Investigation of porosity significance on an Oldroyd‐B fluid flow transport between parallel plates: Closed form solution: Fid-Bau Portal

Investigation of porosity significance on an Oldroyd‐B fluid flow transport between parallel plates: Closed form solution

Sunder Ram, Mutnuri / Shravani, Kasarla / Shamshuddin, MD / Salawu, Sulyman O.

Abstract

The current work focuses on the analytical investigation of the laminar flow of Oldroyd‐B fluid between parallel plates influenced by the inner surface of the plates with porous lining. The Oldroyd‐B fundamental equation is featured to energize the realistic captivation of dilute polymeric solutions in parallel plates. Furthermore, the transport of momentum energy is controlled by the significant influence of the porous medium. The flow mechanics of transport through the parallel plates is developed utilizing nondimensional variables' coupled system of higher‐order equations, transformed into partial order from partial models with appropriate nondimensionalities. The altered equations are computed analytically by the usage of linear partial differential equations with the constant coefficients method through MATLAB software. The noteworthy impact of different parameters like Reynolds number, pressure gradient, material parameters related to relaxation and retardation, permeability parameter, and time parameter is observed along the flow rate and velocity in clear and porous region distributions graphically. Variation of thickness with total velocity has been displayed through tables. It is examined through graphical discussion that low Reynolds number values accomplish maximum velocity in both cases. Material parameters relaxation and retardation show opposite in nature irrespective of porous and nonporous cases. The flow rate in the absence of porosity significantly upsurges within the bounded domain, that is, as values of pressure gradient increase, the flow rate is enhanced. The observation aligned well with various reports and the impact of pressure gradient on a fluid. It is noticed that the fluid motion for the unsteady case is higher and gradually increases as the time parameter grows, and shows opposite trends as compared to the case of the porous medium. Finally, the presence of porous medium has manifested an impact on the flow field.