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Rheology of mixed convective Casson nanofluid in a convectively heated stratified medium

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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.

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Abbreviations

\({u,}\,{v}\) :

Velocity components

\(\rho_{\text{f}}\) :

Density of base liquid

\(x,\,\;y\) :

Space coordinates

\(\nu\) :

Kinematic viscosity

\(\mu\) :

Dynamic viscosity

\(\alpha\) :

Thermal diffusivity

\(k\) :

Thermal conductivity

\((\rho c)_{\text{f}}\) :

Liquid heat capacity

\(\tau\) :

Heat capacity ratio

\(\pi_{\text{c}}\) :

Critical value of non-Newtonian model

\(p_{\text{y}}\) :

Fluid yield stress

\(u_{\text{w}} (x)\) :

Stretching velocity

\(c\) :

Stretching rate

\(\lambda\) :

Thermal buoyancy parameter

\(D_{\text{B}}\) :

Brownian movement coefficient

\(D_{\text{T}}\) :

Thermophoresis diffusion coefficient

\(\sigma\) :

Electrical conductivity

\(B_{0}\) :

Magnetic field strength

T :

Temperature

C :

Concentration

\(a_{1} ,\;a_{2} ,\;d_{1} ,\;d_{2}\) :

Dimensional constants

\(C_{{{\text{f}}_{x} }} \;Re_{x}^{{\tfrac{1}{2}}}\) :

Dimensionless drag force

\(Nu\;Re_{x}^{{ - \tfrac{1}{2}}}\) :

Dimensionless heat transfer rate

\(Sh\;Re_{x}^{{ - \tfrac{1}{2}}}\) :

Dimensionless mass transfer rate

\(T_{\text{f}}\) :

Hot fluid temperature

\(C_{\text{f}}\) :

Hot fluid concentration

\(T_{\infty }\) :

Ambient fluid temperature

\(C_{\infty }\) :

Ambient fluid concentration

\(T_{0}\) :

Reference temperature

\(C_{0}\) :

Reference concentration

\(\pi\) :

Deformation rate

\(\beta\) :

Material parameter of Casson fluid

\(\gamma_{1}\) :

Thermal Biot number

\(N_{\text{t}}\) :

Thermophoretic variable

\(\gamma_{2}\) :

Solutal Biot number

\(N_{\text{b}}\) :

Brownian motion variable

\(Ha\) :

Hartman number

\(N\) :

Buoyancy ratio parameter

\(Sc\) :

Schmidt number

\(S_{1}\) :

Thermal stratified variable

\(S_{2}\) :

Solutal stratified variable

\(Pr\) :

Prandtl number

\(Re_{x}\) :

Reynolds numbers

\(f(\eta )\) :

Dimensionless velocity

\(\theta (\eta )\) :

Dimensionless temperature

\(\phi (\eta )\) :

Dimensionless concentration

\(\hbar_{f} ,\;\hbar_{\theta } ,\;\hbar_{\phi }\) :

Auxiliary variables

\(\eta\) :

Dimensionless variable

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Authors and Affiliations

  1. NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan

    M. Mudassar Gulzar, M. Waqas & Zeeshan Asghar

  2. Faculty of Engineering Sciences, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, 44000, Pakistan

    Shafqat Ali

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  1. M. Mudassar Gulzar
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  2. M. Waqas
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  3. Zeeshan Asghar
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  4. Shafqat Ali
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Correspondence to M. Mudassar Gulzar.

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Gulzar, M.M., Waqas, M., Asghar, Z. et al. Rheology of mixed convective Casson nanofluid in a convectively heated stratified medium. Appl Nanosci 10, 3227–3233 (2020). https://doi.org/10.1007/s13204-019-01166-3

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