In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.
This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.
The toxicity of hexavalent chromium (Cr(VI)) present in the environment has exceeded the current limits or standards and thus may lead to biotic and abiotic catastrophes. Accordingly, several treatments, including chemical, biological, and physical approaches, are being used to reduce Cr(VI) waste in the surrounding environment. This study compares the Cr(VI) treatment approaches from several areas of science and their competence in Cr(VI) removal. As an effective combination of physical and chemical approaches, the coagulation-flocculation technique removes more than 98% of Cr(VI) in less than 30 min. Most membrane filtering approaches can remove up to 90% of Cr(VI). Biological approaches that involve the use of plants, fungi, and bacteria also successfully eliminate Cr(VI) but are difficult to scale up. Each of these approaches has its benefits and drawbacks, and their applicability is determined by the research aims. These approaches are also sustainable and environmentally benign, thus limiting their effects on the ecosystem.