Significance of dust particles volume fraction to optimization of entropy in magnetohydrodynamic mixed convection flow via inclined surface

The main purpose of this study is to assessment the rate of entropy generation in magneto-hydrodynamic free convection with flow through the boundary layers of a fluid that is viscous and dusty fluid flow subject to dispersed dust particles across the stretching surface. Dusty fluids are utilized in a wide range of construction and manufacturing sectors, included the transportation of petroleum, gas purification, auto exhaust fumes, power station piping, sedimentation process, and many more. The primary objective of this elaborated fluid problem is to observe the influence of dust particles volume fraction on the heat transfer rate and entropy generation. By using appropriate similarity transformation, for first fluid phase and second dust phase simulations, the governing partial differential equations are transfigured into nonlinear non-dimensional ordinary differential equations. The final forms of obtained equations are solved numerically via MATLAB built-in bvp4c solver scheme. When the scientific validity of the findings is analyzed, it is found that there is substantial agreement among the latest results and the existing research. The entropy generation and thermal performance in fluid is influenced by the growing volume fraction of dust particles and significance variation is noted. As volume fraction of dust particles increased, causes a decrease in fluid flow, and reduced the velocity of both fluid and dusty fluid phases. But, it plays remarkable improvement in fluid temperature and entropy generation, and cause a decline in Bejan number. In fluid phase and dust fluid phase, temperatures are increased while inclined angle fluid parameter strength increases while the fluid velocity is decreased. Additionally, dimensionless variable expressions for Bejan number (Be) and entropy generation (Ns) are produced. It is noticed how several physical attributes influence entropy generation values. •In this study we have explored the importance of dusty fluid and heat flux induced by the stretched sheet’s thermal boundary gradient.•We have also study the rate of entropy generation in magneto-hydrodynamic free convection flow through the boundary layers of a fluid that is viscous and dusty fluid flow.•The most significant source of efficient heat source is nanofluids, which have many uses in scientific and technical procedures.•By using appropriate similarity adjustments, for both phase simulations, the governing PDEs are transformed into nonlinear non-dimensi