Linear and non-linear magnetoconvection in a porous medium
The author has studied convection in an electrically conducting Boussinesq fluid flowing through a porous medium in the presence of a vertical magnetic field. Boundaries are taken to be flat. The boundary conditions are used to examine two types of bifurcations - simple and Hopf bifurcation. The concept of self adjoint operator is used to find out the conditions under which the critical Rayleigh number for marginal convection is an upper bound for finite Biot number. The finite amplitude analysis is discussed by considering a truncated representation of Fourier series for velocity and magnetic and temperature fields. It is reported that heat transport increases with an increase in Rayleigh number, ratio of thermal diffusivity to magnetic diffusivity and porous parameter but decreases with an increase in Chandrasekhar number. The study is useful in understanding the field behaviour in the extraction of energy in the geothermal regions.
convection in an electrically conducting Boussinesq fluid
critical Rayleigh number for marginal convection
truncated representation of Fourier series
extraction of energy in the geothermal regions
scientific article; zbMATH DE number 3952364
scientific article