The cooling demand in micro-scale electrical equipment, such as energy storage systems, is consistently growing. This is accented by developing micro-scale fabrications in various industries. The numerical works play an important role during the development of micro-scale cooling systems, due to the ability to predict at low cost. By keeping this purpose, the current study aims at simulating a hybrid nanofluid flow sinusoidally excited at the inlet in a micro-scale channel around a battery under imposing a constant-strength magnetic field, which may be applied deliberately or found in the normal function of the battery. To do so, a transient numerical code is developed and the effects of various critical parameters, such as Hartmann number, Reynolds number, frequency, and amplitude of the inlet velocity are assessed. Increasing the Reynolds number from 100 to 500 and Hartmann number from 0 to 50 respectively makes the increment about 300 and 25 percent in the average Nusselt number. It is found that the sinusoidal velocity characteristics remain a minor effect on the heat transfer, while the pressure drop is influenced considerably. There is a spatial lag between the inlet velocity manipulation and outlet temperature response. Compared to the traditional systems, it is shown that micro-scale cooling is more beneficial for the thermal management of the batteries.