Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy
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O R I G I NA L
M. Bilal
· Y. Urva
Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy
Received: 6 July 2020 / Accepted: 2 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The main motive of this work is to study the effects of nonlinear radiation and mixed convection for the Casson nanofluid through the thin needle. Mass transfer is further characterized by activation energy. Temperature-dependent viscosity and a variable magnetic field are assumed for the current problem. The consequences of the physical framework on the velocity, temperature and species including the impact of radiative heat flux are discussed. The partial differential equations of the physical model are achieved using the concept of boundary layer approximation and are remolded into the ordinary differential mathematical statement which is coupled nonlinear, by substituting specific similarity transformations. By making the use of built-in MATLAB bvp4c function, the results are calculated and arranged in the manner of graphs and tables. The effects of different physical parameters of our interest such as the Casson fluid parameter, Brownian motion, Prandtl number, buoyancy ratio parameter, thermal radiation, thermophoresis parameter, Schmidt number and relaxation time are examined for the velocity, concentration and temperature profiles. Keywords Heat transfer · Magnetohydrodynamics · Casson nanofluid · Thin needle · Activation energy · Variable thermal viscosity
List of symbols Bo σ k ke DB Tw T∞ C Cw C∞ ν P v ρ T qr
Uniform magnetic field strength (Tesla) Electric conductivity (Siemens/m) Thermal conductivity [W/(mK)] Mean adsorption coefficient Effective diffusion coefficient (m2 /s) Temperature of the wall (K) Ambient temperature (K) Concentration (mol/m3 ) Wall concentration (mol/m3 ) Ambient concentration (mol/m3 ) Dynamic viscosity (Pa.s) Pressure (Pa) Kinematic viscosity (m2 /s) Density (kg/m3 ) Temperature (K) Radiative heat flux (W/m2 )
M. Bilal (B) · Y. Urva Department of Mathematics, University of Lahore Gujrat Campus, Gujrat, Pakistan E-mail: [email protected]
M. Bilal, Y. Urva
Nt (u, v) (x, y) Cf Nux Sh x Pr R Re α β λ Nr Nb σs ξ Gr x Rex Sc δ E
Thermophoresis parameter Components of the velocity (m/s) Cartesian co-ordinates (m) Local skin friction Local Nusselt number Local Sherwood number Prandtl number Radiation parameter Reynolds number Thermal diffusivity (m2 /s) Casson parameter Velocity ratio parameter Buoyancy ratio parameter Brownian motion parameter Stefan–Boltzmann constant (W/m2 K4 ) Constant mixed convection Local Grashof number Local Reynolds number Schmidt number Relaxation time Temperature difference ratio Activation energy
1 Introduction In industries, the symmetrical boundary layer flow and the transfer of heat about an axis are significant. The thin needle geometry is the slandering surface obtained by the revolution of a parabola around its axis. In such geometries, the physical phenomenon is very cl
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