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.

This paper investigates the Sakiadis flow of a Al2O3‐H2O nanoliquid with consistently scattered dust particles over a vertical plate. To account for the effect of the Brownian movement, the Koo‐Kleinstreuer‐Li model is considered. In some thermal systems such as reactor safety areas, and solar collectors, combustion works from moderate to high temperature, making the relationship between the temperature and density nonlinear. To consider this temperature‐dependent density, the nonlinear Boussinesq estimation is utilized. The present physical structure, which includes energy and momentum equations, is converted into a system of ordinary, coupled, and nonlinear differential conditions through the help of similarity transformations. By using the finite difference code, the subsequent equations have been numerically solved. The impact on the velocity and the thermal profiles of the nondimensional parameters is visualized through graphs. Both the Nusselt number and friction factor strengthen with a higher nonlinear thermal parameter in the case of nonlinear Boussinesq approximation compared to the linear Boussinesq case. Growing estimations of nonlinear thermal parameter deteriorate the thermal profile but it boosts the velocity profile of both liquid and dust phases.

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