotubes significance in Darcy-Forchheimer flow towards a rotating disk by response surface methodology. Scientific Reports, 11, 8812(2021)
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