Rheology of Burgers' model with Cattaneo-Christov heat flux in the presence of heat source/sink and magnetic field

Document Type : Article


1 Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

2 Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan


This investigation presents the characteristics of Cattaneo-Christov heat flux model for the boundary layer flow of Burgers’ fluid model. Instead of simple Fourier’s law of heat conduction, we presented the Cattaneo-Christov model to analyze the thermal relaxation properties when the heat source/sink is present in the system. Mathematical modeling the laws of momentum and energy are presented under the order analysis approach. It is revealed that the term “” is for the hydro-magnetic rheology of the Newtonian model whereas the generalized magnetic field term (as mentioned in Eq. 2) is for the Burgers’ model which is incorporated in the current analysis. Suitable transformations are utilized for the conversion of partial differential system into coupled nonlinear set of ordinary differential equations which are tackled analytically through homotopy analysis technique. The plots of various physical quantities are presented showing the dynamics of the considered analysis. Streamlines for Burgers’ and Newtonian model are presented which show a difference of rheology. Numerical values for skin friction and surface heat transfer rate are presented in the form of tables.


Main Subjects

1. Cattaneo, C. "Sulla Conduzione del calore", Atti Semin. Mat. Fis. Univ. Modea Reggio Emilia, 3, pp. 83-101 (1948).
2. Christov, C.I. "On frame indifferent formulation of Maxwell Cattaneo model of finite speed heat conduction", Mech. Res. Comm., 36(4), pp. 481-486 (2009).
3. Tibullo, V. and Zampoli, V. "A uniquemess result for the Cattaneo-Christov heat conduction model applied to incompressible  fluids", Mech. Res. Comm., 38(1), pp. 77-79 (2011).
4. Haddad, S.A.M. "Thermal instability in Brinkman porous media with Cattaneo-Christov heat  flux", Int. J. Heat Mass Trans., 68, pp. 659-668 (2014).
5. Han, S., Zheng, L., Li, C., and Zhang, X. "Coupled flow and heat transfer in viscoelastic fluids with Cattaneo-Christov heat flux model", Appl. Math. Lett., 38, pp. 87-93 (2014).
6. 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. Mag. Mag. Mat., 401, pp. 296-303(2016).
7. Ali, M.E. and Sandeep, N. "Cattaneo-Christov model for radiative heat transfer of magnetohydrodynamic Casson-ferro fluid: A numerical study", Results Physics, 7, pp. 21-30 (2017).
8. Kumar, K.A., Reddy, J.V.R., Sugunamma, V., and Sandeep, N. "Magnetohydrodynamic Cattaneo- Christov  flow past a cone and a wedge with variable heat source/sink", Alex. Engng. J., 57, pp. 435-443 (2018).
9. Babu, M.J., Sandeep, N., and Saleem, S. "Free convective MHD Cattaneo-Christov  flow over three different geometries with thermophoresis and Brownian motion", Alex. Engng. J., 56, pp. 659-669 (2017).
10. Reddy, J.V.R., Sugunamma, V., and Sandeep, N. "Cross diffusion effects on MHD  flow over three different geometries with Cattaneo-Christov heat flux", J. Mol. Liq., 223, pp. 1234-1241 (2016).
11. Zhao, J., Zheng, L., Chen, X., and Zhang, X. "Unsteady Marangoni convection heat transfer of fractional Maxwell fluid with Cattaneo heat  flux", Appl. Math. Mod., 44, pp. 497-507 (2017).
12. Sui, J., Zheng, L., and Zhang, X. "Boundary layer heat and mass transfer with Cattaneo-Christov doubledi ffusion in upper-convected Maxwell nano fluid past a stretching sheet with slip velocity", Int. J. Therm. Sci., 104, pp. 461-468 (2016).
13. Li, J., Zheng, L., and Liu, L. "MHD viscoelastic  flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects", J. Mol. Liquids, 221, pp. 19-25 (2016).
14. Liao, S.J. "Notes on the homotopy analysis method: Some definitions and theorems", Commun. Nonlinear. Sci. Numer. Simulat., 14, pp. 983-997 (2009).
15. Rashidi, M.M., Pour, S.A.M., Hayat, T., and Obaidat, S. "Analytic approximate solutions for steady  flow over a rotating disk in porous medium with heat transfer by homotopy analysis method", Comp. Fluids, 54, pp. 1-9 (2012).
16. Rashidi, M.M., Feridoonimehr, N., Hosseini, A., Beg, O.A., and Hung, T.K. "Homotpy simulations of nano fluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration", Meccanica, 49, pp. 469-482 (2014).
17. Hayat, T., Hussain, Z., Farooq, M., and Alsaedi, A. "Effects of homogeneous and heterogeneous reactions and melting heat in the viscoelastic  fluid flow", J. Mol. Liq., 215, pp. 749-755 (2016).
18. Khan, M. and Malik, R. "Forced convective heat transfer to Sisko nano fluid past a stretching cylinder in the presence of variable thermal conductivity", J. Mol. Liquids, 218, pp. 1-7 (2016).
19. Ganji, D.D., Fakour, M., Vahabzadeh, M., and Kachapi, S.H.H. "Accuracy of VIM, HPM and ADM in solving nonlinear equations for the steady threedimensional flow of a Walter's B fluid in vertical channel", Walailak J. Sci. Tech., 11, pp. 593-609(2014).
20. Sheikholeslami, M., Ashorynejad, H.R., Domairry, G., and Hashim, I. "Flow and heat transfer of Cu-water nano fluid between a stretching sheet and a porous surface in a rotating system", Hindawi Publ. Corp. J. Appl. Math., 2012, Article ID 421320 (2012).
21. Ganji, D.D., Abbasi, M., Rahimi, J., Gholami, M., and Rahimipetroudi, I. "On the MHD squeezing flow between two parallel disks with suction or injection via HAM and HPM", Fron. Mech. Engng., 9, pp. 270-280 (2014).
22. Awais, M., Hayat, T., Nawaz, M., and Alsaedi, A. "Newtonian heating, thermal diffusion and diffusion thermo effects in an axisymmetric  flow of Jeffery fluid with convective conditions", Bra. J. Che. Engng., 32, pp. 555-561 (2015).
23. Awais, M., Hayat, T., Alsaedi, A., and Asghar, S. "Time-dependent three-dimensional boundary layer flow of a Maxwell fluid", Comp. Fluids, 91, pp. 21-27 (2014).
24. Awais, M., Hayat, T., Irum, S., and Alsaedi, A. "Heat generation/absorption effects in a boundary layer stretched flow of Maxwell nano fluid: Analytic and numeric solutions", PLOS ONE, Article ID e0129814 (2015).
25. Saleem, S., Nadeem, S., and Awais, M. "Timedependent second-order viscoelastic  fluid flow on rotating cone with heat generation and chemical reaction", J. Aerospace Engng., 29(4), Article No. 04016009 (2016).
26. Sadeghy, K., Hajibeygi, H., and Taghavi, S.M. "Stagnation-point flow of upper-convected Maxwell  fluids", Int. J. Non-Linear Mechanics, 41, pp. 1242- 1247 (2006).
27. Mukhopadhyay, S. "Heat transfer analysis of the unsteady flow of a Maxwell  fluid over a stretching surface in the presence of a heat source/sink", Chinese Physics Letters, 29, p. 054703 (2012).
28. Hayat, T., Ali, S., Awais, M., and Obaidat, S. "Stagnation point flow of Burgers' fluid over a stretching surface", Progress in Computational Fluid Dynamics, 13, pp. 48-53 (2013).