In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.