A Novel Methodology for Analysis of Thermo-Viscous Unsteady Fluid Motion over an Oscillating Horizontal Moving Rectangular Surface

• The flows through rectangular surface, especially with the oscillating objects have been a growing and relevance importance of non-Newtonian fluids in chemical technology, petroleum and nuclear industry, geophysical fluid dynamics. • The present paper attempts to study the various thermal and viscous effects on flows of thermo-viscous fluids through rectangular surface using MATHEMATICA ND solve with R-K 6 th order shooting technique. The impacts of all these factors on flow fields also been explored and presented with graphs and illustrations. • Some of the applications of these kind of flows arises in “The flow of oils through porous rocks, the extraction of energy from geo-thermal regions, the filtration of solids from liquids, the flow of liquids through ion-exchange beds are some of the areas in which thermo-viscous flows through are noticed”. • It is observed that, the excellent agreement exists between the current analytical results and the findings of the literature. • Researchers and scientists who cite and follow the papers from the journal will perhaps have a better grasp of the current work. This study presents computational numerical methodology to explore unsteady thermo-viscous fluid movement over an infinitely stretched oscillating horizontal moving rectangular surface. The numerical results have been found employing Runge-Kutta(R-K) method of order 6 shooting techniques developed in Mathematica software ND(Numerical Differentiation) solve for the flow adaptable equations comprising temperature and velocity. The flow behavior and the impacts of material constraints on the flow region have been analyzed and deliberated taking the help from the generated 3D graphs. The nonlinear coupled PDEs in terms of temperature and velocity, subject to the corresponding boundary conditions, control the fluid motion. The numerical computations of R-K 6 th order results are presented in form of tables and also represented for numerous thermo physical coefficient values. The variations of these flow fields have been studied for wide spectrum of physical characteristics which influences the nature of thermo-viscous fluid. The analysis for slow motion of the fluid also discussed with the generated 2D graphs. The impact of viscosity, constant pressure and temperature gradients, thermo physical factors and the fourier conductivity parameter effect on flow region have explored using graphical illustrations with the wide range of values. The results acquired in the literature are in great accord with the outcomes that are currently being worked on.