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Modified Homogeneous and Heterogeneous Chemical Reaction and Flow Performance of Maxwell Nanofluid with Cattaneo–Christov Heat Flux Law

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Journal of Engineering Thermophysics Aims and scope

Abstract

An MHD boundary layer flow of upper-convected Maxwell (UCM) nanofluid over an extending surface has been studied in the current literature. The most recent double diffusive heat flux model proposed by Cattaneo and modified by Christov has been incorporated into the energy equation instead of the conventional Fourier model in the governing equation of the flow. Homogeneous and heterogeneous chemical reaction is incorporated in the fluid system with heat generation due to the homogeneous chemical reaction and chemical reaction dependent thermal intake capacity of nanoparticles. After an arduous numerical calculation, the impact of numerous germane factors on the heat and mass relocation characteristics of flow has been illustrated through charts and graphs, and the consequences have been explained with proper reasoning. In every graph and table, we compare the outcomes for the conventional Fourier law and the Cattaneo–Christov law. To measure the relation of the flow regulator factor with the flow performance, we introduce correlation coefficients and coefficients of determination and present them with proper charts. It is observed that the correlation is high.

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REFERENCES

  1. Sadeghy, K., Najafi, A.H., and Saffaripour, M., Sakiadis Flow of an Upper-Convected Maxwell Fluid, Int. J. Non-Lin. Mech., 2005, vol. 40, no. 9, pp. 1220–1228.

    Article  Google Scholar 

  2. Hayat, T., Abbas, Z., and Ali, N., MHD Flow and Mass Transfer of a Upper-Convected Maxwell Fluid past a Porous Shrinking Sheet with Chemical Reaction Species, Phys. Lett. A, 2008, vol. 372, no. 26, pp. 4698–4704.

    Article  ADS  Google Scholar 

  3. Abel, M.S., Tawade, J.V., and Nandeppanavar, M.M., MHD Flow and Heat Transfer for the Upper-Convected Maxwell Fluid over a Stretching Sheet, Meccanica, 2012, vol. 47, no. 2, pp. 385–393.

    Article  MathSciNet  Google Scholar 

  4. Hayat, T., Mustafa, M., Shehzad, S.A., and Obaidat, S., Melting Heat Transfer in the Stagnation-Point Flow of an Upper-Convected Maxwell (UCM) Fluid past a Stretching Sheet, Int. J. Numer. Meth. Fluids, 2012, vol. 68, no. 2, pp. 233–243.

    Article  MathSciNet  Google Scholar 

  5. Hayat, T., Shehzad, S.A., and Alsaedi, A., MHD Three-Dimensional Flow of Maxwell Fluid with Variable Thermal Conductivity and Heat Source/Sink, Int. J. Numer. Meth. Heat Fluid Flow, 2014, vol. 24, no. 5, pp. 1073–1085.

    Article  MathSciNet  Google Scholar 

  6. Mushtaq, A., Mustafa, M., Hayat, T., and Alsaedi, A., A Numerical Study for Three-Dimensional Viscoelastic Flow Inspired by Non-Linear Radiative Heat Flux, Int. J. Non-Lin. Mech., 2016, vol. 79, pp. 83–87.

    Article  Google Scholar 

  7. Hayat, T., Muhammad, T., Shehzad, S.A., Chen, G.Q., and Abbas, I.A., Interaction of Magnetic Field in Flow of Maxwell Nanofluid with Convective Effect, J. Magnetism Magn. Mat., 2015, vol. 389, pp. 48–55.

    Article  ADS  Google Scholar 

  8. Hussain, T., Hussain, S., and Hayat, T., Impact of Double Stratification and Magnetic Field in Mixed Convective Radiative Flow of Maxwell Nanofluid, J. Molec. Liquids, 2016, vol. 220, pp. 870–878.

    Article  Google Scholar 

  9. Kumar, S.G., Varma, S., Prasad, P.D., Raju, C.S., Makinde, O.D., and Sharma, R., MHD Reacting and Radiating 3-D Flow of Maxwell Fluid past a Stretching Sheet with Heat Source/Sink and Soret Effects in a Porous Medium, Defect Diffusion Forum, 2018, vol. 387, pp. 145–156.

    Article  Google Scholar 

  10. Ahmed, J., Khan, M. and Ahmad, L., Stagnation Point Flow of Maxwell Nanofluid over a Permeable Rotating Disk with Heat Source/Sink, J. Molec. Liquids, 2019, vol. 287, article 110853.

    Article  Google Scholar 

  11. Khan, M., Salahuddin, T., Tanveer, A., Malik, M.Y., and Hussain, A., Change in Internal Energy of Thermal Diffusion Stagnation Point Maxwell Nanofluid Flow along with Solar Radiation and Thermal Conductivity, Chinese J. Chem. Engin., 2019, vol. 27, no. 10, pp. 2352–2358.

    Article  Google Scholar 

  12. Fourier, J.B.J., Théorie analytique de la chaleur, Paris: Didot, 1822.

    MATH  Google Scholar 

  13. Christov, C.I., On Frame Indifferent Formulation of the Maxwell–Cattaneo Model of Finite-Speed Heat Conduction, Mech. Res. Commun., 2009, vol. 36, no. 4, pp. 481–486.

    Article  MathSciNet  Google Scholar 

  14. Straughan, B., Thermal Convection with the Cattaneo–Christov Model, Int. J. Heat Mass Transfer, 2010, vol. 53, nos. 1–3, pp. 95–98.

    Article  Google Scholar 

  15. Tibullo, V. and Zampoli, V., A Uniqueness Result for the Cattaneo–Christov Heat Conduction Model Applied to Incompressible Fluids, Mech. Res. Commun., 2011, vol. 38, no. 1, pp. 77–79.

    Article  Google Scholar 

  16. Hayat, T., Khan, M.I., Farooq, M., Alsaedi, A., Waqas, M., and Yasmeen, T., Impact of Cattaneo–Christov Heat Flux Model in Flow of Variable Thermal Conductivity Fluid over a Variable Thicked Surface, Int. J. Heat Mass Transfer, 2016, vol. 99, pp. 702–710.

    Article  Google Scholar 

  17. Mushtaq, A., Abbasbandy, S., Mustafa, M., Hayat, T., and Alsaedi, A., Numerical Solution for Sakiadis Flow of Upper-Convected Maxwell Fluid Using Cattaneo–Christov Heat Flux Model, AIP Advances, 2016, vol. 6, no. 1, article 015208.

    Article  ADS  Google Scholar 

  18. 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, Int. J. Thermal Sci., 2016, vol. 104, pp. 461–468.

    Article  Google Scholar 

  19. Makinde, O.D., Sandeep, N., Animasaun, I.L., and Tshehla, M.S., Numerical Exploration of Cattaneo–Christov Heat Flux and Mass Transfer in Magnetohydrodynamic Flow over Various Geometries, Defect Diffusion Forum, 2017, vol. 374, pp. 67–82.

  20. Gangadhar, K., Ramana, K.V., Makinde, O.D., and Kumar, B.R., MHD Flow of a Carreau Fluid past a Stretching Cylinder with Cattaneo–Christov Heat Flux Using Spectral Relaxation Method, Defect Diffusion Forum, 2018, vol. 387, pp. 91–105.

  21. Scott, S.K., Isolas, Mushrooms and Oscillations in Isothermal, Autocatalytic Reaction-Diffusion Equations, Chem. Engin. Sci., 1987, vol. 42, no. 2, pp. 307–315.

    Article  Google Scholar 

  22. Merkin, J.H., A Model for Isothermal Homogeneous-Heterogeneous Reactions in Boundary-Layer Flow, Math. Computer Model., 996, vol. 24, no. 8, pp. 125–136.

    Article  MathSciNet  Google Scholar 

  23. Bachok, N., Ishak, A., and Pop, I., On the Stagnation-Point Flow towards a Stretching Sheet with Homogeneous-Heterogeneous Reactions Effects, Comm. Nonlin. Sci. Numer. Simul., 2011, vol. 16, no. 11, pp. 4296–4302.

    Article  ADS  Google Scholar 

  24. Khan, W.A. and Pop, I.M., Effects of Homogeneous-Heterogeneous Reactions on the Viscoelastic Fluid toward a Stretching Sheet, J. Heat Transfer, 2012, vol. 134, no. 6, p. 064506.

    Article  Google Scholar 

  25. Kameswaran, P.K., Shaw, S., Sibanda, P.V.S.N., and Murthy, P.V.S.N., Homogeneous-Heterogeneous Reactions in a Nanofluid Flow due to a Porous Stretching Sheet, Int. J. Heat Mass Transfer, 2013, vol. 57, no. 2, pp. 465–472.

    Article  Google Scholar 

  26. Hayat, T., Farooq, M., and Alsaedi, A., Homogeneous-Heterogeneous Reactions in the Stagnation Point Flow of Carbon Nanotubes with Newtonian Heating, AIP Advances, 2015, vol. 5, no. 2, article 027130.

    Article  ADS  Google Scholar 

  27. Hayat, T., Imtiaz, M., and Alsaedi, A., Effects of Homogeneous-Heterogeneous Reactions in Flow of Powell-Eyring Fluid, J. Central South Univ., 2015, vol. 22, no. 8, pp. 3211–3216.

    Article  Google Scholar 

  28. Makinde, O.D. and Animasaun, I.L., Thermophoresis and Brownian Motion Effects on MHD Bioconvection of Nanofluid with Nonlinear Thermal Radiation and Quartic Chemical Reaction past an Upper Horizontal Surface of a Paraboloid of Revolution, J. Molec. Liquids, 2016, vol. 221, pp. 733–743.

    Article  Google Scholar 

  29. Hayat, T., Imtiaz, M., Alsaedi, A., and Almezal, S., On Cattaneo–Christov Heat Flux in MHD Flow of Oldroyd-B Fluid with Homogeneous-Heterogeneous Reactions, J. Magnetism Magn. Mat., 2016, vol. 401, pp. 296–303.

    Article  ADS  Google Scholar 

  30. Salahuddin, T., Malik, M.Y., Hussain, A., Bilal, S., and Awais, M., MHD Flow of Cattanneo–Christov Heat Flux Model for Williamson Fluid over a Stretching Sheet with Variable Thickness: Using Numerical Approach, J. Magnetism Magn. Mat., 2016, vol. 401, pp. 991–997.

    Article  ADS  Google Scholar 

  31. Malik, M.Y., Khan, M., Salahuddin, T., and Khan, I., Variable Viscosity and MHD Flow in Casson Fluid with Cattaneo–Christov Heat Flux Model: Using Keller Box Method, Engin. Sci. Technol., Int. J., 2016, vol. 19, no. 4, pp. 1985–1992.

    Article  Google Scholar 

  32. Xu, N. and Xu, H., A Modified Model for Isothermal Homogeneous and Heterogeneous Reactions in the Boundary-Layer Flow of a Nanofluid, Appl. Math. Mech., 2020, vol. 41, no. 3, pp. 479–490.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, A.B.N. Seal College, Cooch Behar, West Bengal, India

    Sk Md Tausif

  2. Department of Mathematics, Krishnagar Government College, Nadia, West Bengal, India

    K. Das

  3. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India

    P. K. Kundu

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  1. Sk Md Tausif
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  2. K. Das
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Correspondence to Sk Md Tausif, K. Das or P. K. Kundu.

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Tausif, S.M., Das, K. & Kundu, P.K. Modified Homogeneous and Heterogeneous Chemical Reaction and Flow Performance of Maxwell Nanofluid with Cattaneo–Christov Heat Flux Law. J. Engin. Thermophys. 31, 64–77 (2022). https://doi.org/10.1134/S1810232822010064

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  • DOI: https://doi.org/10.1134/S1810232822010064

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