EFFECTS OF HEAT SOURCE/SINK ON DARCIAN-B_ENARD-MAGNETO-MARANGONI CONVECTIVE INSTABILITY IN A COMPOSITE LAYER SUBJECTED TO NONUNIFORM TEMPERATURE GRADIENTS

EFFECTS OF HEAT SOURCE/SINK ON DARCIAN-B_ENARD-MAGNETO-MARANGONI CONVECTIVE INSTABILITY IN A COMPOSITE LAYER SUBJECTED TO NONUNIFORM TEMPERATURE GRADIENTS

N. Manjunatha, R. Sumithra

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Abstract

The problem of B enard-Magneto-Marangoni convection in a composite layer which is in nite along x and y directions is considered for the Darcian case in the pres- ence of constant heat source/sink in both the layers. This composite layer is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in closed form with the lower surface rigid and upper surface free with surface tension e ects for the velocity and isothermal temperature boundary combi- nations. The in uence of porous parameter, magnetic  eld and nonuniform temperature gradients on the Eigen value problem are discussed. It is experiential that the e ect of heat source/sink in the uid layer is dominant on the eigenvalue over the same in the porous layer. The important parameters like Chandrasekhar number, modi ed internal Rayleigh number and thermal ratio which control B enard-Magneto-Marangoni convec- tion are discussed in detail.

Keywords

Heat source (sink), B enard-Magneto-Marangoni convection, Exact method, Depth ratio, Temperature gradients, Isothermal boundaries.