Viscoelastic boundary layer

Thereafter, a series of studies on heat transfer effects on viscoelastic fluid have been made by many authors under different physical situations including (Abel et al., 2002, Bhattacharya et al., 1998, Datti et al., 2004, Idrees Abel, 1996, Lawrence Rao, 1992, Prasad et al., 2000, 2002). (Khan Sanjayanand, 2005) have derived similarity solution of viscoelastic boundary layer flow and heat transfer over an exponential stretching surface. (Cortell, 2006) have studied flow and heat transfer of a viscoelastic fluid over stretching surface considering both constant sheet temperature and prescribed sheet temperature. (Abel et al., 2007) carried out a study of viscoelastic boundary layer flow and heat transfer over a stretching surface in the presence of non-uniform heat source and viscous dissipation considering prescribed surface temperature and prescribed surface heat flux. 

Khan, 2006) studied the case of the boundary layer problem on heat transfer in a viscoelastic boundary layer fluid flow over a non-isothermal porous sheet, taking into account the effect a continuous suction/blowing of the fluid, through the porous boundary. The effects of a transverse magnetic field and electric field on momentum and heat transfer characteristics in viscoelastic fluid over a stretching sheet taking into accoimt viscous dissipation and ohmic dissipation is presented by (Abel et al., 2008). (Hsiao, 2007) studied... 

Abel, M. S. Siddheshwar, P. G. Nandeppanavar, M. M. (2007). Heat transfer in a viscoelastic boundary layer low over a stretching sheet with viscous dissipation and non-uniform heat source, Int.. Heat Mass Transfer, 50, pp. 960-966, ISSN 0017-9310. 

Khan, S. K Sanjayanand, E. ( 2005). Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet, Int J. Heat Mass Transfer, 48, p>p. 1534-1542, ISSN 0017-9310. 

From the results obtained in [344] it follows that the composites with PMF are more likely to develop a secondary network and a considerable deformation is needed to break it. As the authors of [344] note, at low frequencies the Gr(to) relationship for Specimens Nos. 4 and 5 (Table 16) has the form typical of a viscoelastic body. This kind of behavior has been attributed to the formation of the spatial skeleton of filler owing to the overlap of the thin boundary layers of polymer. The authors also note that only plastic deformations occurred in shear flow. 

B. Thickness of the Hydrodynamic Boundary Layer for a Viscoelastic Fluid... 

In a car ully designed high quality resonator, the dissipation processes 2), 3), and 4) can be kept negligibly small. It is important to minimize the perturbations caused by these effects, because a theoretical treatment is difficult. It was shown in Ref. and that such an optimization of the cell is in fact possible and then only viscous and thermal boundary layer losses ne be taken into account. Throughout the principal portion of the volume of the resonator, the expansion and contraction of the gas occurs adiabatically. Near the walls, however, this process becomes isothermal. This leads to heat conduction, which is responsible for the thermal dissipation process. The viscous dissipation can be explained by the boundary conditions imposed by the wails. At the surface, the tangential component of the acoustic velocity is 2 0, whereas in the interior of the cavity, it is proportional to the gradient of the acoustic pressure. Thus, viscoelastic dissipation occurs in the transition region. 

For flow over a bluff body, the fluid elements are subjected to a rapid change in deformations near the frontal face hence elastic effects are likely to be important in this region and the simple boundary layer approximations shoifld not be apphed to visco-elastic materials in this region. However, if elastic effects are negligibly small, the previous approach is reasonably satisfactory for viscoelastic fluids. For instance, the normal stresses developed in visco-elastic fluids will give rise to additional terms in the vr-component of the momentum balance. 

In two-dimensional Cartesian coordinate system x,y) we consider magneto-convection, steady, laminar, electrically conduction, boundary layer flow of a viscoelastic fluid caused by a stretching surface in the presence of a uniform transverse magnetic field and a heat source. The x -axis is taken in the direction of the main flow along the plate and the y -axis is normal to the plate with velocity components u,v in these directions. 

Quantity Laminar boundary layer Turbulent boundary layer Percolation+ viscous BL loss Coulomb friction loss Viscoelastic (KV) Viscous mud Viscoelastic (Jeffreys)... 

All the studies conducted on fracture of bulk polymers are certainly relevant to the adherence of polymers, the mechanisms of losses at a crack tip being the same viscoelastic losses due to moving stresses, work to extract chains or fibrils, and viscous drag in the presence of a liquid. It is probable that the various theories of adhesion, namely, theory of wetting, theory of the rheological factor, theory of the chemical bond, theory of the weak boundary layer, and theory of interdiffusion, are all valid, each corresponding to an emphasis on a dominant mechanism. 

In summary, we have discussed how interfacial effects can influence the viscoelastic properties of polymer coatings, polymer melts and solutes, and even simple nonpolar liquids within an interfacial boundary regime. In high molecular weight polymer systems, the interfacial boundary regime can reach up to hundreds of nanometers. The interfacial boundary layer of simple nonpolar fluids is restricted to a few nanometers. While outside the critical interfacial boundary layer interfacial effects on properties can be approached with phenomenological theories, modified or new theories are in demand within the structurally - or entropically cooled interfacial boundary layer. The modern theoretical approach of the fractal dimensionality will be discussed next. 

Aside from the studies referred to in this chapter, there is a lot of information available on the boundary layer flows of non-Newtonian fluids over plates, cylinders, and needles. A partial review of momentum boundary layers has been provided by Schowalter (1977), whereas that of heat and mass boundary layers have been given by Shenoy and Mashelkar (1982), Chhabra (1993b, 1993c), and, more recently, Ghosh et al. (1994). The viscoelastic diffusion and thermal boundary layers have been revisited recently by Ruckenstein (1994). 

Ruckenstein, E., Thermal and diffusion boundary layers in viscoelastic flows, Ind. Eng. Chem. Res. 55 2331-2335 (1994). 

Note that in viscoelastic turbulent flows, because of the shear thinning effect [3 5,79], we have to distinguish between two different types of wall units. One is based on the zero shear properties and the other, applicable for channel and boundary layer... 

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