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Impacts of nanoparticle shapes on Ag-water nanofluid thin film flow through a porous medium with thermal radiation and ohmic heating

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Abstract

Our present study intends to examine the unsteady thin film flow and heat transfer of \({{\rm Ag}{-}{\rm H}_2 {\rm O}}\)nanofluid on a stretching sheet embedded in a porous medium. Radiative heat, Ohmic heating with slip, and convective boundary conditions are taken into account. The effect of various nanoparticle shape factors is also investigated. Nanofluid thermal conductivity depends on nanoparticle shape. The primary time-dependent equations are transformed using similarity transformation and solved using a prominent Runge–Kutta fourth-order and shooting iterative process. Graphs and numerical values of physical factors pertinent to fluid flow are obtained using MATLAB software. The skin friction coefficient and the heat transfer rate are also investigated and tabulated. Results reveal that magnetic, porosity, and unsteady parameters all have a diminishing impact on velocity profiles. Radiation parameter has a positive impact on temperature distribution, while an opposite trend is observed for magnetic fields. Findings indicate that magnetic field and porosity enhance the skin friction coefficient, whereas heat transfer rate increases with Biot number and slip parameter. Platelet-shaped nanoparticles are shown to be the most efficient in heat transfer. The outcomes were compared to previously reported results and found excellent agreement.

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Abbreviations

a, b :

Stretching rate constants    (\({\rm s}^{-1}\))

\(A_1, A_2\) :

Viscosity enhancement coefficients    (–)

B :

Applied magnetic field    (Tesla)

\(c_{\rm p}\) :

Specific heat    (\({\rm J\,K}^{-1}\))

\(Cf_{\rm x}\) :

Skin friction coefficient    (–)

Ec:

Eckert number    (–)

f :

Dimensionless velocity function    (–)

h :

Height    (m)

\(k^*\) :

Absorption coefficient    (\({\rm m}^{-2}\))

\(k_{\rm f}\) :

Thermal conductivity of base fluid    (\({\rm W\,m}^{-1}\,{\rm K}^{-1}\))

\(k_{\rm nf}\) :

Thermal conductivity of nanofluid    (\({\rm W\,m}^{-1}\,{\rm K}^{-1}\))

K :

Variable permeability of porous medium    (\({\rm m}^2\))

\(K_1\) :

Porosity parameter    (–)

\(K_2\) :

Slip parameter    (-)

m :

Shape factor    (–)

M :

Magnetic parameter    (–)

\({\rm Nu}_{\rm x}\) :

Nusselt number    (–)

Pr:

Prandtl number    (–)

\(q_{\rm w}\) :

Heat flux    (\({\rm W\,m}^{-2}\))

R :

Radiation parameter    (–)

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

Reynolds number    (–)

S :

Unsteadiness parameter    (–)

T :

Temperature field    (K)

\(T_0\) :

Temperature at the slit    (K)

\(T_{\rm ref}\) :

Constant reference temperature    (K)

\(T_{\rm s}\) :

Stretched sheet’s temperature    (K)

u, v :

Velocity component in x, y axis    (\(m s^{-1}\))

U :

Stretching sheet velocity    (\(m s^{-1}\))

\(\beta\) :

Film thickness    (–)

\(\eta\) :

Similarity variable    (–)

\(\gamma\) :

Biot number    (–)

\(\mu _{\rm f}\) :

Dynamic viscosity of base fluid    (\({\rm Nsm}^{-2}\))

\(\mu _{\rm nf}\) :

Dynamic viscosity of nanofluid    (\({\rm Nsm}^{-2}\))

\(\nu _{\rm f}\) :

Kinematic viscosity of base fluid    (\({\rm m}^2\,{\rm s}^{-1}\))

\(\nu _{\rm nf}\) :

Kinematic viscosity of nanofluid    (\({\rm m}^2\,{\rm s}^{-1}\))

\(\rho _{\rm f}\) :

Density of base fluid    (\({\rm kg\,m}^{-3}\))

\(\rho _{\rm nf}\) :

Density of nanofluid    (\({\rm kg\,m}^{-3}\))

\(\rho _{\rm s}\) :

Density of nanoparticle    (\({\rm kg\,m}^{-3}\))

\((\rho c_{\rm p})_{\rm nf}\) :

Heat capacitance of nanofluid    (\({\rm J\,kg}^{-1}\,{\rm K}^{-1}\))

\(\sigma _{\rm nf}\) :

Nanofluid electrical conductivity    (\({\rm Sm}^{-1}\))

\(\sigma _{\rm s}\) :

Nanoparticle electrical conductivity    (\({\rm Sm}^{-1}\))

\(\sigma ^*\) :

Stefan–Boltzmann constant    (\({\rm Wm}^{-2}{\rm s}^{-4}\))

\(\tau _{\rm w}\) :

Shear stress    (\({\rm Nm}^{-2}\))

\(\theta\) :

Dimensionless temperature function    (–)

\(\phi _1\) :

Volume fraction    (–)

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  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    G Gomathy & B. Rushi Kumar

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Gomathy, G., Kumar, B.R. Impacts of nanoparticle shapes on Ag-water nanofluid thin film flow through a porous medium with thermal radiation and ohmic heating. J Therm Anal Calorim (2023). https://doi.org/10.1007/s10973-023-12609-z

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