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1、JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH INCIVIL ENGINEERINGFLOW OF A SECOND ORDER FLUID OVERAN INCLINED RIGID PLANE1CH.V. RAMANA MURTHY, 2K.GOWTHAMI 3K.R. KAVITHA*, 4P. SUMATHI KUMARI1Professor, K.L.University, Vaddeswaram, Guntur District, Pin : 522 502 (INDIA)2, 4Lecturer, K.L.University, V
2、addeswaram, Guntur District, Pin : 522 502 (INDIA)Asst. Professor, N.R.I. Institute of Technology, Pothavarappadu , Pin : 521 212 ABSTRACT : The unsteady state flow of a visco elastic fluid of second order type over an inclined rigid plane is examined, taking into account of a uniform tangential for
3、ce F which acts on the free surface for a finite interval of time. , Keywords: Visco elastic fluids, second order fluid, visco elasticity, steady state flow 1. NOMENCLATUREAi:Acceleration component in i th directionai:Non dimensional acceleration in i th direction:Given history :Retarded HistoryH:Ch
4、aracteristic lengthP:Indeterminate hydrostatic pressurep: Non-dimensional indeterminate pressure:Coefficient of viscosity:Coefficient of elastico viscosity:Coefficient of cross viscosity:Stress tensorT:Dimensional time parametert:Non-dimensional time parameterUi:Non dimensional velocity component in
5、 i th direction:Visco elasticity parameter :Density of fluids:Frequency of excitation6ISSN: 0975 6744| NOV 09 TO OCT 10 | Volume 1, Issue 1 Page 62. INTRODUCTION Due to wide ranging applications in the fields of Physics, Chemistry, Chemical Technology and in situations demanding efficient transfer o
6、f mass over inclined beds, the viscous drainage over an inclined rigid plane has been the subject of considerable interest to theoretical and experimental investigators during the last several years.In all experiments, where the transfer of viscous liquid from one container to another is involved, t
7、he rate at which the transfer takes place and the thin film adhering to the surfaces of the container is to be taken into account for the purpose of chemical calculations. Failure to do so leads to experimental error. Hence, the need for such analysis.The problem of flow of viscous incompressible fl
8、uid moving under gravity down a fixed inclined plane with the assumption that the velocity of the fluid at the free surface is given has been examined earlier by Sneddon. Later Bhattacharya 1 examined the problem when uniform tangential force S acts on the upper surface for a finite interval of time
9、. Jeffreys 2 initiated the problem of steady state profile over a vertical flat plate which was further examined by Green 3. Later, Gutfinger and Tallmadge 4 investigated steady state drainage over a vertical cylinder. These authors examined the problem in the absence of fluid inertia.Noll 5 defined
10、 a simple material as a substance for which stress can be determined with the entire knowledge of the history of the strain. This is called a simple fluid, if it has the property that at all local states, with the same mass density, are intrinsically equal in response, with all observable difference
11、s in response being due to definite differences in the history. For any given history , a retarded history can be defined as (1) being termed as a retardation factor. Assuming that the stress is more sensitive to recent deformation that to the deformations at distant past, Coleman and Noll 6 proved
12、that the theory of simple fluids yields the theory of perfect fluids as and that of Newtonian Fluids as a correction (up to the order of ) to the theory of the perfect fluids. Neglecting all the terms of the order of higher than two in , we have incompressible elastic viscous fluid of second order t
13、ype whose constitutive relation is governed by (2) where (3) and (4)In the above equations, is the stress-tensor, are the components of velocity and acceleration in the direction of the i th coordinate , P is indeterminate hydrostatic pressure and the coefficients and are material constants.The cons
14、titutive relation for general Rivlin-Ericksen 7 fluids also reduces to equation (2) when the squares and higher orders of are neglected, the coefficients being constants. Also the non-Newtonian models considered by Reiner 8 could be obtained from equation (2) when, naming as the coefficient of cross
15、 viscosity. With reference to the Rivlin Ericksen fluids, may be called as the coefficient of viscosity. It has been reported that a solution of poly-iso-butylene in cetane behaves as a second order fluid and Markovitz 9 determined the constants and.Viscous fluid flow over wavy wall had attracted the attention of relatively few researchers although the analysis of such flows finds application in different areas such as
