The thermal analysis and Lorentz force influence on Micropolar fluid in the presence of Brownian motion of solid particles across the extending surface subject to two-phase fluid is investigated. Recent years have seen a growing interest among researchers in two-phase fluids due to highly extensive modern technological applications. The comprehensive scrutiny is conducted on an electrically conducting Micropolar dusty nanofluid with a magnetic field. The mathematical model is developed in the form of nonlinear in nature partial differential equations (PDEs) for a two-phase Micropolar nanofluid and dusty phase. The flow governed equations are reduced to ordinary ones by applying similarity transformations. The reduced system of ordinary differential equations (ODEs) has been integrated with the aid of the built-in function MATLAB solver bvp4c with the shooting technique. The results for different values of prominent parameters for both the Micropolar nanofluid phase and dusty phase are estimated and elaborated through graphical results. From the results, it is concluded that the dust particle fraction causes a reduction in fluid velocity, while the thermal field for both phases is boosted. The thermal and concentration species are boosted with the thermophoresis parameter.
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