The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) a...The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter <img alt="" src="Edit_ba52bac5-73fb-46dc-87b2-9ab918cb67c9.bmp" /> and spin diffusion (couple stress) parameter <em>N</em><sub>3</sub> is to hasten coupling parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">1 </sub>and micropolar heat conduction parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub> is to delay the onset of convection. Further, increase in the value of <em style="white-space:normal;">N</em><sub style="white-space:normal;">1</sub>, <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub>, <img alt="" src="Edit_2d2de547-a7ed-4351-b3c4-8d1c36d83a20.bmp" /> and as well as decrease in <em style="white-space:normal;">N</em><sub style="white-space:normal;">3</sub> is to diminish the size of convection cells.展开更多
Penetrative Bénard-Maranagoni convection in micropolar ferromagnetic fluid layer in the presence of a uniform vertical magnetic field has been investigated via internal heating model. The lower boundary is consid...Penetrative Bénard-Maranagoni convection in micropolar ferromagnetic fluid layer in the presence of a uniform vertical magnetic field has been investigated via internal heating model. The lower boundary is considered to be rigid at constant temperature, while the upper boundary free open to the atmosphere is flat and subject to a convective surface boundary condition. The resulting eigenvalue problem is solved numerically by Galerkin method. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, magnetic parameter M1, the non-linearity of magnetization parameter M3, coupling parameter N1, spin diffusion parameter N3 and micropolar heat conduction parameter N5. The results show that the onset of ferroconvection is delayed with an increase in N1 and N5 but hastens the onset of ferroconvection with an increase in M1, M3, N3 and Ns. The dimension of ferroconvection cells increases when there is an increase in M3, N1, N5 and Ns and decrease in M1 and N3.展开更多
文摘The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter <img alt="" src="Edit_ba52bac5-73fb-46dc-87b2-9ab918cb67c9.bmp" /> and spin diffusion (couple stress) parameter <em>N</em><sub>3</sub> is to hasten coupling parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">1 </sub>and micropolar heat conduction parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub> is to delay the onset of convection. Further, increase in the value of <em style="white-space:normal;">N</em><sub style="white-space:normal;">1</sub>, <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub>, <img alt="" src="Edit_2d2de547-a7ed-4351-b3c4-8d1c36d83a20.bmp" /> and as well as decrease in <em style="white-space:normal;">N</em><sub style="white-space:normal;">3</sub> is to diminish the size of convection cells.
文摘Penetrative Bénard-Maranagoni convection in micropolar ferromagnetic fluid layer in the presence of a uniform vertical magnetic field has been investigated via internal heating model. The lower boundary is considered to be rigid at constant temperature, while the upper boundary free open to the atmosphere is flat and subject to a convective surface boundary condition. The resulting eigenvalue problem is solved numerically by Galerkin method. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, magnetic parameter M1, the non-linearity of magnetization parameter M3, coupling parameter N1, spin diffusion parameter N3 and micropolar heat conduction parameter N5. The results show that the onset of ferroconvection is delayed with an increase in N1 and N5 but hastens the onset of ferroconvection with an increase in M1, M3, N3 and Ns. The dimension of ferroconvection cells increases when there is an increase in M3, N1, N5 and Ns and decrease in M1 and N3.
