Development of modern electronic devices demands a creation of effective cooling systems in the form of active or passive nature. More optimal technique for an origination of such cooling arrangement is a mathematical simulation taking into account the major physical processes which define the considered phenomena. Thermogravitational convection in a partially open alumina-water nanoliquid region under the impacts of constant heat generation element and heat-conducting solid wall is analyzed numerically. A solid heat-conducting wall is a left vertical wall cooled from outside, while a local solid element is placed on the base and kept at constant volumetric heat generation. The right border is supposed to be partially open in order to cool the local heater. The considered domain of interest is an electronic cabinet, while the heat-generating element is an electronic chip. Partial differential equations of mathematical physics formulated in non-primitive variables are worked out by the second order finite difference method. Influences of the Rayleigh number, heat-transfer capacity ratio, location of the local heater and nanoparticles volume fraction on liquid circulation and thermal transmission are investigated. It was ascertained that an inclusion of nanosized alumina particles to the base liquid can lead to the average heater temperature decreasing, that depends on the heater location and internal volumetric heat generation. Therefore, an inclusion of nanoparticles inside the host liquid can essentially intensify the heat removal from the heater that is the major challenge in different engineering applications. Moreover, an effect of nanosized alumina particles is more essential in the case of low intensive convective flow and when the heater is placed near the cooling wall.