<p>The suspension of nanoparticles in base fluids has garnered significant attention due to its ability to enhance thermophysical properties, with ternary hybrid nanofluids (THNFs) emerging as a promising advancement in the pursuit of improved energy efficiency and sustainable thermal systems. This study presents a comprehensive numerical investigation of Jeffrey fluid flow involving a ternary hybrid nanofluid composed of MgO, SWCNT, and MoS₂ nanoparticles dispersed in a sodium alginate base fluid over an exponentially stretching permeable sheet. The analysis incorporates critical physical effects, including Joule heating, nonuniform heat source/sink, viscous dissipation, and porous medium. The governing nonlinear partial differential equations are transformed into ordinary differential equations via similarity transformations and then solved using the bvp4c solver in MATLAB. Key parameters influencing the flow profiles, accompanied by pertinent engineering quantities, are analysed in detail through graphical illustrations. The results reveal that an increase in the Deborah number enhances the velocity profile while reducing the temperature distribution. The heat transfer rate of the Eckert number for the MgO-SWCNT-MoS₂ based THNF is 6.53% higher than that of the binary hybrid (MgO-MoS₂) nanofluid. An increase in the activation energy parameter results in a 1.56% enhancement in the Sherwood number for the MgO-SWCNT-MoS₂/C₆H₇NaO₆ THNF compared to the MgO/C₆H₇NaO₆ NF. This study underscores the superior thermal and mass transfer performance of Jeffrey-type THNFs and provides valuable insights for their potential application in thermal systems, energy storage, and cooling technologies.</p>