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This paper presents the effects of cross fluid model associated with entropy generation and melt process. The Cross-fluid viscosity model based on the infinite shear rate effect is taken with attaching Riga plate. Physical interpretation generates a system of partial differential equations (PDEs), and further, these are processed with similarity variables to attain a system of ordinary differential equations (ODEs). The numerical experiments are presented compared and discussed. Here, the numerical Keller Box approach is utilized. The obtained results indicate that the melt process loses the temperature and entropy generation enlarges the temperature visibility.