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Numerical analysis of chemical reaction and non-linear radiation for magneto-cross nanofluid over a stretching cylinder

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Abstract

This work is focused on the numerical solution of non-Newtonian unsteady flow of a Cross nanofluid over a continuously expanding/contracting horizontal cylinder. The flow study and joule heating are obtainable in the presence of a binary chemical reaction, radiation and nanofluid for a devised Nanomaterial model, considering the phenomena of Brownian motion and thermophoresis. The idea of Boussinesq-approximations is developed with the help of momentum, temperature and concentration equations by using appropriate transformations. The nonlinear partial differential equations (PDE’s) are converted to ordinary ones via appropriate transformations. A numerical solution is obtained through the implementation of a boundary value problem fourth-order (bvp4c) technique. Flow parameters are discussed graphically. Physical engineering quantities, like surface drag forces, Nusselt and Sherwood numbers are examined numerically. It is concluded that heat transfer rates are enhanced for heat source/sink and Brownian motion.

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Abbreviations

\(u,v\) :

Velocity components

\(r,x\) :

Cylindrical coordinates

\(\rho\) :

Fluid density

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

Brownian diffusion coefficient

\(\delta\) :

Chemical reaction parameter

\(a,c\) :

Constants

\(\Gamma\) :

Material parameter

\(\tau_{{\text{w}}}\) :

Surface shear stress

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

Thermophoresis diffusion coefficient

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

Brownian motion parameter

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

Surface temperature

\(T_{\infty }\) :

Ambient fluid temperature

\(n\) :

Power law index

\(\mu\) :

Dynamic viscosity

\(\theta\) :

Dimensionless temperature

\(c_{{\uprho }}\) :

Specific heat

\(u_{w} \left( {x,t} \right)\) :

Stretching velocity

\(C_{\infty }\) :

Ambient nanoparticle concentration

\(q_{{\text{w}}}\) :

Wall heat flux

\(\mu_{\infty }\) :

Infinite shear viscosity

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

Skin friction coefficient

\(k_{c}\) :

Rate of chemical reaction

\({\text{Sh}}\) :

Sherwood number

\(Q_{0}\) :

Heat generation/absorption coefficient

\(\sigma^{*}\) :

Stefan Boltzmann

\(\alpha\) :

Thermal diffusivity

\(q_{{\text{r}}}\) :

Radiative heat flux

\(q_{{\text{w}}}\) :

Wall heat flux

\(\eta\) :

Dimensionless variable

\(\psi\) :

Stream function

\({\text{We}}\) :

Local Weissenberg number

\({\Pr}\) :

Prandtl number

\(T\) :

Temperature of fluid

\(C\) :

Nanoparticles concentration

\(M\) :

Magnetic parameter

\({\text{Sc}}\) :

Schmidt number

\(\gamma\) :

Curvature parameter

\(\beta\) :

Heat generation/absorption parameter

\(\theta_{{\text{w}}}\) :

Temperature ratio parameter

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

Thermophoresis parameter

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

Radiation parameter

\(f\) :

Dimensionless stream function

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

Surface concentration

\(\phi\) :

Dimensionless concentration

\(\tau_{{{\text{rx}}}}\) :

Wall shear stress

\(\mu_{0}\) :

Zero shear viscosity

\(q_{{\text{m}}}\) :

Wall mass flux

\(\tau\) :

Ratio of heat capacity

\({\text{Re}}_{x}\) :

Local Reynolds number

\({\text{Nu}}\) :

Local Nusselt Number

\(\upsilon\) :

Kinematic viscosity

\(k^{*}\) :

Mean absorption coefficient

\(\beta_{0}\) :

Magnetic field strength

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

Heat capacity of the base fluid

\(\tau_{{{\text{rx}}}}\) :

Wall shear stress

\(q_{{\text{m}}}\) :

Wall mass flux

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan

    Mehboob Ali, Muhammad Shahzad & Faisal Sultan

  2. Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif 12010, Islamabad, Azad Jammu and Kashmir, Pakistan

    Waqar Azeem Khan

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  1. Mehboob Ali
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  2. Muhammad Shahzad
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  4. Waqar Azeem Khan
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Ali, M., Shahzad, M., Sultan, F. et al. Numerical analysis of chemical reaction and non-linear radiation for magneto-cross nanofluid over a stretching cylinder. Appl Nanosci 10, 3259–3267 (2020). https://doi.org/10.1007/s13204-020-01385-z

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