Zero gravity evaporation of a Dicholoromethane (DCM) liquid film is explored. The resulting film dynamics are presented and a criterion for stable films is described based on the long wave theory. It is concluded that films subject to long wave instabilities shows the appearance of the mode of maximum growth rate at rupture, irrespective of the initial condition or domain size conditions. Films stable in Earth's gravity are destabilized in zero gravity.
An evolution equation describing the dynamics of an evaporating liquid film has previously been developed from the governing equations of fluid dynamics after the application of the lubrication approximation and the choice of a viscous time scale.
The authors have solved the evaporating liquid film evolution equation with a validated numeric program. Different mechanical boundary conditions were successfully applied and their effect on the film dynamics was examined. The evolution equation has also been modified to include buoyancy driven instabilities.
This paper outlines a linear stability analysis that was performed on the time dependent, evaporating liquid film evolution equation. The effect of the evaporation rate, departure from equilibrium at the interface and variable gravity is examined by solving the equation as an initial value problem.
Modern day finite element methods (FEM) are closely attached to the advent of mathematical and matrix algebra methods in the design of aeronautical structures. Primarily, FEM is an approximation technique for partial differential equations. The power of FEM is realized when the fundamental field problems governing the engineering design are "encompassed" in irregular shapes. In other words, FEM is particularly useful in resolving the effect of static or dynamic loads (structural or thermal) on complex shapes. In this paper, regular shapes are: square/rectangular geometrics, circular cross sections.Modern day finite element method (post 1940s-50s) as taught in undergraduate level (senior level) electives shows bifurcation from classical methods (pre 1900s) in at least its abstraction from rigorous mathematical concepts through the use of powerful software tools. However, it is beneficial for students of FEM to be made aware of the connection between classical methods (differential equations) and computer tool based analysis.The overall objective is to introduce the Galerkin method of weighted residuals for linear ordinary differential equations and to extend that idea to linear, steady state problems in structural mechanics and thermal transport. Exposure to the Galerkin method allows students to connect differential equation based mathematical models to plane-problems in elasticity, lubrication theory problems in fluid dynamics and steady state thermal transport problems. Students are made aware of the concept of "global" vs "local" shape functions, "element order", "convergence" and "error". The Poisson's equation u"(x)=f is primarily utilized to build the students' confidence in solving differential equations and applying the Galerkin method. This allows students to forge a connection between differential equations and simple linear (yet powerful) mathematical models. An incremental approach is taken by making the Poisson's equation hetergenous from homogenous (i.e, f =0 or f=f(x) from f=0). Students find appropriate polynomial functions for use in the Galerkin method of weighted residual for the Poisson's equation. The choice and order of polynomial functions and its relation to modifying or refining a shape function in software is realized.Finally, MATLAB and its partial differential equation toolbox, pdetool, is used to connect the Galerkin Method to classical engineering problems. How boundary conditions could have an effect of reducing a 2-D problem to a 1-D problem was explored. This exercise allowed students to be conscientious of boundary conditions and the variety and applicability thereof, as evidenced through examination and homework assignment results.Homework assignments, examinations, end of semester design problem/project and student exit surveys are used as metrics to check efficacy of pedagogy. This course on finite element methods targets ABET criteria a,b,e,g,i,k.
Paper OutlineThis paper describes (i) analytical mathematical techniques, viz., solution of differential equations by the...
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