Abstract
The main objective of the present examination is to design a stable mathematical model of a two-phase dusty hybrid nanofluid flow over a stretching sheet with heat transfer in a porous medium, and the Darcy-Forchheimer flow is taken into account with viscous dissipation and melting effect. The equations of motion are reduced to nonlinear ordinary differential equations by considering suitable similarity variables. These dimensionless expressions are solved by a well-known numerical technique known as Runge-Kutta-Fehlberg fourth-fifth order method. The behavioral study and analysis of the velocity and thermal profile in dual phases (fluid phase and dust phase) for diverse values of parameters are estimated using graphs and tables. The result outcome reveals that the velocity gradient declines in the fluid phase and increases in the dust phase for a rise in values of the velocity interaction parameter. Also, the velocity gradients of the both phases diminish for increasing values of the porosity parameter. Furthermore, it is determined that the increase in the value of melting parameter leads to a decline in the thermal gradient of both phases.