The present study uses the dielectrophoresis (DEP) and electrothermal (ET) forces to develop on-chip micromixers and microconcentrators. A microchannel with rectangular array of microelectrodes, patterned either on its bottom surface only or on both the top and the bottom surfaces, is considered for the analysis. A mathematical model to compute electrical field, temperature field, the fluid velocity, and the concentration distributions is developed. Both analytical and numerical solutions of standing wave DEP (SWDEP), traveling wave DEP (TWDEP), standing wave ET (SWET), and traveling wave ET (TWET) forces along the length and the height of the channel are compared. The effects of electrode size and their placement in the microsystem on micromixing and microconcentrating performance are studied and compared to velocity and concentration profiles. SWDEP forces can be used to collect the particles at different locations in the microchannel. Under positive and negative DEP effect, the particles are collected at electrode edges and away from the electrodes, respectively, irrespective of the position, size, and number of electrodes. The location of the concentration region can be shifted by changing the electrode position. SWET and TWET forces are used for mixing and producing concentration regions by circulating the fluid at a given location. The effect of forces can be changed with the applied voltage. The TWDEP method is the better method for mixing along the length of the channels among the four options explored in the present work. If two layers of particle suspension are placed side by side in the channel, triangular electrode configuration can be used to mix the suspensions. Triangular and rectangular electrode configurations can efficiently mix two layers of particle suspension placed side-by-side and one-atop-the-other, respectively. Hence, SWDEP forces can be successfully used to create microconcentrators, whereas TWDEP, SWET, and TWET can be used to produce efficient micromixers in a microfluidic chip.