MHD Heat Transfer in a Rectangular Domain

MHD Heat Transfer in a Rectangular Domain#

Domain: Consider a rectangular domain \([0, L_x] \times [0, L_y]\).

Boundary Conditions:

  • Inlet (\(x=0\)): Velocity \(\mathbf{v} = [V_0, 0]\), Magnetic field \(\mathbf{B} = [B_0, 0]\), Temperature \(T = T_0\).

  • Outlet (\(x=L_x\)): Outflow conditions.

  • Top and Bottom: No-slip conditions for velocity, insulated conditions for heat transfer.

  • Magnetic Insulation: \(\frac{\partial \mathbf{B}}{\partial n} = 0\) (normal component of magnetic field is conserved).

Initial Conditions:

  • Initial fluid velocity \(\mathbf{v} = [0, 0]\), magnetic field \(\mathbf{B} = [B_0, 0]\), and uniform temperature \(T = T_0\).