Theoretical analysis of cross-nanofluid flow with nonlinear radiation and magnetohydrodynamics
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ORIGINAL PAPER
Theoretical analysis of cross-nanofluid flow with nonlinear radiation and magnetohydrodynamics M Shahzad1*, M Ali1*, F Sultan1, W A Khan2,3 and Z Hussain4 1
Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan
2
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
3
Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu & Kashmir 12010, Pakistan 4
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan Received: 16 May 2019 / Accepted: 27 September 2019
Abstract: In this article, the characteristics of physical model steady axisymmetric flow of cross-fluid over a stretching sheet are explored numerically. Furthermore, steady flow of nanofluid is expressed by means of Buongiorno’s model for nanoparticles. Moreover, the features of thermal radiation and chemical reaction processes with partial velocity slip condition are adopted here. Nonlinear PDEs are converted to ODEs using suitable transformation variables. The reduced systems of ODEs are resolved using an effective bvp4c scheme implemented. Numerical computation for physical parameters such as skin friction, Nusselt and Sherwood numbers are also examined. Magnetic field plays a vital role in controlling the flow of fluid and has the tendency to enhance the thermal boundary layer and concentration. Similarly, skin friction, Nusselt and Sherwood numbers depreciate by improving the values of velocity slip parameter, magnetic parameter, magnetic parameter, thermophoresis parameter in shear thickening fluids. Keywords: Steady axisymmetric flow; Velocity slip condition; MHD cross-nanofluid; Numerical solutions; Chemical reaction PACS Nos.: 47.10.A-; 44.05.?e; 44.10.?i; 44.05; 44.40.?a List of symbols u; w Velocity components r; z Cylindrical coordinates m Kinematics viscosity qf Fluid density C Cross-time constant n Fitted rate constant T Fluid temperature C Fluid concentration ðqcÞf Heat capacity of the fluid DB Brownian diffusion coefficient DT Thermophoresis diffusion coefficient k Thermal conductivity a Thermal diffusivity s Effective heat capacity ratio Uw ðr; tÞ Stretching velocity
*Corresponding author, E-mail: [email protected]; [email protected]
qr r k kc Tw d g Pr We L Wðr; zÞ Nb r Rd Le M hf Cw B0 a
Radiative heat flux Stefan–Boltzmann constant Mean absorption coefficient Rate of chemical reaction Surface temperature Chemical reaction parameter Dimensionless variable Prandtl number Local Weissenberg number Velocity slip parameter Stream function Brownian motion parameter Reaction rate parameter Radiation parameter Lewis number Magnetic parameter Temperature ratio parameter Concentration at the surface Magnetic parameter Constant
2019 IACS
M Shahzad et al.
T1 Cf f Nu h Sh / Re
Ambient fluid temperature Skin fraction Dimensionless velocity Local Nusselt number Dimensionless temperature Sherwood number Dimensionless concentration Reynolds number
1. Introduction Chemical reacti
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