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Heat generation in mixed convected Williamson liquid stretching flow under generalized Fourier concept

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Abstract

We addressed mixed convected stretching flow considering Williamson liquid subjected to variable conductivity. Transportation of heat is investigated employing generalized Fourier law and heat generation. Governing non-linear expressions are achieved through well-known boundary-layer concept. Transformation procedure converts PDEs into ODEs. Homotopy concept is used for non-linear analysis. Novel attributes of non-dimensional variables are scrutinized via graphical outcomes. We found higher temperature subjected to generalized Fourier law in comparison to well-known Fourier law.

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References

  • Acharya N, Das K, Kundu PK (2017) Cattaneo-Christov intensity of magnetised upper-convected Maxwell nanofluid flow over an inclined stretching sheet: a generalised Fourier and Fick’s perspective. Int J Mech Sci 130:167–173

    Article  Google Scholar 

  • Ahmed A, Khan M, Irfan M, Ahmed J (2020) Transient MHD flow of Maxwell nanofluid subject to non-linear thermal radiation and convective heat transport. Appl Nanosci. https://doi.org/10.1007/s13204-020-01375-1

    Article  Google Scholar 

  • Cattaneo C (1948) Sulla conduzione del calore, Atti Semin. Mat Fis Univ Modena Reggio Emilia 3:83–101

    Google Scholar 

  • Christov CI (2009) On frame indifferent formulation of the Maxwell-Cattaneo model of finite speed heat conduction. Mech Res Commun 36:481–486

    Article  Google Scholar 

  • Dogonchi AS, Ganji DD (2017) Impact of Cattaneo-Christov heat flux on MHD nanofluid flow and heat transfer between parallel plates considering thermal radiation effect. J Taiwan Inst Chem Eng 80:52–63

    Article  CAS  Google Scholar 

  • Doh DH, Cho GR, Ramya E, Muthtamilselvan M (2019) Cattaneo-Christov heat flux model for inclined MHD micropolar fluid flow past a non-linearly stretchable rotating disk. Case Stud Thermal Eng 14:100496

    Article  Google Scholar 

  • Fourier JBJ (1822) Theorie analytique. De La chaleur, Paris

    Google Scholar 

  • Hayat T, Waqas M, Shehzad SA, Alsaedi A (2014) Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions. Sci Iran B 21:682–692

    Google Scholar 

  • Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016a) On 2D stratified flow of an Oldroyd-B fluid with chemical reaction: an application of non-Fourier heat flux theory. J Mol Liq 223:566–571

    Article  CAS  Google Scholar 

  • Hayat T, Qayyum S, Waqas M, Alsaedi A (2016b) Thermally radiative stagnation point flow of Maxwell nanofluid due to unsteady convectively heated stretched surface. J Mol Liq 224:801–810

    Article  CAS  Google Scholar 

  • Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016c) Mixed convection flow of a Burgers nanofluid in the presence of stratifications and heat generation/absorption. Euro Phys J Plus 131:253

    Article  Google Scholar 

  • Hayat T, Waqas M, Alsaedi A, Bashir G, Alzahrani F (2017) Magnetohydrodynamic (MHD) stretched flow of tangent hyperbolic nanoliquid with variable thickness. J Mol Liq 229:178–184

    Article  CAS  Google Scholar 

  • Ibrahim SM, Lorenzini G, Kumar PV, Raju CSK (2017) Influence of chemical reaction and heat source on dissipative MHD mixed convection flow of a Casson nanofluid over a nonlinear permeable stretching sheet. Int J Heat Mass Transf 111:346–355

    Article  CAS  Google Scholar 

  • Irfan M, Khan M, Khan WA (2018) Interaction between chemical species and generalized Fourier’s law on 3D flow of Carreau fluid with variable thermal conductivity and heat sink/source: a numerical approach. Res Physics 10:107–117

    Google Scholar 

  • Irfan M, Khan WA, Khan M, Gulzar MM (2019) Influence of Arrhenius activation energy in chemically reactive radiative flow of 3D Carreau nanofluid with nonlinear mixed convection. J Phys Chem Solids 125:141–152

    Article  CAS  Google Scholar 

  • Irfan M, Khan WA, Khan M, Waqas M (2020) Evaluation of Arrhenius activation energy and new mass flux condition in Carreau nanofluid: dual solutions. Appl Nanosci. https://doi.org/10.1007/s13204-020-01449-0

    Article  Google Scholar 

  • Khan M, Khan WA (2016) Three-dimensional flow and heat transfer to burgers fluid using Cattaneo-Christov heat flux model. J Mol Liq 221:651–657

    Article  CAS  Google Scholar 

  • Khan WA, Waqas M, Kadry S, Asghar Z, Abbas SZ, Irfan M (2020a) On the evaluation of stratification based entropy optimized hydromagnetic flow featuring dissipation aspect and Robin conditions. Comput Methods Biomed 190:105347

    Article  CAS  Google Scholar 

  • Khan M, Shahid A, Salahuddin T, Malik MY, Hussain A (2020b) Analysis of two dimensional Carreau fluid flow due to normal surface condition: a generalized Fourier’s and Fick’s laws. Phys A 540:123024

    Article  Google Scholar 

  • Liao S (2012) Homotopic analysis method in nonlinear differential equations. Springer, Heidelberg, Germany

    Book  Google Scholar 

  • Mahanthesh B, Gireesha BJ, Raju CSK (2017) Cattaneo–Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source. Inform Med Unlocked 9:26–34

    Article  Google Scholar 

  • Reddy JVR, Sugunamma V, Sandeep N (2016) Cross diffusion effects on MHD flow over three different geometries with Cattaneo–Christov heat flux. J Mol Liq 223:1234–1241

    Article  Google Scholar 

  • Rosali H, Ishak A, Nazar R, Pop I (2016) Mixed convection boundary layer flow past a vertical cone embedded in a porous medium subjected to a convective boundary condition. Propuls Power Res 5:118–122

    Article  Google Scholar 

  • Sohail M, Naz R, Abdelsalam SI (2020) Application of non-Fourier double diffusions theories to the boundary-layer flow of a yield stress exhibiting fluid model. Phys A 537:122753

    Article  CAS  Google Scholar 

  • Straughan B (2010) Thermal convection with the Cattaneo-Christov model. Intern J Heat Mass Transf 53:95–98

    Article  Google Scholar 

  • Turkyilmazoglu M (2018) Convergence accelerating in the homotopy analysis method: a new approach. Adv Appl Math Mech 10:925–947

    Article  Google Scholar 

  • Waqas M, Farooq M, Ijaz Khan M, Alsaedi A, Hayat T, Yasmeen T (2016a) Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Intern J Heat Mass Transf 102:766–772

    Article  Google Scholar 

  • Waqas M, Hayat T, Farooq M, Shehzad SA, Alsaedi A (2016b) Cattaneo–Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. J Mol Liq 220:642–648

    Article  CAS  Google Scholar 

  • Waqas M, Hayat T, Shehzad SA, Alsaedi A (2018) Analysis of forced convective modified burgers liquid flow considering Cattaneo-Christov double diffusion. Res Physics 8:908–913

    Google Scholar 

  • Waqas M, Shehzad SA, Hayat T, Ijaz Khan M, Alsaedi A (2019a) Simulation of magnetohydrodynamics and radiative heat transport in convectively heated stratified flow of Jeffrey nanofluid. J Physics Chem Solids 133:45–51

    Article  CAS  Google Scholar 

  • Waqas M, Jabeen S, Hayat T, Ijaz Khan M, Alsaedi A (2019b) Modeling and analysis for magnetic dipole impact in nonlinear thermally radiating Carreau nanofluid flow subject to heat generation. J Magn Mater 485:197–204

    Article  CAS  Google Scholar 

  • Waqas M, Khan MI, Hayat T, Gulzar MM, Alsaedi A (2020a) Transportation of radiative energy in viscoelastic nanofluid considering buoyancy forces and convective conditions. Chaos Solitons Fractals 130:109415

    Article  Google Scholar 

  • Waqas M, Khan WA, Asghar Z (2020b) An improved double diffusion analysis of non-Newtonian chemically reactive fluid in frames of variables properties. Int Commun Heat Mass Transf 115:104524

    Article  Google Scholar 

  • Waqas M, Dogonchi AS, Shehzad SA, Khan MI, Hayat T, Alsaedi A (2020c) Nonlinear convection and joule heating impacts in magneto-thixotropic nanofluid stratified flow by convectively heated variable thicked surface. J Mol Liq 300:111945

    Article  CAS  Google Scholar 

  • Waqas M, Hayat T, Alsaedi A, Khan WA (2020d) Analytical evaluation of Oldroyd-B nanoliquid under thermo-solutal Robin conditions and stratifications. Comput Methods Biomed. https://doi.org/10.1016/j.cmpb.2020.105474

    Article  Google Scholar 

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Asghar, Z., Kousar, M., Waqas, M. et al. Heat generation in mixed convected Williamson liquid stretching flow under generalized Fourier concept. Appl Nanosci 10, 4439–4444 (2020). https://doi.org/10.1007/s13204-020-01500-0

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  • DOI: https://doi.org/10.1007/s13204-020-01500-0

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