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Try to find a way to treat wastewater and achieve its purification from suspended waste, which was removed by examining the magneto-Williamson fluid on a horizontal cylindrical tube while taking advantage of solar radiation and nanotechnology.

The effect of Cattaneo–Christoph law of heat transfer, solar radiation, oblique magnetic field, porosity and internal heat generation on the flow was studied. The control system was solved by the numerical technique of Chebyshev pseudospectrum (CPS) with the help of the program MATHEMATICA 12. The tables comparing the published data results with the existing numerical calculation match exactly.

The tables comparing the published data results with the existing numerical calculation match exactly. The current simulation results indicate that when using variable viscosity, the Nusselt number and surface friction decrease significantly compared to their value in the case of constant viscosity, and variable viscosity has a significant effect on flow, which reduces speed. Curves and increasing temperature profiles.

Developing a theoretical framework for the problem of sewage turbidity in a healthier and less costly way, by studying the flow of Williamson fluid with variable viscosity (to describe the intensity of sewage turbidity) on a horizontal cylindrical tube, and taking advantage of nanotechnology, solar radiation, Christoph’s thermal law and internal heat generation to reach water free of impurities. Inclined magnetic force and porous force were used, both of which played an effective role in the purification process.