Cattaneo-Christov heat and mass flux models on time-dependent swirling flow through oscillatory rotating disk

Document Type : Research Note

Authors

1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

2 - Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan. - Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, 57000, Pakistan.

3 Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, 57000, Pakistan

4 Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia

10.24200/sci.2020.53248.3139

Abstract

This analysis emphasis on the time invariant impressions of Cattaneo-Christov heat and mass flux theories are implemented to overcome the initial instant disturbances throughout whole medium. The motion of three-dimensional, incompressible, magnetized viscous fluid flow induced by the oscillatory disk. Porous media is used to saturate the rotating disk. Similarity transformations are accomplished to normalize the flow problem. Successive over Relaxation (SOR) technique is implemented to discuss the new findings of normalized non-linear resulting system. It is perceived that increase in porosity parameter results in decrease of oscillatory velocity profiles. The characterization of porous media is useful in geothermal and petroleum reservoirs. Time varying oscillatory curves for concentration and temperature decay for varying concentration and thermal relaxation times parameters, respectively. Moreover, an interesting nature of phase-log shift is also observed in temperature and concentration profiles. Three-dimensional flow features are also labeled for velocity, temperature and concentration fields.

Keywords


References: 
1. Bargmann, S. and Steinmann, P. On the propagation  of second sound in linear and non-linear media, results  from Green-Naghdi theory", Phys. Lett. A, 372, pp.  4418{4424 (2008).  2. Christov, C.I. On frame indi_erent formulation of  the Maxwell-Cattaneo model of _nite-speed heat conduction",  Mech. Research Commun., 36, pp. 481{486  (2009).  3. Khan, W.A., Khan, M., and Alshomrani, A.S. Impact  of chemical processes on 3D Burgers uid utilizing  Cattaneo-Christov double-di_usion: Applications of  non-Fourier's heat and non-Fick's mass ux models",  J. Mol. Liq., 223, pp. 1039{1047 (2016).  4. Liu, L., Zheng, L., Liu, F., and Zhang, X. An  improved heat conduction model with Riesz fractional  Cattaneo-Christov ux", Int. J. Heat Mass Transf.,  103, pp. 1191{1197 (2016).  5. Upadhay, M.S., Mahesha, and Raju, C.S.K.  Cattaneo-Christov on heat and mass transfer of  unsteady Eyring Powell dusty nanouid over sheet  with heat and mass ux conditions", Inform. Med.  Unlock., 9, pp. 76{85 (2017).  6. Farooq, M., Ahmad, S., Javed, M., and Anjum, A.  Analysis of Cattaneo-Christov heat and mass uxes  in the squeezed ow embedded in porous medium with  variable mass di_usivity", Results Phys., 7, pp. 3788{  3796 (2017).  7. Shehzad, S.A., Hayat, T., Alsaedi, A., and Meraj,  M.A. Cattaneo-Christov heat and mass ux model for  3D hydromagnetic ow of chemically reactive Maxwell  liquid", Appl. Math. Mech., 38, pp. 1347{1356 (2018).  8. Rauf, A., Abbas, Z., Shehzad, S.A., Alsaedi, A.,  and Hayat, T. Numerical simulation of chemically  reactive Powell-Eyring liquid ow with double di_usive  Cattaneo-Christov heat and mass ux theories", Appl.  Math. Mech., 39, pp. 467{476 (2018).  9. Aqsa, Malik, M.Y., Imtiaz, A., and Awais, M. Rheology  of Burgers' model with Cattaneo-Christov heat  ux in the presence of heat source/sink and magnetic  _eld", Sci. Iran., 26, pp. 323{330 (2019).  10. Khan, S.U., Shehzad, S.A., Ali, N., and Bashir,  M.N. Analysis of second-grade uid ow in porous  channel with Cattaneo-Christov and generalized Fick's  theories", Sci. Iran., 27, pp. 1945{1954 (2020).  11. Chawla, S.S., Srivastava, P.K., and Gupta, A.S.  Rotationally symmetric ow over a rotating disk",  International Journal of Non-Linear Mechanics, 44,  pp. 717{726 (2009).  12. Mahmood, K., Sajid, M., Ali, N., and Javed, T. Heat  transfer analysis in the time-dependent slip ow over  a lubricated rotating disc", Eng. Sci. Tech., an Int. J.,  19, pp. 1949{1957 (2016).  13. Yin, C., Zheng, L., Zhang, C., and Zhang, X. Flow  and heat transfer of nanouids over a rotating disk  with uniform stretching rate in the radial direction",  Prop. Power Research, 6, pp. 25{30 (2017).  14. Mustafa, M. MHD nanouid ow over a rotating disk  with partial slip e_ects: Buongiorno model", Int. J.  Heat Mass Transf., 108, pp. 1910{1916 (2017).  15. Turkyilmazoglu, M. Fluid ow and heat transfer over  a rotating and vertically moving disk", Phys. Fluids,  30, p. 063605 (2018).  1340 Z. Abbas et al./Scientia Iranica, Transactions B: Mechanical Engineering 28 (2021) 1329{1341  16. Lok, Y.Y., Merkin, J.H., and Pop, I. Axisymmetric  rotational stagnation-point ow impinging on a permeable  stretching/shrinking rotating disk", Euro. J.  Mech.-B/Fluids, 72, pp. 275{292 (2018).  17. Hayat, T., Khan, M.I., Qayyum, S., Khan, M.I., and  Alsaedi, A. Entropy generation for ow of Sisko uid  due to rotating disk", J. Mol. Liq., 264, pp. 375{385  (2018).  18. Gholinia, M., Hosseinzadeh, K., Mehrzadi, H., Ganji,  D.D., and Ranjbar, A.A. Investigation of MHD  Eyring-Powell uid ow over a rotating disk under  e_ect of homogeneous-heterogeneous reactions", Case  Stud. Therm. Eng., 13, p. 100356 (2018).  19. Liu, Q. and He, Y. Lattice Boltzmann simulations of  convection heat transfer in porous media", Phys. A:  Stat. Mech. Appl., 465, pp. 742{753 (2017).  20. Jourabian, M., Darzi, A.A.R., Toghraie, D., and  Akbari, O.A. Melting process in porous media around  two hot cylinders: Numerical study using the lattice  Boltzmann method", Phys. A: Stat. Mech. Appl., 509,  pp. 316{335 (2018).  21. Kefayati, G.H.R. Lattice Boltzmann method for natural  convection of a Bingham uid in a porous cavity",  Phys. A: Stat. Mech. Appl., 521, pp. 146{172 (2019).  22. Jahanbakshi, S., Pishvaie, M.R., and Boozarjomehry,  R.B. Characterization of three-phase ow in porous  media using the ensemble Kalman _lter", Sci. Iran.,  24, pp. 1281{1301 (2017).  23. Gha_arpasand, O. and Fazeli, D. Numerical analysis  of MHD mixed convection ow in a parallelogramic  porous enclosure _lled with nano uid and in presence  of magnetic _eld induction", Sci. Iran., 25, pp. 1789{  1807 (2018).  24. Nuori-Borujerdi, A. A new approach to thermo-Fluid  behavior through porous layer of heat pipes", Sci.  Iran., 25, pp. 1236{1242 (2018).  25. Sheikholeslami, M., Ganji, D.D., Li, Z., and Hosseinnejad,  R. Numerical simulation of thermal  radiative heat transfer e_ects on Fe3O4-Ethylene  glycol nanouid EHD ow in a porous enclosure",  Sci. Iran., 26(3), pp. 1405{1414 (2018).  doi:10.24200/SCI.2018.5567.1348.  26. Darcy, H.R.P.G., Les Fontaines Publiques de la Volle  de Dijon, Vector Dalmont. Paris (1856).  27. Attia, H.A. Asymptotic solution for rotating disk ow  in porous medium", Mech. Mech. Eng., 14, pp. 119{  136 (2010).  28. Khan, S.U., Ali, N., and Abbas, Z. Hydromagnetic  ow and heat transfer over a porous oscillating stretching  surface in a viscoelastic uid with porous medium",  Plos One, 10, p. 0144299 (2015).  29. Ali, N., Khan, S.U., Sajid, M., and Abbas, Z. MHD  ow and heat transfer of couple stress uid over an  oscillatory stretching sheet with heat source/sink in  porous medium", Alex. Eng. J., 55, pp. 915{924  (2016).  30. Ali, N., Khan, S.U., Sajid, M., and Abbas, Z. Slip  e_ects in the hydromagnetic ow of a viscoelastic  uid through porous medium over a porous oscillatory  stretching sheet", J. Porous Med., 20, pp. 249{262  (2017).  31. Hasnain, J. and Abbas, Z. Hydromagnetic convection  ow in two immiscible uids through a porous medium  in an inclined annulus", J. Porous Med., 20, pp. 977{  987 (2017).  32. Sheikholeslami, M. and Shehzad, S.A. CVFEM simulation  for nanouid migration in a porous medium  using Darcy model", Int. J. Heat Mass Transf., 122,  pp. 1264{1271 (2018).  33. Sheikholeslami, M., Kataria, H.R., and Mittal, A.S.  E_ect of thermal di_usion and heat-generation on  MHD nanouid ow past an oscillating vertical plate  through porous medium", J. Mol. Liq., 257, pp. 12{25  (2018).  34. Rauf, A., Abbas, Z., and Shehzad, S.A. Utilization of  Maxwell-Cattaneo law for MHD swirling ow through  oscillatory disk subject to porous medium", Appl.  Math. Mech., 40, pp. 837{850 (2019).  35. Munawar, S., Ali, A., Saleem, N., and Naqeeb, A.  Swirling ow over an oscillatory stretchable disk", J.  Mech., 30, pp. 339{347 (2014).  36. Rauf, A., Abbas, Z., and Shehzad, S.A. Chemically  hydromagnetic ow over a stretchable oscillatory rotating  disk with thermal radiation and heat source/sink:  A numerical study", Heat Transf. Research, 50, pp.  1495{1512 (2019).  37. Rauf, A., Abbas, Z., and Shehzad, S.A. Interactions  of active and passive control of nanoparticles  on radiative magnetohydrodynamics ow of nanouid  over oscillatory rotating disk in porous medium", J.  Nanouids, 8, pp. 1385{1396 (2019).  38. Milne, W.E., Numerical Solutions of Di_erential Equations,  John Willey and Sons Inc., New York (1953).  39. Hachbusch, W., Iterative Solution of Large Sparse Systems  of Equations, Springer International Publishing,  Switzerland (2016).