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Simulation by Heat and Mass Lines Technique of Double-Diffusive Convection Under Magnetic Field of Exponentially Heated and Soluted Enclosure

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Abstract

The present numerical study explores an unsteady double-diffusive convection phenomenon for different fluids (air at \(17^\circ \text {C}\), water at \(17^ \circ \text {C}\), and ethylene glycol \(50\%\) at \(44^ \circ \text {C}\) ) under the influence of uniform magnetic field induced along the horizontal direction. Temperature and solute vary exponentially at left solid wall, whereas right-solid wall maintains lower temperature and solute. Furthermore, horizontal walls are insulated and impermeable. After transferring flow equations into stream function vorticity form, an iterative second-order finite difference based method along with successive over-relaxation (SOR) technique has been utilized to solve them. New types of visualization techniques are used to explore the heat and mass flows, known as heat and mass lines visualization techniques. In-house CFD (computational fluid dynamics) code was developed to solve the flow governing equation used after validation with experimental and numerical benchmarks results available in the literature. The influence of various forces (viscous, buoyancy, and electromagnetic) and different type of diffusivity (momentum, thermal, and mass) on flow structure, heat, and mass flows inside the enclosure in addition to local and overall heat and mass transfers have been discussed. Results showed that solute mixing could be minimized by raising the Lewis number and thus direct mass transfer maximize. When Rayleigh number increases from \(10^3\) to \(10^4\) and \(10^4\) to \(10^5\) enhancement in overall heat transfer are about \(112\%\) and \(117\%\), respectively, whereas overall mass transfer has been enhanced by \(116\%\) and \(94\%\). As Hartmann number increases from \({\text {Ha}}=0\) to \({\text {Ha}}=20\), there is a significant fall in the overall heat and mass transfers by \(29\%\) and \(15\%\), respectively. It can be concluded that direct heat and mass transfer can be optimized by imposing a magnetic field of suitable strength.

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Abbreviations

\(\left( u',v'\right) \) :

Dimensional velocity components \(\left( \mathrm {ms}^{-1}\right) \)

\(\left( U,V\right) \) :

Dimensionless velocity components

\(\left( x',y'\right) \) :

Dimensional coordinates \(\left( \text {m}\right) \)

\(\left( X,Y\right) \) :

Dimensionless coordinates

\(\textit{g}\) :

Gravitational acceleration \(\left( \mathrm {ms}^{-2}\right) \)

\(\text {C}\) :

Celsius

D :

Mass diffusivity \(\left( \mathrm {m}^{2}\mathrm {s}^{-1}\right) \)

H :

Enclosure side

N :

Buoyancy ratio

P :

Dimensionless pressure

p :

Dimesional pressure \(\left( \mathrm {N}\mathrm {m}^{-2}\right) \)

S :

Dimensionless solute

\(S'\) :

Dimensional solute \(\left( \mathrm {kgm}^{-3}\right) \)

T :

Dimensionless temperature

t :

Dimensionless time

\(T'\) :

Dimensional temperature \(\left( \mathrm {K}\right) \)

\(t'\) :

Dimensional time \(\left( \mathrm {s}\right) \)

CFD:

Computational Fluid Dynamics

\(\alpha \) :

Thermal diffusivity \(\left( \mathrm {m}^{2}\mathrm {s}^{-1}\right) \)

\(\mu \) :

Dynamic viscosity \(\left( \mathrm {Kg}\mathrm {m}^{-1}\mathrm {s}^{-1}\right) \)

\(\nu \) :

Kinematic viscosity \(\left( \mathrm {m}^{2}\mathrm {s}^{-1}\right) \)

\(\Omega \) :

Dimensionless vorticity

\(\omega \) :

Dimensional vorticity

\(\rho \) :

Fluid density \(\left( \mathrm {Kg}\mathrm {m}^{-3}\right) \)

\(\sigma \) :

Electrical conductivity \(\left( \mathrm {W}\mathrm {m}^{-1}\mathrm {K}^{-1}\right) \)

k :

Thermal conductivity \(\left( \mathrm {W}\mathrm {m}^{-1}\mathrm {K}^{-1}\right) \)

\(\text {max}\) :

Maximum

\(\text {min}\) :

Minimum

h :

Higher

l :

Lower

\('\) :

Dimensional variables

\(^\circ \) :

Degree

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

    Dwesh K. Singh

  2. Department of Mathematics, Maharajah Agrasen College, University of Delhi, Delhi, India

    Sushil Yadav

  3. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India

    Durgesh Kushawaha

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Singh, D.K., Yadav, S. & Kushawaha, D. Simulation by Heat and Mass Lines Technique of Double-Diffusive Convection Under Magnetic Field of Exponentially Heated and Soluted Enclosure. Int. J. Appl. Comput. Math 7, 234 (2021). https://doi.org/10.1007/s40819-021-01189-x

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