A cooling apparatus includes a heat pipe base covering a heat source; a heat sink with a plurality of heat sink fins; a plurality of heat pipes connecting the heat pipe base and the heat sink; and a magneto-hydrodynamic (MHD) pump assembly connected to the heat sink. In a method for cooling a heat source with heat pipes, magneto-hydrodynamic (MHD) fluid pipes, and a heat sink, the method includes transmitting heat from evaporating ends of the heat pipes connected to a heat source to condensing ends of the heat pipes connected to the heat sink; and circulating MHD fluid inside the MHD fluid pipes embedded in the heat sink to dissipate heat. In a method for cooling a heat sink connected to a plurality of heat pipes and containing a plurality of MHD fluid pipes, the method includes generating a plurality of magnetic fields using an array of magnets; creating an electric potential from a top surface to a bottom surface of each MHD fluid pipe using a plurality of metal films; and inducing electrically-conductive MHD fluid to circulate in the plurality of MHD fluid pipes by the plurality of magnetic fields and the electric potential.