Linear stability of a plane poiseuille flow of oldroyd fluid

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. i, pp. 5–10, January–February, 1988.     

Stability of plane poiseuille flow of a viscous anisotropic fluid

Experimental investigations show that the presence in a fluid of fibers and rigid asymmetric particles leads to a greater stability of flow in tubes and lowers the turbulent frictional resistance in a certain range of Reynolds numbers [1]. In the present paper, the anisotropic structure of a fluid with additives is described by Ericksen's rheological model [2]. The parameters of the model are particularized in accordance with the paper [3] of Pilipenko, Kalinichenko, and Lemak, and in the limiting case of weak Brownian motion allowance is made for the effect of the predominant orientation of the particles and the influence of additives on the longitudinal and shear viscosity. The stability of the Poiseuille flow is considered in the linear formulation. In an anisotropic viscous fluid, an equation of Orr-Sommerfeld type has a singular point. A rule for choosing the path of integration avoiding the singular point is obtained on the basis of a generalization of the method of Dikii [4] proposed in an investigation of the stability of the flow of an ideal fluid. The results of numerical calculations of the neutral stability curve for two-dimensional perturbations are given.     

Analytical and numerical solution of the poiseuille flow of a Johnson-Segalman fluid

The axisymmetric Poiseuille flow of a Johnson-Segalman fluid is selected as a specific one-dimensional example for testing numerical algorithms, while analytical results are also made available. A particular emphasis is put on the appearance of limit points with some numerical algorithms.     

Stability of plane poiseuille and couette flow of a Maxwell fluid

The classical Orr-Sommerfeld analysis is extended to a Maxwell fluid in fully developed Poiseuille flow between two flat plates and Couette flow between two flat plates. For the Poiseuille flow problem eigenmodes that are anti-symmetric in position are considered to augment the literature results for the symmetric eigenmodes. A shooting method with a stiff integrator, orthonormalization, and Newton-Raphson iterations on the eigenvalue are used to find the eigenvalues. The most dangerous mode is the anti-symmetric one, and both symmetric and anti-symmetric modes are more dangerous when the wave number and the Weissenberg number are large. No unstable eigenvalues are found.     

Effect of ion slip on the time-varying Hartmann flow of a non-Newtonian viscoelastic fluid with heat transfer

Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.     

Effect of free surface heat transfer on thermocapillary flow in double-layer fluid structures

In this paper, we examine the effect of heat transfer at the free encapsulant-air surface on thermocapillary flow in a rectangular melt-encapsulant double-layer fluid structure. We show that increased heat transfer to the double-layer system through the free surface weakens thermocapillary convection in the encapsulant phase and enhances the convection in the melt phase.     

Oblique stagnation-point flow of a viscoelastic fluid with heat transfer

The two-dimensional forced convection stagnation-point flow and heat transfer of a viscoelastic second grade fluid obliquely impinging on an infinite plane wall is considered as an exact solution of the full partial differential equations. This oblique flow consists of an orthogonal stagnation-point flow to which a shear flow whose vorticity is fixed at infinity is added. The relative importance of these flows is measured by a parameter γ. The viscoelastic problem is reduced to two ordinary differential equations governed by the Weissenberg number W_e, two parameters α and β, the later being a free parameter β, introduced by Tooke and Blyth [A note on oblique stagnation-point flow, Physics of Fluids 20 (2008) 033101-1–3], and the Prandtl number Pr. The two cases when α=β and α≠β are, respectively, considered. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. It is found that the location of the separation point x_s of the boundary layer moves continuously from the left to the right of the origin of the axes (x_s<0).     

Effect of heat transfer on the flow of a second‐grade fluid in divergent/convergent channel

This paper studies the effects of a second‐grade fluid on the flow and heat transfer characteristics in a divergent/convergent channel. The momentum and energy equations are first given in a nondimensional form and then solved analytically using the method of homotopy analysis method. Convergence of derived series solutions is shown. Graphical results for the velocity and the temperatures are presented and discussed for various emerging parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

Groove geometry effects on turbulent heat transfer and fluid flow

The present work represents a two-dimensional numerical prediction of forced turbulent flow heat transfer through a grooved tube. Four geometric groove shapes (circular, rectangular, trapezoidal and triangular) were selected to perform the study, as well as two aspect ratios of groove-depth to tube diameter (e/D = 0.1 and 0.2). The study focuses on the influence of the geometrical shapes of grooves and groove-depth on heat transfer and fluid flow characteristics for Reynolds number ranging from 10,000 to 20,000. The characteristics of Nusselt number, friction factor and entropy generation are studied numerically by the aid of the computational fluid dynamics (CFD) commercial code of FLUENT. It is observed that the best performance occurs with the lower depth-groove ratio, whereas it is found that the grooved tube provides a considerable increase in heat transfer at about 64.4 % over the smooth tube and a maximum gain of 1.52 on thermal performance factor is obtained for the triangular groove with (e/D = 0.1).     

Effect of high-amplitude flow pulsations on heat transfer

We present results of an experimental study of the effect of flow pulsations on turbulent heat transfer in the transverse direction in propagation of sound waves. A significant increase in heat-transfer intensity was recorded at mean-square pressure pulsation amplitude p=168–180 dB at frequency f=100–150 Hz. The dependence of heat-transfer intensity on acoustic field characteristics is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–172, March–April, 1975.     

Conjugate heat transfer in the unbounded flow of a viscoelastic fluid past a sphere

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime (Re = 0.01). The problem is numerically solved with the finite-volume method assuming axisymmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah (0 ≤ De ≤ 100), Prandtl (10⁰ ≤ Pr ≤ 10⁵) and Brinkman (0 ≤ Br ≤ 100) numbers, in the presence or absence of thermal contact resistance at the solid–fluid interface and for different conductivity ratios (0.1 ≤ κ ≤ 10). The drag coefficient shows a monotonic decrease with De, whereas the normalized stresses on the sphere surface and in the wake first increase and then decrease with De. A negative wake was observed for the two solvent viscosity ratios tested (β = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with De after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The dimensionless temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as Br increases. Overall, a simplified PTT fluid can moderately enhance heat transfer compared to a Newtonian fluid, but increasing De does not necessarily improve heat exchange.     

Instability of a horizontal plane-channel flow of a dilute suspension

The stability of a horizontal plane-channel flow of a dilute suspension is studied theoretically. It is shown that the mechanism of action of the sedimenting particles on the flow stability parameters is equivalent to the effect of a distributed flow stratification and is attributable to the vertical nonuniformity of the body force induced by the excess weight of the sedimenting particles. A strong dependence of the disturbance growth rate on the location of the interface between the suspension and the pure liquid is detected.     

On flow of a fourth‐grade fluid with heat transfer

The influence of heat transfer on the steady flow of a fourth‐grade fluid between two stationary parallel porous plates is studied. The flow is engendered under the application of a constant pressure gradient. The concept of homotopy analysis method is utilized for the series solution of the governing problem. Numerical solution has been also carried out. In addition, both analytic and numerical solutions are compared. The variations of embedded parameters into the solution are predicted through the graphical representations. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady fluid flow and heat transfer over a bank of flat tubes

Transient numerical simulations of fluid flow and heat transfer over a bank of flat tubes have been carried for both in-line and staggered configurations for the following boundary conditions: (a) isothermal and (b) isoflux. The effect of Reynolds number, Prandtl number, length ratio, and the height ratio, on the Nusselt number, and the dimensionless pressure drop are elucidated. Correlations are proposed for both pressure drop and Nusselt number and optimum configurations have been determined.     

Laminar fluid flow and heat transfer in a duct of cross-shaped cross-section

Fully-developed flow calculations were performed on ducts of cross-shaped cross-section, which may be regarded as possible candidates for compact heat exchanger configurations. A parametric study was made on the friction and heat transfer characteristics in terms of the parameter α associated with the decrease in the cross-sectional area (namely, α=0 for a square duct and α→1 for infinite parallel plates). As increasing α, both the Nusselt number and friction coefficient decrease toward their minimum levels, but then, increase gradually, and overshoot those of a square duct. Consequently, the heat transfer coefficient shows a significant increase for α>0.4, suggesting an excellent performance of heat transfer surfaces in the duct of cross-shaped cross-section.     

A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case).     

Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

A computational study of heat transfer from rectangular cylinders is carried out. Rectangular cylinders are distinguished based on the ratio of the length of streamwise face to the height of the cross-stream face (side ratio, R). The simulations were performed to understand the heat transfer in a flow field comprising separation, reattachment, vortex shedding and stagnation. The Partially-Averaged Navier–Stokes (PANS) modeling approach is used to solve the turbulent flow physics associated and the wall resolve approach is used for the near wall treatment because of the flow separation involved. The simulations were performed using a finite volume based opensource software, OpenFOAM, at Reynolds number (Re) = 22,000 for rectangular cylinder at constant temperature kept in an air stream. Two critical side ratios were obtained, R = 0.62 and 3.0. At R = 0.62, the maximum value of the drag coefficient (C_d) = 2.681 was observed which gradually reduced by 54% at R = 4.0. The base pressure coefficient and global Nusselt number also attained the maximum value at R = 0.62 and from R = 2.5 to 3.0 a sharp discontinuous increase by 140% in the Strouhal number was observed. At R = 0.62, it was observed that the separated flow reattaches at the trailing edge after rolling over the side face and therefore increases the overall Nusselt number. The phase averaging was also performed to analyze the unsteady behavior of heat transfer.