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Alexander E. Mamontov - One of the best experts on this subject based on the ideXlab platform.
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Global regularity estimates for multidimensional equations of compressible non-newtonian Fluids
Annali Dell'universita' Di Ferrara, 2000Co-Authors: Alexander E. MamontovAbstract:The present paper is devoted to the problem of global existence of sufficiently regular solutions to two- and three-dimensional equations of compressible nonNewtonian Fluids. In the case of potential stress tensor, we develop the technique of derivation of energy identities that do not include the density derivatives. Basing on these identities, in the case of sufficiently fast-increasing potentials, we obtain an extended system of a priori estimates for the named equations. We also study the related problem of estimates for the solutions to non-linear elliptic system generated by stress tensor.
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Global regularity estimates for multidimensional equations of compressible non-newtonian Fluids
Annali dell’Università di Ferrara, 2000Co-Authors: Alexander E. MamontovAbstract:The present paper is devoted to the problem of global existence of sufficiently regular solutions to two- and three-dimensional equations of compressible nonNewtonian Fluids. In the case of potential stress tensor, we develop the technique of derivation of energy identities that do not include the density derivatives. Basing on these identities, in the case of sufficiently fast-increasing potentials, we obtain an extended system of a priori estimates for the named equations. We also study the related problem of estimates for the solutions to non-linear elliptic system generated by stress tensor. Il presente lavoro è dedicato al problema dell’esistenza globale di soluzioni sufficientemente regolari delle equazioni del moto di fluidi comprimibili non-Newtoniani in due e tre dimensioni. Nel caso di tensore degli sforzi potenziale, viene sviluppata una tecnica per la derivazione di identità dell’energia che non includono derivate della densità. Basandosi su tali identità, nel caso di potenziali che crescono abbastanza rapidamente viene ottenuto un sistema esteso di stime a priori per le equazioni del moto. Viene inoltre studiato il problema correlato delle stime di soluzioni di sistemi ellittici non lineari generati dal tensore degli sforzi.
Nilanjan Chakraborty - One of the best experts on this subject based on the ideXlab platform.
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laminar natural convection of power law Fluids in a square enclosure with differentially heated sidewalls subjected to constant wall heat flux
Journal of Heat Transfer-transactions of The Asme, 2012Co-Authors: Osman Turan, Anuj Sachdeva, Robert J Poole, Nilanjan ChakrabortyAbstract:Two-dimensional steady-state laminar natural convection of inelastic power-law nonNewtonian Fluids in square enclosures with differentially heated sidewalls subjected to constant wall heat flux (CHWF) are studied numerically. To complement the simulations, a scaling analysis is also performed to elucidate the anticipated effects of Rayleigh number (Ra), Prandtl number (Pr) and power-law index (n) on the Nusselt number. The effects of n in the range 0.6 � n � 1.8 on heat and momentum transport are investigated for nominal values Ra in the range 10 3 ‐10 6 and a Pr range of 10‐10 5 . In addition the results are compared with the constant wall temperature (CWT) configuration. It is found that the mean Nusselt number Nu increases with increasing values of Ra for both Newtonian and power-law Fluids in both configurations. However, the Nu values for the vertical walls subjected to CWHF are smaller than the corresponding values in the same configuration with CWT (for identical values of nominal Ra, Pr and n). The Nu values obtained for power-law Fluids with n 1) are greater (smaller) than that obtained in the case of Newtonian Fluids with the same nominal value of Ra due to strengthening (weakening) of convective transport. With increasing shear-thickening (i.e., n >1) the mean Nusselt number Nu settles to unity (Nu ¼ 1:0) as heat transfer takes place principally due to thermal conduction. The effects of Pr are shown to be essentially negligible in the range 10‐10 5 . New correlations are proposed for the mean Nusselt number Nu for both Newtonian and power-law Fluids. [DOI: 10.1115/1.4007123]
M. Ramezan - One of the best experts on this subject based on the ideXlab platform.
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Heat transfer analysis of a viscoelastic fluid at a stagnation point
Mechanics Research Communications, 1992Co-Authors: Mehrdad Massoudi, M. RamezanAbstract:Among the many models that have been used to describe the non-Newtonian behavior exhibited by certain Fluids, the Fluids of differential type [I] have received special attention. In recent years, interest in the boundary layer flows of nonNewtonian Fluids has increased [2,3,4]. Recently, Rajagopal, et al. [5], looked at the boundary layer flows of Fluids of second grade, and later, Rajagopal, et al. [6], studied the Falkner-Skan flows of a homogeneous incompressible fluid of second grade. Heat transfer plays an important role during the handling and processing of non-Newtonian Fluids [7]. In this paper, we use the results of our previous study [8] and consider the heat transfer of a second grade fluid at a stagnation point for a nonisothermal surface. The stress in a second grade fluid is related to the motion in the following manner [i]:
Khalid Hanif - One of the best experts on this subject based on the ideXlab platform.
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Accelerated flows of viscoelastic Fluids with no-slip and partial slip conditions
2004Co-Authors: Khalid HanifAbstract:There has been a great deal of interest in understanding the behaviour of non-Newtonian Fluids as they are used in various branches of science, engineering and technology: particularly in material processing, chemical industry, geophysics and bie-engineering. The study of non-Newtonian fluid flow is also of significant interest in oil reservoir engineering. Moreover, the non-Newtonian Fluids such as mercury amalgams, liquid metals, biological Fluids, plastic extrusions, paper coating, lubrication oils and greases have applications in many areas with or without magnetic field. Many magnetohydrodynamic problems of practical interest involving Fluids as a working medium have attracted engineers, physicists and mathematicians alike. These problems are challenging because of non-linearity of the governing equations, field coupling, and complex boundary conditions. Further, using Newtonian fluid models to analyse, predict and simulate the behaviour of viscoelastic Fluids has been widely adopted in industries. However, the flow characteristics of viscoelastic Fluids are quite different from those of Newtonian Fluids. This suggests that in practical applications the behaviour of viscoelastic Fluids cannot be represented by that of Newtonian Fluids. Hence, it is necessary to study the flow behaviour of viscoelastic Fluids in order to obtain a thorough cognition and improve the utilization in various manufactures. Due to complexity of Fluids in nature, non-Newtonian Fluids are classified on the basis of their behaviour in shear. Amongst the many fluid models which have been used to describe the visco elastic behaviour exhibited by these Fluids, the Fluids of second and third grades have received a special attention. The major attraction of these fluid models is due to their popularity and the fact that they are derived from the first principle. Unlike many other phenomenological models, there are no curve-fittings or parameters to adjust for these models. Though, in both of these grade models, there are material properties that need to be measured. Also, the second grade fluid is a subclass of nonNewtonian Fluids for which one can reasonably hope to obtain an analytical solution. Another important aspect in fluid mechanics is the consideration of partial slip condition. One of the cornerstones on which the fluid mechanics is built is the no-slip condition. But, there are situations wherein this condition does not hold. In certain cases, partial slip between the fluid and the moving surface may occur. Mention may be made to the situations when the fluid is particulate such as emulsions, suspensions, foams and polymer solutions. However, literature for non-Newtonian Fluids with wall slippage is scarce. Keeping the above facts in mind, this thesis has been organized offering five chapters. Chapter zero is introductory. In chapter one, the basic equations and mathematical techniques are included for the succeeding chapters. The modeling of the general equation which govern the magnetohydrodynamic (MHD) flow of a third grade fluid is also given. Chapter two deals with the MHD flows due to non-coaxial rotations of a porous disk and a viscous fluid at infinity. Three types of unsteady flows namely, the flows induced by a constant accelerated disk with no-slip and partial slip and the flow due to variable accelerated disk with no-slip. Exact analytical solutions are constructed using Laplace transform technique. It is noted that in presence of partial slip, the reduced shearing force from the boundary causes the velocity to become flatter than that for no-slip case. Moreover, the velocity profiles in case of constant accelerated flow are greater than for the variable accelerated case for all values of time less than one. However, this situation is quite reverse for all times greater than one. Chapter three is devoted to the flows of a second grade fluid generated by a constant accelerated disk with no-slip and partial slip conditions. The influence of second grade parameters arises in the governing equation and the boundary conditions. Both analytical and numerical solutions are given and are compared for the no-slip case. But only the numerical solution is obtained for the partial slip case. It is worth noting that material parameter of the second grade fluid reduces the velocity profiles. In chapter four, the constant accelerated flows of a third grade fluid with no-slip and partial slip have been presented. The analysis of this chapter involves the solvability of a non-linear equation. Also, the boundary condition in partial slip situation is non-linear. Numerical solutions are given using the Crank-Nicolson scheme with modification. The objective of chapter five is to extend the contents of chapter four to the case of variable accelerated flows. The influence of acceleration against time in third grade fluid is found to be smaller than that of Newtonian fluid.
T.-y. Wang - One of the best experts on this subject based on the ideXlab platform.
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Mixed convection heat transfer from a vertical plate to non-Newtonian Fluids
International Journal of Heat and Fluid Flow, 1995Co-Authors: T.-y. WangAbstract:Abstract The nonsimilar boundary-layer analysis of steady laminar mixed-convection heat transfer between a vertical plate and non-Newtonian Fluids is extended and unified. A mixed-convection parameter ζ is proposed to replace the conventional Richardson number, Gr /Re 2 /(2− n ) and to serve as a controlling parameter that determines the relative importance of the forced and the free convection. The value of mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for nonNewtonian Fluids with exponent n n = 1 for Newtonian Fluids; and n > 1 for dilatant Fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian Fluids, from pseudoplastics to dilatant Fluids. The effects of the mixed-convection parameter, the power-law viscosity index, and the generalized Prandtl number on the velocity profiles, the temperature profiles, as well as on the wall skin friction and heat transfer rate are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.
