Heat and mass transfer are crucial to numerous technical and commercial operations, including air conditioning, machinery power collectors, crop damage, processing food, heat transfer mechanisms, and cooling, among numerous others. The fundamental purpose of this research is to use the Cattaneo-Christov heat flux model to disclose an MHD flow of ternary hybrid nanofluid through double discs. The results of a heat source and a magnetic field are therefore included in a system of PDEs that model the occurrences. These are transformed into an ODE system using similarity replacements. The first-order differential equations that emerge are then handled using the computational technique Bvp4c shooting scheme. The Bvp4c function in MATLAB is used to numerically solve the governing equations. The influence of the key important factors on velocity, temperature, nanoparticles concentration, and is illustrated visually. Furthermore, increasing the volume fraction of nanoparticles improves thermal conduction, increasing the heat transfer rate at the top disc. The graph indicates that a slight increase in melting parameter rapidly declines the velocity distribution profile of nanofluid. The temperature profile was boosted due to the growing outcomes of the Prandtl number. The increasing variations of the thermal relaxation parameter decline the thermal distribution profile. Furthermore, for some exceptional instances, the obtained numerical answers were compared to previously disclosed data, yielding a satisfactory compromise. We believe that this discovery will have far-reaching ramifications in engineering, medicine, and the field of biomedical technology. Additionally, this model can be used to examine biological mechanisms, surgical techniques, nano-pharmacological drug delivery systems, and the therapy of diseases like cholesterol using nanotechnology.