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

Document Type : Research Note


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


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.


[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 indifferent formulation of the Maxwell-Cattaneo model of finite-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 fluid utilizing Cattaneo-Christov double-diffusion: Applications of non-Fourier’s heat and non-Fick’s mass flux 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 flux”, 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 nanofluid over sheet with heat and mass flux 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 fluxes in the squeezed flow embedded in porous medium with variable mass diffusivity”, Results Phys., 7, pp. 3788-3796 (2017).
[7] Shehzad, S.A., Hayat, T., Alsaedi, A. and Meraj, M.A. “Cattaneo-Christov heat and mass flux model for 3D hydromagnetic flow 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 flow with double diffusive Cattaneo-Christov heat and mass flux 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 flux in the presence of heat source/sink and magnetic field”, Sci. Iran., 26, pp. 323-330 (2019). 
[10] Khan, S.U., Shehzad, S.A., Ali, N. and Bashir, M.N. “Analysis of second-grade fluid flow in porous channel with Cattaneo-Christov and generalized Fick’s theories”, Sci. Iran., Articles in Press (2019).
[11] S. S. Chawla, P. K. Srivastava, A. S. Gupta, Rotationally symmetric flow over a rotating disk, International Journal of Non-Linear Mechanics, 44, (2009) pp. 717-726
[12] Mahmood, K., Sajid, M., Ali, N. and Javed, T. “Heat transfer analysis in the time-dependent slip flow 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 nanofluids over a rotating disk with uniform stretching rate in the radial direction”, Prop. Power Research, 6, pp.  25-30 (2017). 
[14] Mustafa, M. “MHD nanofluid flow over a rotating disk with partial slip effects: Buongiorno model”, Int. J. Heat Mass Transf., 108, pp. 1910-1916 (2017). 
[15] Turkyilmazoglu, M. “Fluid flow and heat transfer over a rotating and vertically moving disk”, Phys. Fluids, 30, pp. 063605 (2018).
[16] Lok, Y.Y., Merkin, J.H. and Pop, I. “Axisymmetric rotational stagnation-point flow 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 flow of Sisko fluid 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 fluid flow over a rotating disk under effect of homogeneous-heterogeneous reactions”, Case Stud. Therm. Eng., 13, pp. 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 fluid 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 flow in porous media using the ensemble Kalman filter”, Sci. Iran., 24, pp. 1281-1301 (2017). 
[23] Ghaffarpasand, O. and Fazeli, D. “Numerical Analysis of MHD mixed convection flow in a parallelogramic porous enclosure filled with nano fluid and in presence of magnetic field 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 effects on Fe3O4-Ethylene glycol nanofluid EHD flow in a porous enclosure, Sci. Iran., (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 flow in porous medium”, Mech. Mech. Eng., 14, pp. 119-136 (2010). 
[28] Khan, S.U., Ali, N. and Abbas, Z. “Hydromagnetic flow and heat transfer over a porous oscillating stretching surface in a viscoelastic fluid with porous medium”, Plos One, 10, pp. 0144299 (2015). 
[29] Ali, N., Khan, S.U., Sajid, M. and Abbas, Z. “MHD flow and heat transfer of couple stress fluid over an oscillatory stretching sheet with heat source/sink in porous medium”, Alex. Eng. J., 55, 915-924 (2016). 
[30] Ali, N., Khan, S.U., Sajid, M. and Abbas, Z. “Slip effects in the hydromagnetic flow of a viscoelastic fluid 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 flow in two immiscible fluids 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 nanofluid 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. “Effect of thermal diffusion and heat-generation on MHD nanofluid flow 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 flow 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 flow over an oscillatory stretchable disk”, J. Mech., 30, pp. 339-347 (2014).
[36] Rauf, A., Abbas, Z. and Shehzad, S.A. “Chemically hydromagnetic flow over a stretchable oscillatory rotating disk with thermal radiation and heat source/sink: A numerical study”, Heat Transf. Research, 50, 1495-1512 (2019).
[37] Rauf, A., Abbas, Z. and Shehzad, S.A. “Interactions of active and passive control of nanoparticles on radiative magnetohydrodynamics flow of nanofluid over oscillatory rotating disk in porous medium”, J. Nanofluids, 8, pp. 1385-1396 (2019).
[38] W. E. Milne, Numerical solutions of differential 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).