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Abstract
Numerical analysis of hydromagnetic mixed convective transport in a differentially heated vertical lid-driven square enclosure is performed in this article. Two heat-conducting solid circular cylinders of identical shape are placed within the enclosure. The cylinders may be either stationary or rotating about their centroidal axes. Two different combinations of cylinder rotations are considered: one when the top cylinder rotates and the bottom one is kept stationary, and the other when the bottom cylinder rotates and the top one is kept stationary. Simulations are performed for a range of controlling parameters such as the Richardson number (1 to 10), Hartmann number (0 to 50), and dimensionless rotational speed (0 to 5), keeping the Reynolds number based on the lid velocity fixed as 100. Furthermore, three different Prandtl numbers, 0.02, 0.71, and 7, are considered. The flow and thermal fields are analyzed through streamline and isotherm plots for various Hartmann and Richardson numbers and rotational speeds. Additionally, the Nusselt number and the bulk fluid temperature are also computed to understand the effects of Hartmann and Richardson numbers and rotational speeds on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder.
NOMENCLATURE
| B0 | = | magnetic field strength (Wb/m2) |
| cp | = | specific heat at constant pressure (J/kg-K) |
| CCW | = | counterclockwise |
| CFD | = | computational fluid dynamics |
| CW | = | clockwise |
| Ha | = | Hartmann number, |
| kf | = | thermal conductivity of fluid (W/m-K) |
| ks | = | thermal conductivity of solid (W/m-K) |
| K | = | solid fluid thermal conductivity ratio, |
| L | = | length of square enclosure (m) |
| MHD | = | magnetohydrodynamics |
| N | = | Stuart number, |
| Nu | = | Nusselt number, |
| p | = | pressure (N/m2) |
| P | = | dimensionless pressure, |
| Pr | = | Prandtl number, |
| QUICK | = | quadratic upstream interpolation convective kinetics |
| Ra | = | Rayleigh number, |
| Re | = | Reynolds number, |
| Ri | = | Richardson number, |
| SIMPLEC | = | Semi-Implicit Method for Pressure-Linked Equations—Consistent |
| Ta | = | Taylor number, |
| u, v | = | velocity components (m/s) |
| U, V | = | dimensionless velocity components, |
| V0 | = | lid velocity (m/s) |
| = | enclosure volume (m3) | |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates, |
Greek Symbols
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| φ | = | polar angle |
| θ | = | dimensionless temperature, |
| ρ | = | density of fluid (kg/m3) |
| σ | = | electrical conductivity ( |
| = | kinematic viscosity of fluid (m2/s) | |
| ω | = | rotational speed (rad/s) |
| Ω | = | dimensionless rotational speed, |
Subscripts
| av | = | average |
| c | = | cold |
| f | = | fluid |
| h | = | hot |
| s | = | solid |
Additional information
Notes on contributors
Dipankar Chatterjee
Dipankar Chatterjee is a senior scientist at the CSIR–Central Mechanical Engineering Research Institute, India. Earlier he was associated with LPMI, Arts et Métiers Paris Tech, France, as a postdoctoral researcher. He received his Ph.D. from the Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, India. He has published 90 international journal and conference papers. His main interests are computational modeling of fluid flow and heat transfer over bluff obstacles, turbulence, phase change and reactive flow process modeling, lattice Boltzmann modeling, and electromagnetohydrodynamic interactions in macro- and microflows.
Pabitra Halder
Pabitra Halder is an assistant professor at the Indian Institute of Engineering Science and Technology, Shibpur, India. Earlier he was associated with CSIR–Central Mechanical Engineering Research Institute, India. He received his Ph.D. in engineering from the Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur. His area of research includes high-speed compressible flow CFD, wake dynamics, and computational heat transfer. He has about 15 research publications in peer-reviewed journals and conferences.