magnetic field effect on natural convection flow with internal heat generation using fast method

The magnetic field effect on laminar natural convection flow is investigated in a filled enclosure with internal heat generation using two-dimensional numerical simulation. the enclosure is heated by a uniform volumetric heat density and walls have constant temperature. a fixed magnetic field is applied to the enclosure. the dimensionless governing equations are solved numerically for the stream function, vorticity and temperature using finite difference method for various rayleigh (ra) and hartmann (ha) numbers in matlab software. the stream function equation is solved using fast poisson's equation solver on a rectangular grid (poicalc function in matlab), voricity and temperature equations are solved using red-black gauss-seidel and bi-conjugate gradient stabilized (bicgstab) methods respectively. the results show that the strength of the magnetic field has significant effects on the flow and temperature fields. for the square cavity, the maximum temperature reduces with increasing ra number. it is also observed that at low ra number, location of the maximum temperature is at the centre of the cavity and it shifts upwards with increase in ra number. circulation inside the enclosure and therefore the convection becomes stronger as the ra number increases while the magnetic field suppresses the convective flow and the heat transfer rate. the ratio of the lorentz force to the buoyancy force (ha²/ra) is as an index to compare the contribution of natural convection and magnetic field strength on heat transfer.