On the falling of objects in non-Newtonian fluids
TLDR
In this article, the velocity of a lamina in between two parallel plates containing a fluid of second grade was determined by solving the mixed initial-boundary value problem using Laplace transform.Abstract:
The falling of a lamina in between two parallel plates containing a fluid of second grade is studied. The velocity of the lamina and the fluid are determined by solving the mixed initial—boundary value problem using Laplace transform. Explicit exact solutions are obtained for the velocity of the lamina and the fluid. Next, the falling of a cylinder in a tube containing a fluid of second grade is analyzed using Laplace transform, and once again exact solutions are found.read more
Citations
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Homotopy solutions for a generalized second-grade fluid past a porous plate
Tasawar Hayat,Masood Khan +1 more
TL;DR: In this article, a modified model of second-grade fluid that has shear-dependent viscosity and can predict the normal stress difference is used, and the differential equations governing the flow are solved using homotopy analysis method.
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Transient flows of a second grade fluid
TL;DR: In this article, the authors constructed exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid, which are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient.
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Magnetohydrodynamic transient flows of a non-Newtonian fluid
TL;DR: In this paper, exact solutions of the time-dependent partial differential equations for flows of an Oldroyd-B fluid are discussed for flows generated by the impulsive motion of a boundary or by application of a constant pressure gradient.
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Effects of partial slip on flow of a third grade fluid
TL;DR: In this paper, an analytical study of the rotating flow of a third grade fluid past a porous plate with partial slip effects was performed using the homotopy analysis method (HAM).
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On the need for compatibility of thermal and mechanical data in flow problems
TL;DR: In this paper, it is shown that many classical solutions would not be possible if the problem is not cast within a thermodynamic framework with critical boundary conditions being specified for appropriate thermal quantities.
References
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Book
Low Reynolds number hydrodynamics
John Happel,Howard Brenner +1 more
TL;DR: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, and a host of other disciplines.
Book
Advanced Calculus for Applications
TL;DR: In this paper, the Laplace Transform is used to solve the problem of linear differential equations with constant coefficients, which is a special case of the problem we are dealing with here, and the results are shown to be valid for large values of x.
Journal ArticleDOI
Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
J. Ernest Dunn,Roger Fosdick +1 more
Journal ArticleDOI
Fluids of differential type: Critical review and thermodynamic analysis
TL;DR: In this paper, the authors provide an extended analysis of the genesis and development of fluids of differential type, and show that certain ideas of flow retardation and model approximation have been consistently misinterpreted.