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Abstract
In the present study, analysis has been performed to investigate the surface radiation effect on hydro-magnetic buoyant convection of an electrically conducting fluid in a differentially heated cavity. The fluid is enclosed within a gray chamber and imposed with a uniform magnetic field orthogonal to the vertical cross-sectional plane of the chamber. Numerical solution is done by control volume integration. A modified Marker and Cell method is used for the solution of the governing equation for flow transport. A gradient-dependent consistent hybrid upwind scheme of second order is used for discretization of the convective terms. The transport equation for surface radiation is solved using a net radiation method. Cross-string method is used to compute the view factor. Comprehensive studies on the controlling parameters that affect the flow and heat transfer characteristics are delineated. The results are presented in tabular and graphical form. The heat transfer and flow characteristics are depicted in form of isotherms and streamlines revealing the concealed physics of a complex phenomenon.
ACKNOWLEDGMENTS
The authors acknowledge Prof. S. N. Panigrahi (Indian Institute of Technology Bhubaneswar) and Prof. T. Sundararajan (Indian Institute of Technology Madras) for all their help, support, and motivation.
NOMENCLATURE
| B | = | magnetic field, Wbm−2 |
| B0 | = | magnitude of the applied magnetic field, Wbm−2 |
| Cp | = | specific heat capacity, J kg−1 K−1 |
| E*b | = | dimensional emissive power, Wm−2 |
| Eb | = | dimensionless emissive power, |
| E | = | electric field, V m−1 |
| = | electromagnetic body force per unit volume, Nm−3 | |
| = | non electromagnetic body force per unit volume, Nm−3 | |
| Fi − j | = | view factor between segment i and j, dimensionless |
| g | = | acceleration due to gravity, ms−2 |
| G* | = | dimensional irradiation, Wm−2 |
| G | = | dimensionless irradiation, |
| = | Hartmann number, dimensionless | |
| j | = | dimensional radiosity, Wm−2 |
| J | = | dimensionless radiosity, |
| Je | = | current density, Am−2 |
| k | = | thermal conductivity, Wm−1 K−1 |
| L1, L2, L3 | = | dimension of the cavity, m |
| L = L1 = L2 | = | characteristic length, m |
| Nu | = | local Nusselt number, dimensionless |
| = | average Nusselt number, dimensionless | |
| p | = | dimensional pressure, Nm−2 |
| P | = | dimensionless pressure, |
| = | Prandtl number, dimensionless | |
| qr | = | dimensional net radiative heat flux, W m−2 |
| Qr | = | dimensionless net radiative heat flux, |
| = | Rayleigh number, dimensionless | |
| = | radiation conduction number, dimensionless | |
| = | positional vector, m | |
| r, r′ | = | dimensionless positional vector, |
| t | = | time, s |
| T | = | temperature in absolute scale, K |
| u, v, w | = | dimensional velocity component, m s−1 |
| U, V, W | = | dimensionless velocity component, |
| V | = | velocity, ms−1 |
| x, y, z | = | dimensional coordinates, m |
| X, Y, Z | = | dimensionless coordinate, |
Greek Symbols
| α | = | thermal diffusivity, m2 s−1 |
| α′ | = | absorptivity of the wall, dimensionless |
| βT | = | coefficient of thermal expansion, K−1 |
| ϵ | = | emissivity, dimensionless |
| δX, δY, δZ | = | grid size in X, Y, Z direction respectively, dimensionless |
| μ | = | dynamic viscosity, kgm−1s−1 |
| ν | = | kinematic viscosity, m2 s−1 |
| Θ | = | dimensionless temperature, |
| τ | = | dimensionless time, |
| ρ | = | density, kgm−3 |
| ρe | = | charge density, Cm−3 |
| ϕ | = | electric potential, Vm−1 |
| σe | = | electrical conductivity of the medium, Ω−1 m−1 |
| σ | = | Stefan-Boltzmann constant, Wm−2 K−4 |
Subscripts
| L | = | lower |
| H | = | higher |
| C | = | convective |
| R | = | radiative |
| 0 | = | reference |
Additional information
Notes on contributors
Sofen K. Jena
Sofen K. Jena is a Ph.D. student in the Department of Mechanical Engineering, Jadavpur University, Kolkata, India. He is working under the supervision of Prof. Swarup K. Mahapatra and Prof. Amitava Sarkar. In the past, he worked as a junior research fellow in the School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, India, and as a visiting research scholar at Fraunhofer ITWM, Kaiserslautern, Germany. His research interests include magnetohydrodynamics, conjugate heat and mass transfer, flow in porous media, double diffusion, non-Newtonian flow, and thermal radiation modeling.
Swarup K. Mahapatra
Swarup K. Mahapatra is working as Professor and Head, School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, India. He has 24 years of teaching and research experience. He is involved in many research projects. His research interests are computational fluid dynamics, conjugate heat transfer, and radiative heat transfer modeling. In addition, he is working on the development of mathematical model for transient radiative heat transfer for its application in the field of bio-heat transfer. He received his Ph.D. from Jadavpur University, India, in 2000. He has also organized many conferences and short-term courses in his field of research.