# Nonlinear convective flow with variable thermal conductivity and Cattaneo-Christov heat flux

- 141 Downloads
- 7 Citations

## Abstract

An analysis is introduced to investigate the salient features of nonlinear convective flow of thixotropic fluid in the version of Cattaneo-Christov heat flux theory. The stagnation point flow is present. The flow phenomenon is by an impermeable stretching sheet. The energy expression is modeled through the theory of Cattaneo-Christov heat flux. Characteristics of heat transfer phenomenon are described within the frame of variable thermal conductivity. Suitable variables reduced to the nonlinear partial differential expressions to the ordinary differential expressions. Series solutions of resulting systems are acquired within the frame of homotopy theory. Convergence analysis is achieved and suitable values are determined by capturing the so-called *ℏ*−curves. Graphical results for velocity and temperature are displayed and argued for sundry physical variables. Expression of skin friction coefficient is calculated through numerical values. Higher values of mixed convection parameter, Prandtl number, and thermal relaxation time lead to decay the temperature and layer thickness.

## Keywords

Thixotropic liquid Cattaneo-Christov heat flux Nonlinear convection Variable thermal conductivity Stagnation point flow## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Funding

This research is a self-funded project.

## References

- 1.Cattaneo C (1948) Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena Reggio Emilia 3:83–101MathSciNetzbMATHGoogle Scholar
- 2.Christov CI (2009) On frame indifferent formulation of the Maxwell-Cattaneo model of finite speed heat conduction. Mech Res Commun 36:481–486MathSciNetCrossRefzbMATHGoogle Scholar
- 3.Straughan B (2010) Thermal convection with the Cattaneo-Christov model. Int J Heat Mass Transf 53:95–98CrossRefzbMATHGoogle Scholar
- 4.Han S, Zheng L, Li C, Zhang X (2014) Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Appl Math Lett 38:87–93MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Ciarletta M, Straughan B (2010) Uniqueness and structural stability for the Cattaneo-Christov equations. Mech Res Comm 37:445–447CrossRefzbMATHGoogle Scholar
- 6.Hayat T, Imtiaz M, Alsaedi A, Almezal S (2016) On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. J Mag Mag Mat 401:296–303CrossRefGoogle Scholar
- 7.Mustafa M (2015) Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. AIP Adv 5:047109CrossRefGoogle Scholar
- 8.Waqas M, Hayat T, Farooq M, Shehzad SA, Alsaedi A (2016) Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. J Mol Liq 220:642–648CrossRefGoogle Scholar
- 9.Li J, Zheng L, Liu L (2016) MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects. J Mol Liq 221:19–25CrossRefGoogle Scholar
- 10.Shehzad SA, Abbasi FM, Hayat T, Alsaedi A (2016) Cattaneo-Christov heat flux model for Darcy-Forchheimer flow of an Oldroyd-B fluid with variable conductivity and non-linear convection. J Mol Liq 224:274–278CrossRefGoogle Scholar
- 11.Hayat T, Qayyum S, Imtiaz M, Alsaedi A (2017) Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model. Res Physics 7:126–133Google Scholar
- 12.Sui J, Zheng L, Zhang X (2016) 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 Therm Sci 104:461–468CrossRefGoogle Scholar
- 13.Ali ME, Sandeep N (2017) Cattaneo-Christov model for radiative heat transfer of magnetohydrodynamic Casson-ferrofluid: a numerical study. Res. Physics 7:21–30Google Scholar
- 14.Abel MS, Siddheshwar PG, Mahesha N (2009) Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source. Int J Non-Linear Mech 44:1–12CrossRefzbMATHGoogle Scholar
- 15.Ezzat MA, El-Bary AA (2016) Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder. Int J Thermal Sci 108:62–69CrossRefGoogle Scholar
- 16.Hayat T, Shafiq A, Alsaedi A, Asghar S (2015) Effect of inclined magnetic field in flow of third grade fluid with variable thermal conductivity. AIP Adv 5:087108CrossRefGoogle Scholar
- 17.Si X, Zhu X, Zheng L, Zhang X, Lin P (2016) Laminar film condensation of pseudo-plastic non-Newtonian fluid with variable thermal conductivity on an isothermal vertical plate. Int J Heat Mass Transf 92:979–986CrossRefGoogle Scholar
- 18.Wang Y, Liu D, Wang Q, Zhou J (2016) Problem of axisymmetric plane strain of generalized thermoelastic materials with variable thermal properties. European J Mech A/Solids 60:28–38MathSciNetCrossRefzbMATHGoogle Scholar
- 19.Akbar NS, Raza M, Ellahi R (2015) Peristaltic flow with thermal conductivity of H
_{2}O + Cu nanofluid and entropy generation. Res Physics 5:115–124Google Scholar - 20.Akbar NS, Raza M, Ellahi R (2016) Endoscopic effects with entropy generation analysis in peristalsis for the thermal conductivity of H
_{2}O + Cu nanofluid. J Appl Fluid Mech 9:1721–1730CrossRefGoogle Scholar - 21.Akbar NS, Raza M, Ellahi R (2016) Anti-bacterial applications for new thermal conductivity model in arteries with CNT suspended nanofluid. Int J Mech Medicine Biology 16:1650063CrossRefGoogle Scholar
- 22.Su X, Zheng L, Zhang X, Zhang J (2012) MHD mixed convective heat transfer over a permeable stretching wedge with thermal radiation and ohmic heating. Chem Eng Sci 78:1–8CrossRefGoogle Scholar
- 23.Zhang C, Zheng L, Zhang X, Chen G (2015) MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl Math Model 39:165–181MathSciNetCrossRefzbMATHGoogle Scholar
- 24.Duan D, Ge P, Bi W, Ji J (2016) Numerical investigation on synthetical performance of heat transfer of planar elastic tube bundle heat exchanger. Appl Ther Eng 109:295–303CrossRefGoogle Scholar
- 25.Hayat T, Bashir G, Waqas M, Alsaedi A (2016) MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer. J Mol Liq 223:836–844CrossRefGoogle Scholar
- 26.Ebrahimi B, Taghavi SM, Sadeghy K (2015) Two-phase viscous fingering of immiscible thixotropic fluids: a numerical study. J Non-Newtonian Fluid Mech 218, 40:–52Google Scholar
- 27.Shehzad SA, Hayat T, Asghar S, Alsaedi A (2015) Stagnation point flow of thixotropic fluid over a stretching sheet with mass transfer and chemical reaction. J Appl Fluid Mech 8:465–471CrossRefGoogle Scholar
- 28.Oishi CM, Thompson RL, Martins FP (2016) Transient motions of elasto-viscoplastic thixotropic materials subjected to an imposed stress field and to stress-based free-surface boundary conditions. Int J Eng Sci 109:165–201MathSciNetCrossRefzbMATHGoogle Scholar
- 29.Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710CrossRefGoogle Scholar
- 30.López-Aguilar JE, Webster MF, Tamaddon-Jahromi HR, Maner O (2016) Convoluted models and high-Weissenberg predictions for micellar thixotropic fluids in contraction-expansion flows. J Non-Newtonian Fluid Mech 232:55–66MathSciNetCrossRefGoogle Scholar
- 31.S. Liao (2012) Homotopy analysis method in nonlinear differential equations, Springer & Higher Education PressGoogle Scholar
- 32.Shahzad A, Ali R (2012) MHD flow of a non-Newtonian power law fluid over a vertical stretching sheet with the convective boundary condition. Walailak J Sci Tech 10:43–56Google Scholar
- 33.Turkyilmazoglu M, Pop I (2013) Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid. Int J Heat Mass Transf 57:82–88CrossRefGoogle Scholar
- 34.Shehzad SA, Alsaadi FE, Monaquel SJ, Hayat T (2013) Soret and Dufour effects on the stagnation point flow of Jeffrey fluid with convective boundary condition. Eur. Phys. J. Plus 128:56CrossRefGoogle Scholar
- 35.Shahzad A, Ali R (2012) Approximate analytic solution for magneto-hydrodynamic flow of a non-Newtonian fluid over a vertical stretching sheet. Can J Appl Sci 2:202–215Google Scholar
- 36.Farooq U, Zhao YL, Hayat T, Alsaedi A, Liao SJ (2015) Application of the HAM-based mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nanofluid. Comp Fluid 111:69–75CrossRefzbMATHGoogle Scholar
- 37.Ali R, Shahzad A, Khan M, Ayub M (2016) Analytic and numerical solutions for axisymmetric flow with partial slip. Eng Comp 32:149–154CrossRefGoogle Scholar
- 38.Hayat T, Asad S, Mustafa M, Alsaedi A (2015) MHD stagnation-point flow of Jeffrey fluid over a convectively heated stretching sheet. Comput Fluids 108:179–185MathSciNetCrossRefzbMATHGoogle Scholar
- 39.Hayat T, Qayyum S, Alsaedi A, Waqas M (2016) Radiative flow of tangent hyperbolic fluid with convective conditions and chemical reaction. Eur Phys J Plus 131:422CrossRefGoogle Scholar
- 40.Hayat T, Qayyum S, Alsaedi A, Shehzad SA (2016) Nonlinear thermal radiation aspects in stagnation point flow of tangent hyperbolic nanofluid with double diffusive convection. J Mol Liq 223:969–978CrossRefGoogle Scholar
- 41.Sui J, Zheng L, Zhang X, Chen G (2015) Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. Int J Heat Mass Transf 85:1023–1033CrossRefGoogle Scholar
- 42.Hayat T, Qayyum S, Waqas M, Alsaedi A (2016) Thermally radiative stagnation point flow of Maxwell nanofluid due to unsteady convectively heated stretched surface. J Mol Liq 224:801–810CrossRefGoogle Scholar