Rheology of mixed convective Casson nanofluid in a convectively heated stratified medium
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ORIGINAL ARTICLE
Rheology of mixed convective Casson nanofluid in a convectively heated stratified medium M. Mudassar Gulzar1 · M. Waqas1 · Zeeshan Asghar1 · Shafqat Ali2 Received: 25 March 2019 / Accepted: 13 September 2019 © King Abdulaziz City for Science and Technology 2019
Abstract A mathematical framework for mixed convective non-Newtonian nanoliquid subjected to hydromagnetic characteristics is addressed in this attempt. The well-known Buongiorno nanoliquid model which elaborates thermophoretic and Brownian diffusions aspect is opted for formulation. In addition, heat generation, double stratification and convective conditions are retained. Apposite variables are introduced for dimensionless procedure. Homotopy scheme is employed to attain convergent expressions. Graphs are presented for description of sundry variables effect versus dimensionless quantities. Keywords Casson nanoliquid · Thermophoretic and Brownian diffusions · Heat generation · Double stratification · Convective conditions List of symbols u, v Velocity components 𝜌f Density of base liquid x, y Space coordinates 𝜈 Kinematic viscosity 𝜇 Dynamic viscosity 𝛼 Thermal diffusivity k Thermal conductivity (𝜌c)f Liquid heat capacity 𝜏 Heat capacity ratio 𝜋c Critical value of non-Newtonian model py Fluid yield stress uw (x) Stretching velocity c Stretching rate 𝜆 Thermal buoyancy parameter DB Brownian movement coefficient DT Thermophoresis diffusion coefficient 𝜎 Electrical conductivity B0 Magnetic field strength T Temperature * M. Mudassar Gulzar [email protected] 1
NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad 44000, Pakistan
Faculty of Engineering Sciences, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi 44000, Pakistan
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C Concentration a1 , a2 , d1 , d2 Dimensional constants 1
Cfx Rex2 Dimensionless drag force −
1
Nu Rex 2 Dimensionless heat transfer rate −
1
Sh Rex 2 Dimensionless mass transfer rate Tf Hot fluid temperature Cf Hot fluid concentration T∞ Ambient fluid temperature C∞ Ambient fluid concentration T0 Reference temperature C0 Reference concentration 𝜋 Deformation rate 𝛽 Material parameter of Casson fluid 𝛾1 Thermal Biot number Nt Thermophoretic variable 𝛾2 Solutal Biot number Nb Brownian motion variable Ha Hartman number N Buoyancy ratio parameter Sc Schmidt number S1 Thermal stratified variable S2 Solutal stratified variable Pr Prandtl number Rex Reynolds numbers f (𝜂) Dimensionless velocity 𝜃(𝜂) Dimensionless temperature
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Applied Nanoscience
𝜙(𝜂) Dimensionless concentration ℏf , ℏ𝜃 , ℏ𝜙 Auxiliary variables 𝜂 Dimensionless variable
Introduction An anomalous augmentation of thermal conductivity via solid particles addition into heat transporting liquids has appealed the researchers’ interest of diverse disciplines. These suspensions (identified as nanoliquids) have been deliberated to have a protuberant prospective in heat transport and energy utilizations for the im
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