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ABSTRACT
In this paper double diffusive natural convection in a square cavity in the presence of external magnetic field has been studied numerically by Galerkin’s weighted residual finite element method using velocity-vorticity formulation. Simulation results are reported for 0 < Ha < 200, buoyancy ratio, 2 < N < 2, 104 < Ra < 106 and field inclination angle varying from 00 to 3600 for different fluid systems, namely gas, water, and liquid Gallium. Results indicate that the streamline pattern is greatly influenced by the direction and intensity of magnetic field and at Ra = 1.0e5, the increase in Ha from 0 to 30 has resulted in a decrease in Nusselt number and Sherwood number by about 72% and 78% respectively. The inclination angle has played an important role in the suppression of heat and mass transfer, maximum suppression is experienced at Θ = 45 and 270 while minimum is recorded at Θ = 135 and 315. Liquid Gallium showed the least response to change in magnetic field intensity compared to other two fluids.
Nomenclature
| C | = | concentration of species, kg/m3 |
| D | = | binary diffusion coefficient, m2/s |
| g | = | gravitational acceleration, m/s2 |
| Gr | = | Grashof number |
| Ha | = | Hartmann number |
| N | = | buoyancy ratio |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| Sc | = | Schmidt number |
| Sh | = | Sherwood number |
| t | = | time, s |
| T | = | temperature, K |
| u,v | = | horizontal and vertical velocity components, m/s |
| U, V | = | nondimensional velocity components |
| U0 | = | lid velocity, m/s |
| x, y | = | horizontal and vertical coordinates, m |
| X, Y | = | nondimensional coordinates |
| α | = | thermal diffusivity, m2/s |
| βC | = | concentration volumetric expansion coefficient, m3/kg |
| βT | = | thermal volumetric expansion coefficient, K−1 |
| μ | = | dynamic viscosity, kg/s · m |
| υ | = | kinematic viscosity, m2/s |
| ϕ | = | nondimensional concentration of species |
| θ | = | nondimensional temperature |
| Θ | = | magnetic field inclination angle measure from horizontal anticlockwise |
| ρ | = | density, kg/m3 |
| τ | = | nondimensional time |
| ω | = | vorticity, s—1 |
| Ω | = | nondimensional vorticity |
| Δ | = | difference |
| σ | = | electrical conductivity, s/m |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |
Nomenclature
| C | = | concentration of species, kg/m3 |
| D | = | binary diffusion coefficient, m2/s |
| g | = | gravitational acceleration, m/s2 |
| Gr | = | Grashof number |
| Ha | = | Hartmann number |
| N | = | buoyancy ratio |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| Sc | = | Schmidt number |
| Sh | = | Sherwood number |
| t | = | time, s |
| T | = | temperature, K |
| u,v | = | horizontal and vertical velocity components, m/s |
| U, V | = | nondimensional velocity components |
| U0 | = | lid velocity, m/s |
| x, y | = | horizontal and vertical coordinates, m |
| X, Y | = | nondimensional coordinates |
| α | = | thermal diffusivity, m2/s |
| βC | = | concentration volumetric expansion coefficient, m3/kg |
| βT | = | thermal volumetric expansion coefficient, K−1 |
| μ | = | dynamic viscosity, kg/s · m |
| υ | = | kinematic viscosity, m2/s |
| ϕ | = | nondimensional concentration of species |
| θ | = | nondimensional temperature |
| Θ | = | magnetic field inclination angle measure from horizontal anticlockwise |
| ρ | = | density, kg/m3 |
| τ | = | nondimensional time |
| ω | = | vorticity, s—1 |
| Ω | = | nondimensional vorticity |
| Δ | = | difference |
| σ | = | electrical conductivity, s/m |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |