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Thermophysical aspects of stagnation point magnetonanofluid flow yields by an inclined stretching cylindrical surface: a non-Newtonian fluid model

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Abstract

In various attempts, researchers considered Eyring–Powell fluid flow past a flat stretching surface supported with different physical effects, but as yet few explorations are proposed with accuracy regarding cylindrical stretching surface. In this work, we have considered magnetohydrodynamic Eyring–Powell nanofluid flow brought by an included stretching cylindrical surface under the region of stagnation point. To report thermophysical aspects, Joule heating, thermal radiations, mixed convection, temperature stratification, and heat generation effects are taken into account. The flow conducting differential equations are fairly converted into system of coupled non-linear ordinary differential equations by means of appropriate transformation. A numerical communication is made against these obtained coupled equations through shooting method supported with fifth-order Runge–Kutta scheme. It is found that fluid temperature shows an inciting nature towards Eckert number, thermophoresis parameter, Brownian motion parameter, thermal radiation parameter, and heat generation parameter, but it reflects opposite trends for Lewis number and thermal stratification parameter. Furthermore, the obtained results are validated by providing comparison with existing values which set a benchmark of quality of computational algorithm.

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Abbreviations

\(\overset{\lower0.1em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u} ,\,\,\overset{\lower0.1em\hbox{$\smash{\scriptscriptstyle\frown}$}}{v}\) :

Velocity components

\(\nu\) :

Kinematic viscosity

g :

Gravity

\(\beta ,\,c,\,M,\,\,\lambda\) :

Eyring–Powell fluid parameters

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

Prescribed surface temperature

\(T_{0}\) :

Reference temperature

\(L\) :

Reference length

\(\alpha\) :

Inclination of cylinder

\(\psi\) :

Stream function

\(\alpha_{1}\) :

Thermal stratification parameter

\(Ec\) :

Eckert number

\(F'(\eta )\) :

Velocity of fluid

\(k\) :

Thermal conductivity

\(V\) :

Velocity vector

\(\overset{\lower0.1em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u}_{e}\) :

Free stream velocity

\(T\) :

Fluid temperature

\(R\) :

Radius of cylindrical surface

\(Gr\) :

Temperature Grashof number

\(b,c,d,e\) :

Positive constant

\(Re_{x}\) :

Local Reynolds number

\(Q_{0}\) :

Heat generation coefficient

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

Thermal expansion coefficient

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

Skin friction coefficient

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

Brownian diffusion coefficient

\(C\) :

Fluid concentration

\(C_{0}\) :

Reference concentration

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

Thermal radiation parameter

\(Nb\) :

Brownian motion parameter

\(Le\) :

Lewis number

\(R_{0}\) :

Rate of chemical reaction

\(q_{r}\) :

Roseland radiative heat flux

\(x,r\) :

Space variable

\(\rho\) :

Fluid density

\(\mu\) :

Dynamic viscosity

\(K\) :

Curvature parameter

\(T_{\infty } (x)\) :

Variable ambient temperature

\(U_{0}\) :

Reference velocity

\(F(\eta )\) :

Dimensionless variable

\(Pr\) :

Prandtl number

\(\eta\) :

Similarity variable

\(\gamma\) :

Magnetic field parameter

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

Specific heat at constant pressure

\(A\) :

Velocities ratio parameter

\(N\) :

Ratio of concentration to thermal buoyancy forces

\(\tau_{w}\) :

Shear stress

\(U(x)\) :

Stretching velocity

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

Mixed convection parameter

\(Gr*\) :

Concentration Grashof number

\(Q\) :

Heat generation parameter

\(B_{0}\) :

Uniform magnetic field

\(Nu_{x}\) :

Local Nusselt number

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

Concentration expansion coefficient

\(\alpha *\) :

Thermal diffusivity

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

Thermophoretic diffusion coefficient

\(C_{w}\) :

Prescribed surface concentration

\(C_{\infty }\) :

Variable ambient concentration

\(Rc\) :

Chemical reaction parameter

\(Nt\) :

Thermophoresis parameter

\(\alpha_{2}\) :

Solutal stratification parameter

\(Sh\) :

Local Sherwood number

\(\tau\) :

Ratio of nanoparticles heat capacity to the base fluid heat capacity

\(\prime\) (prime):

Denotes differentiation w.r.t variable \(\eta\)

\(w\) :

Condition at cylindrical surface

\(\infty\) :

Condition away from the surface

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Authors and Affiliations

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

    Khalil Ur Rehman, Abid Ali Khan & M. Y. Malik

  2. Faculty of Military Science, Stellenbosch University, Private X2, Saldanha, 7395, South Africa

    O. D. Makinde

Authors
  1. Khalil Ur Rehman
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  2. Abid Ali Khan
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  3. M. Y. Malik
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  4. O. D. Makinde
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Correspondence to Khalil Ur Rehman.

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In the present work, we have not used any material from published articles; therefore, we have no conflict of interest.

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Technical Editor: Cezar Negrao.

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Rehman, K.U., Khan, A.A., Malik, M.Y. et al. Thermophysical aspects of stagnation point magnetonanofluid flow yields by an inclined stretching cylindrical surface: a non-Newtonian fluid model. J Braz. Soc. Mech. Sci. Eng. 39, 3669–3682 (2017). https://doi.org/10.1007/s40430-017-0860-3

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  • DOI: https://doi.org/10.1007/s40430-017-0860-3

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