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Magneto-Hydro-Dynamic Generator with Joule Heating and Viscous Dissipation: An Analytic Investigation of Mixed Convection Flow

  • Research Article-Mechanical Engineering
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Abstract

This study investigates mixed convection heat transfer in the vertical channel of magneto-hydro-dynamic (MHD) generators, considering the effects of magnetic fields, Joule heating, and viscous dissipation. The key objectives are to derive an accurate analytical solution for the complex non-linear heat transfer equations and provide insights into optimizing MHD generator design. An innovative mathematical approach involving differential transforms and power series expansions is utilized to solve the coupled partial differential equations. Validation is conducted by comparing results to existing numerical and analytical research. Parametric analysis of dimensionless quantities reveals that increasing the Hartmann number enhances fluid velocity in the channel core but suppresses temperature near the walls due to the magnetic dam** effect. Higher Λ (ratio of buoyancy forces to viscous forces) values decrease both velocity and temperature profiles. The magnetic field effectively regulates flow and thermal behavior. Joule heating power rises with a higher Hartmann number but declines as Λ increases due to heightened viscous dissipation. These outcomes elucidate the impacts of critical parameters on heat transfer characteristics and performance. The robust analytical approach and findings pave the pathway for the optimized design of efficient MHD generators. Further work can examine additional configurations and parametric effects to deepen understanding of magneto-hydrodynamic mixed convection phenomena.

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Abbreviations

\(\Lambda\) :

Ratio of buoyancy forces to viscous forces

\(\mathop{B}\limits^{\rightharpoonup}\) :

Magnetic induction field (T)

\(B\) :

Modulus of \(\mathop{B}\limits^{\rightharpoonup}\) (T)

\(\vec{E}\) :

Induced electric field (V/m)

\(\vec{f}\) :

Magnetic body force (N/m3)

\(\vec{g}\) :

Acceleration due to the gravity (m/s2)

\(g\) :

Modulus of \(\vec{g}\) (m/s2)

\({\text{Gr}}\) :

Grashof number (-)

\(\vec{J}\) :

Current density (A/m2)

\(k\) :

Thermal conductivity of the fluid (W/m K)

\(L\) :

Channel width (m)

\({\text{M}}\) :

Hartmann number (-)

\(P\) :

Hydrodynamic pressure (Pa)

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

Power generated per unit volume (W/m3)

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

Reynolds number (-)

\(T\) :

Temperature (K)

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

Wall temperature (K)

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

Reference temperature (K)

\(u\) :

Dimensionless velocity (-)

\(\vec{U}\) :

Velocity (m/s)

\(U\) :

Vertical velocity component (m/s)

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

Reference velocity (m/s)

\(X\) :

Vertical Cartesian coordinate (m)

\(Y\) :

Horizontal Cartesian coordinate (m)

\(y\) :

Dimensionless coordinate (-)

\(\phi\) :

Dimensionless flux (-)

\(\mu\) :

Dynamic viscosity (Pa s)

\(\nu\) :

Kinematic viscosity (m2/s)

\(\theta\) :

Dimensionless temperature (-)

\(\rho\) :

Mass density (kg/m3)

\(\sigma\) :

Electric conductivity (S/m)

\({\text{JH}}\) :

Joule heating (W/m3)

\({\text{VD}}\) :

Viscous dissipation (W/m3)

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Qom, P.O. Box 6765-1719, Qom, Iran

    Mojtaba Babaelahi & Somayyeh Sadri

  2. Thermal Cycles and Heat Exchangers Department, Niroo Research Institute, Tehran, Iran

    Mojtaba Babaelahi & Somayyeh Sadri

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  1. Mojtaba Babaelahi
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Babaelahi, M., Sadri, S. Magneto-Hydro-Dynamic Generator with Joule Heating and Viscous Dissipation: An Analytic Investigation of Mixed Convection Flow. Arab J Sci Eng 49, 11445–11455 (2024). https://doi.org/10.1007/s13369-023-08693-w

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