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Simultaneous impact of nonlinear thermal radiation and heat source/sink in stagnation point flow of viscous nanomaterial

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Abstract

An attempt has been made to study the consequences of stagnation point flow of nanomaterial toward nonlinear variable sheet. Nanoparticles comprise Brownian movement and thermophoresis effects. Thermal radiation and convective boundary conditions are considered. Applied magnetic flux of strength (\(B_{0}\)) is implemented in vertical direction. The nonlinear system is tackled through homotopy method. Energy equation is modeled in the presence of thermal radiation, convective conditions and heat generation/absorption. The impact of several flow variables on the momentum, energy and concentration is graphically discussed. Concluding remarks are presented.

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Abbreviations

\(u,v\) :

Velocity components

\(x,y\) :

Space coordinates

\(T\) :

Fluid temperature

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

Convective fluid temperature

\(T_{\infty }\) :

Ambient temperature

\(C\) :

Fluid concentration

\(C_{\infty }\) :

Ambient concentration

\(u_{w}\) :

Stretching velocity

\(u_{\text{e}}\) :

External flow velocity

\(B_{0}\) :

Strength of magnetic field

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

Particle density

\(c_{p}\) :

Specific heat

\(Q\) :

Heat generation/absorption coefficient

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

Radiative heat flux

\(k\) :

Thermal conductivity

\(h_{f}\) :

Convective heat transfer coefficient

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

Brownian diffusion coefficient

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

Thermophoresis diffusion coefficient

\(f\) :

Dimensionless velocity

\(M\) :

Magnetic parameter

\(A\) :

Ratio of velocities

\(R\) :

Radiation parameter

\(Pr\) :

Prandtl number

\(Nb\) :

Brownian motion parameter

\(Nt\) :

Thermophoresis parameter

\(Sc\) :

Schmidt number

\(\beta_{i}\) :

Biot number

\(Nu\) :

Local Nusselt number

\(Re_{x}\) :

Local Reynolds number

\(k^{*}\) :

Coefficient of mean absorption

\(a,b,c\) :

Positive constants

\(q_{w}\) :

Surface heat flux

\(\alpha^{*}\) :

Thermal diffusivity

\(\tau_{w}\) :

Surface shear stress

\(\sigma^{*}\) :

Stefan-Boltzmann constant

\(\beta_{t}\) :

Biot number

\(\delta\) :

Heat generation/absorption parameter

\(\theta_{w}\) :

Temperature parameter

\(\alpha\) :

Thickness parameter

\(\gamma_{1}\) :

Chemical reaction parameter

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

\(\psi\) :

Stream function

\(\eta\) :

Dimensionless space variable

\(\tau\) :

Capacity ratio

\(\nu\) :

Kinematic viscosity

\(\mu_{f}\) :

Dynamic viscosity

\(\rho\) :

Fluid density

\(\infty\) :

Condition at the free stream

w :

Condition at the surface

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan

    Faisal Shah, M. Ijaz Khan & T. Hayat

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80257, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

Authors
  1. Faisal Shah
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  2. M. Ijaz Khan
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Correspondence to M. Ijaz Khan.

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Shah, F., Ijaz Khan, M., Hayat, T. et al. Simultaneous impact of nonlinear thermal radiation and heat source/sink in stagnation point flow of viscous nanomaterial. Indian J Phys 94, 657–664 (2020). https://doi.org/10.1007/s12648-019-01510-x

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  • DOI: https://doi.org/10.1007/s12648-019-01510-x

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