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ABSTRACT
The aim of the present study is to investigate the effect of the moving wall’s direction on mixed convective flow and heat transfer in an inclined lid-driven square cavity. Sinusoidal heating is applied on the left wall while the right wall is cooled at a constant temperature. The bottom and top walls are taken to be adiabatic. The results are presented graphically in the form of streamlines, isotherms, velocity profiles, and Nusselt numbers to understand the influence of the different directions of the moving wall, Richardson number, and cavity inclination. It is observed that the flow field and temperature distribution in the cavity are affected by the moving wall’s direction. It is also observed that the heat transfer is more pronounced at low Richardson number when the wall is moving to the left.
NOMENCLATURE
| g | = | gravitational acceleration, ms−2 |
| Gr | = | Grashof number, βg(Tref − Tc)L3/ν2, |
| L | = | enclosure height and length, m |
| Nuloc | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | pressure, Pa |
| Pr | = | Prandtl number, ν/α |
| Re | = | Reynold number, U0L/ν |
| Ri | = | Richardson number, Gr/Re2 |
| t | = | dimensionless time |
| t′ | = | time, s |
| T | = | temperature, K |
| u, v | = | velocity components in x- and y-direction, ms−1 |
| U, V | = | dimensionless velocities, (u, v)/U0 |
| U0 | = | moving lid velocity, ms−1 |
| x, y | = | Cartesian coordinates, m |
| X, Y | = | dimensionless Cartesian coordinates, (x, y)/L |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volumetric coefficient of thermal expansion, K−1 |
| ν | = | kinematic viscosity, kgm−1 s−1 |
| ω | = | vorticity function, s−1 |
| Ω | = | dimensionless vorticity function, ωL/U0 |
| ψ | = | stream function, m2 s−1 |
| Ψ | = | dimensionless stream function, ψ/LU0 |
| ρ | = | density, kgm−3 |
| Θ | = | dimensionless temperature, (T − Tc)/(Tref − Tc) |
| ϕ | = | inclination angle, ° |
| Subscripts | = | |
| c | = | cold |
| ref | = | reference state |
NOMENCLATURE
| g | = | gravitational acceleration, ms−2 |
| Gr | = | Grashof number, βg(Tref − Tc)L3/ν2, |
| L | = | enclosure height and length, m |
| Nuloc | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | pressure, Pa |
| Pr | = | Prandtl number, ν/α |
| Re | = | Reynold number, U0L/ν |
| Ri | = | Richardson number, Gr/Re2 |
| t | = | dimensionless time |
| t′ | = | time, s |
| T | = | temperature, K |
| u, v | = | velocity components in x- and y-direction, ms−1 |
| U, V | = | dimensionless velocities, (u, v)/U0 |
| U0 | = | moving lid velocity, ms−1 |
| x, y | = | Cartesian coordinates, m |
| X, Y | = | dimensionless Cartesian coordinates, (x, y)/L |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volumetric coefficient of thermal expansion, K−1 |
| ν | = | kinematic viscosity, kgm−1 s−1 |
| ω | = | vorticity function, s−1 |
| Ω | = | dimensionless vorticity function, ωL/U0 |
| ψ | = | stream function, m2 s−1 |
| Ψ | = | dimensionless stream function, ψ/LU0 |
| ρ | = | density, kgm−3 |
| Θ | = | dimensionless temperature, (T − Tc)/(Tref − Tc) |
| ϕ | = | inclination angle, ° |
| Subscripts | = | |
| c | = | cold |
| ref | = | reference state |