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.
Similar content being viewed by others
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
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
Cattaneo C (1948) Sulla conduzione del calore, Atti Semin. Mat Fis Univ Modena Reggio Emilia 3:83–101
Christov CI (2009) On frame indifferent formulation of the Maxwell-Cattaneo model of finite speed heat conduction. Mech Res Commun 36:481–486
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
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
Fourier JBJ (1822) Theorie analytique. De La chaleur, Paris
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
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
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
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
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
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
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
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
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
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
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
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
Liao S (2012) Homotopic analysis method in nonlinear differential equations. Springer, Heidelberg, Germany
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
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
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
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
Straughan B (2010) Thermal convection with the Cattaneo-Christov model. Intern J Heat Mass Transf 53:95–98
Turkyilmazoglu M (2018) Convergence accelerating in the homotopy analysis method: a new approach. Adv Appl Math Mech 10:925–947
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
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
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
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
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
There is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13204-020-01500-0