The current study aims to analyze the magnetohydrodynamic natural convective fluid flow and heat transmission features of the ternary-hybrid nanofluid filled the partially heated porous square cavity under the impacts of heat absorption/generation and thermal radiation. The governing equations are solved using the Marker and Cell method. In the present study, three different types of nanoparticles, such as molybdenum disulfide (MoS2), single-walled carbon nanotube (SWCNT), and silver (Ag), are suspended in an inorganic (water) or non-polar organic (kerosene) solvent. Nine different shapes of nanoparticles are utilized in this study. The outcomes show that for the fixed pertinent parameter values of the existence and nonexistence of heat generation/absorption, the MoS2+SWCNT+Ag/water ternary-hybrid nanofluids synthesized by lamina-shaped nanoparticles, the average thermal transmission rate is increased by 40.8523%, 36.329%, and 38.7025%, respectively, than sphere-shaped nanoparticles. In addition, utilizing the MoS2+SWCNT+Ag/kerosene ternary-hybrid nanofluids synthesized by lamina-shaped nanoparticles, the average heat transmission rate is augmented by 38.0322%, 33.0464%, and 35.5868%, respectively, than sphere-shaped nanoparticles. The current study reveals that the fluid flow and heat transfer efficiency are significantly increased by improving the nanoparticle volume fraction and shape factors depending upon the existence of heat absorption/generation. The high average heat transfer efficiency is observed when lamina-shaped nanoparticles are dispersed into the water compared to kerosene in the presence of a heat source. This study can enhance heat transmission efficiency in various industrial and engineering fields, such as heat exchangers, solar collectors, and fuel cells.