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Hydromagnetic nanofluid flow past a stretching cylinder embedded in non-Darcian Forchheimer porous media

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Abstract

The present article presents the hydromagnetic nanofluid flow past a stretching cylinder embedded in non-Darcian Forchheimer porous media by using Buongiorno’s mathematical model (Buongiorno in J Heat Transf 128:240–250, 2006; Nadeem et al. in J Taiwan Inst Chem Eng 45:121, 2014, Nadeem et al. Appl Nanosci 4:625–631, 2014). Thermal radiation via Roseland’s approximation (Akbar et al. in Chin J Aeronaut 26:1389–1397, 2013; Nadeem and Haq in J Aerosp Eng 28:04014061, 2012), Brownian motion, thermophoresis and Joule heating effects are also considered. To explore thermal characteristics, prescribed heat flux and prescribed mass flux boundary conditions are deployed. Governing flow problem consists of PDEs in the cylindrical form, which are converted into system of nonlinear ODEs by applying applicable similarity transforms. ODEs are tackled by RK–Fehlberg fourth–fifth-order numerical integration scheme with shooting algorithm. Impact of numerous involving physical parameters on flow features like temperature distribution, velocity distribution, Sherwood number, local Nusselt number and skin friction coefficient is shown through graphs and tables.

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Abbreviations

\( C_{\infty } \) :

Ambient concentration (kg/m3)

\( T_{\infty } \) :

Ambient temperature (K)

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

Brownian coefficient

\( {\text{Nb}} \) :

Brownian motion parameter

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

Concentration at wall (kg/m3)

\( f \) :

Dimensionless stream function

\( \theta \) :

Dimensionless temperature

\( {\text{Ec}} \) :

Eckert number

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

Local Reynolds number

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

Drag coefficient

\( B_{0} \) :

Magnetic field strength (T)

\( k_{2} \) :

Mean absorption coefficient

\( K^{*} \) :

Porosity parameter

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

Nusselt number

\( {\text{Rd}} \) :

Radiation parameter

\( \Pr \) :

Prandtl number

\( T \) :

Nanofluid temperature (K)

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

Temperature at wall (K)

\( C \) :

Nanoparticles concentration (kg/m3)

\( q \) :

Radiative heat flux

\( k \) :

Thermal conductivity (W/(m·K))

\( {\text{Cf}} \) :

Skin friction coefficient

\( M \) :

Magnetic parameter

\( k_{1} \) :

Permeability of porous medium

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

Sherwood number

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

Thermophoretic coefficient

\( {\text{Nt}} \) :

Thermophoretic parameter

\( u,\;v \) :

Velocity in x and r direction (m/s)

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

Wall heat flux (J/s)

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

Wall velocity (m/s)

\( \infty \) :

Ambient

f :

Fluid

p :

Particle

w :

Wall

\( \varepsilon \) :

Curvature parameter

\( \rho \) :

Density

\( \phi \) :

Dimensionless nanoparticles concentration

\( \mu \) :

Dynamic viscosity

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

Effective heat capacity of nanoparticle material

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

Heat capacity of base fluid

\( \nu \) :

Kinematic viscosity

\( F^{*} \) :

Local inertia coefficient

\( \sigma \) :

Magnetic permeability

\( \tau \) :

Ratio of heat capacities of nanoparticles to base fluid

\( \xi \) :

Similarity variable

\( \sigma^{*} \) :

Stefan–Boltzmann constant

\( \alpha \) :

Thermal diffusivity (m2/s)

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

Wall mass flux (kg/s)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, FBAS, International Islamic University, Islamabad, Pakistan

    Ahmad Zeeshan & Muhammad Muddassar Maskeen

  2. Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, 47040, Pakistan

    Obaid Ullah Mehmood

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  1. Ahmad Zeeshan
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  2. Muhammad Muddassar Maskeen
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  3. Obaid Ullah Mehmood
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Correspondence to Obaid Ullah Mehmood.

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Zeeshan, A., Maskeen, M.M. & Mehmood, O.U. Hydromagnetic nanofluid flow past a stretching cylinder embedded in non-Darcian Forchheimer porous media. Neural Comput & Applic 30, 3479–3489 (2018). https://doi.org/10.1007/s00521-017-2934-7

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