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Heat transfer of MHD natural convection Casson nanofluid flows in a wavy trapezoidal enclosure

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Abstract

A two-dimensional problem featuring the buoyancy-driven MHD nanofluid flow in a wavy trapezoidal enclosure is considered. The enclosure’s bottom wall is wavy with a higher temperature than the two sidewalls. The top wall is assumed to be insulated. The chamber is filled with nanofluid where the water Casson liquid is considered as base fluid and the aluminium oxide \(\text {Al}_{2}\text {O}_{3}\) as the nanoparticles. The viscous and Joule dissipation effects are incorporated in the model, considering the temperature difference due to differential wall temperature. The conservation equations are used for the description of flow and heat transfer. The Galerkin finite element method is employed to solve the resulting non-dimensionalized unsteady initial and boundary value problem using Taylor-Hood elements to avoid numerical instabilities. The influence of the Casson parameter, nanoparticle volume fraction and Hartmann number on the streamlines and isotherms are discussed. The rate of heat transfers near the bottom wall is analysed through simulated data and the sensitivity of the average Nusselt number is performed using the response surface methodology (RSM). It is found that the heat transfer rate increases as the Hartmann number increases. The Casson parameter and the nanoparticle volume fraction significantly influence the heat transfer rate in high Hartmann number flows.

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Abbreviations

\(\varGamma \) :

Boundary wall

\(\gamma \) :

Casson parameter

\(\kappa \) :

Thermal conductivity (Wm\(^{-1}\)K\(^{-1}\))

\(\mu \) :

Dynamic viscosity (kgm\(^{-1}\)s\(^{-1}\))

\(\mu _{B}\) :

Plastic dynamic viscosity (kg m\(^{-1}\)s\(^{-1}\))

\(\varOmega \) :

Fluid domain

\(\phi \) :

Solid volume fraction

\(\psi \) :

Stream function

\(\rho \) :

Density (kgm\(^{-3}\))

\(\sigma \) :

Electrical conductivity (\(\varOmega ^{-1}\)m\(^{-1}\))

\(\tau \) :

Shear stress (kg m\(^{-1}\)s\(^{-2}\))

Ec :

Eckert number

Nu :

Nusselt number

Pr :

Prandtl number

Ra :

Rayleigh number

\((T_{1}, T_{2})\) :

Wall temperature (K)

(u, v):

The x and y components of velocity (ms\(^{-1}\))

(x, y):

Distance along x and y coordinates (m)

\(\beta \) :

Coefficient of thermal expansion (K\(^{-1}\))

\(B_{0}\) :

Induced magnetic field (kgA\(^{-1}\)s\(^{-2}\))

\(c_{p}\) :

Specific heat at constant pressure (Jkg\(^{-1}\)K\(^{-1}\))

e :

Deformation rate tensor (s\(^{-1}\))

g :

Gravitational acceleration (ms\(^{-2}\))

h :

Height of the enclosure (m)

l :

Length of the bottom wall (m)

p :

Pressure field (kg m\(^{-1}\)s\(^{-2}\))

\(p_{y}\) :

Yield stress (kg m\(^{-1}\)s\(^{-2}\))

T :

Temperature (K)

t :

Time (s)

av :

Average

f :

Fluid

nf :

Nanofluid

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Calicut, Kerala, 673601, India

    Eda Suresh Reddy & Satyananda Panda

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Suresh Reddy, E., Panda, S. Heat transfer of MHD natural convection Casson nanofluid flows in a wavy trapezoidal enclosure. Eur. Phys. J. Spec. Top. 231, 2733–2747 (2022). https://doi.org/10.1140/epjs/s11734-022-00609-3

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