| Summary: | This research examines the features of liquid film of non-Newtonian fluids under the influence of thermophoresis. For this study, we proposed a mathematical model for Jeffrey, Maxwell, and Oldroyd-B fluids and concluded the unsteady stretched surface in the existence of a magnetic field and also the thermal conductivity was measured which is directly related to the temperature whereas the viscosity inversely related to the temperature. Inserting the thermophoretic effect which improved the thermal conductivity of Jeffrey fluid over the Oldroyd-B and Maxwell fluids. The model is helpful for the liquid flow of Jeffrey, Maxwell, and Oldroyd-B fluid including the Brownian motion parameter effect. The results have been obtained through optimal approach compared with numerical (ND-Solve) method. Study mainly focused to understand the physical appearance of the embedded parameters based on the characteristic length of the liquid flow. The behavior of skin friction, local Nusselt number, and Sherwood number has been described numerically for the dynamic constraints of the problem. The obtained results are drafted graphically and discussed.
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