This study discusses the thermal and mass dispersal of ternary unsteady nanofluid flow in the existence of Soret and Dufour effects over a stretched surface with the Stefan blowing (SB) effect in porous media. The "blowing effect" is created by a large number of molecules or nanoscale particles moving from one point to another. SB is a mass transfer of species application that gives the notion of the blowing effect, as well as the Soret and Dufour effects, which are also being considered in the current study. The governing equations that pose the problem are solved using appropriate similarity variables and then translated into ordinary differential equations. Runge-Kutta-Fehlberg 45 and the shooting process are used to solve the reduced equations. The effect of the different dimensionless restrictions on the relevant profiles is visually depicted. According to the analysis, the rise in the porosity constraint will decline the velocity of the fluid. The SB parameter directly influences velocity, thermal, and concentration profiles. The Soret constraint increases concentration, whereas the Schmidt number has the opposite effect. With the addition of solid volume fraction, the rate of mass transmission and surface drag force reduces while the rate of heat dispersion increases.

The melting effect, a type of heat transferal process, is a fascinating mechanism of thermo-physics. It is related to phase change issues that occur in several industrial mechanisms. Glass treatment, polymer synthesis, and metal processing are among these. In view of this, the current investigation explicates the flow of a dusty nanofluid through a stretching cylinder in a porous medium by considering the effect of the melting heat transfer phenomenon. Using the required similarity transformations, the governing partial differential equations (PDEs) showing the energy transference and fluid motion in both the liquid and dust phases were translated into ordinary differential equations (ODEs). The numerical solutions for the acquired ODEs were developed using the Runge–Kutta–Fehlberg method of fourth–fifth order (RKF-45) and the shooting process. Graphical representations were used to interpret the effects of the governing parameters, including the porosity parameter, the Eckert number, and the stretching and melting parameters, on the respective velocity and temperature profiles for both the fluid and dust phases. The skin friction coefficient and the Nusselt number were also discussed and tabulated. The outcomes show that enhancing the porosity parameter will diminish the fluid- and dust-phase velocities. Fluid velocity, dust-phase velocity, and temperature improve with escalating values of the curvature parameter, whereas the melting effect reduces the thermal profiles of the fluid and dust phases. The surface drag force declines with an improvement in curvature and porosity constraints.