Stability Of Nonisothermal Flow Research Articles

Stability of nonisothermal flow of a viscous liquid in an annular channel

In nonisothermal flow of a viscous liquid in an annular channel between coaxial cylinders where the outer cylinder has finite dimensions and is stationary, and the inner cylinder infinitely moves along the axis, the central position of the latter is unstable. When superimposing a thermal field, principally it is possible to create as large a force as required which holds the inner cylinder exactly on center.

An experimental study of the stability of displacement of a cold fluid by a hot fluid in a porous medium

The stability of non-isothermal flow through porous media is investigated experimentally when both density and viscosity are functions of temperature. The instability phenomena are due to the buoyancy effect of an upward-directed density gradient and to the fingering effect of the displacement of a more viscous fluid by a less viscous one. A series of centre-line temperatures in a packed column have been obtained where hot fluid displaces the same cold fluid (miscible thermal displacement) in a vertically upward direction. Based on these temperatures a stability criterion has been established in terms of Rayleigh number. Results are compared with available theoretical data.

Stability of non isothermal flow of a film of viscous liquid on an inclined plane

A study is made of the stability of nonisothermal flow of a film of viscous liquid down an inclined plane under the influence of gravity with allowance for dissipation of energy in the flow. It is assumed that the liquid is incompressible, and that its physical properties do not depend on the temperature. On the free surface of the film, allowance is made for evaporation and condensation effects. The treatment is in the long-wavelength approximation of the method proposed by Yih Chia-shun [1]. The expression obtained for the critical Reynolds number at which the flow becomes unstable indicates that viscous dissipation plays a destabilizing part in a nonisothermal flow.

Stability of displacement of a cold fluid by a hot fluid in a porous medium

The stability of nonisothermal flow through porous media is investigated, when both density and viscosity variations with temperature are present. The instability phenomena are due to the buoyancy effect of a density gradient directed upward, and to the fingering effect of the displacement of a more viscous fluid by a less viscous one. Small perturbations are superimposed on the basic flow, and their development is investigated in order to establish the criteria of flow stability. The flow variables are expanded in a series of eigenfunctions, and the ensuing system of ordinary differential equations is solved numerically. Criteria of flow stability and parameters affecting flow conditions are studied.

Stability of non-isothermal flow in channels—III. Temperature-dependent power-law fluids with heat generation

The simplified lubrication type model used in Parts I and II of this work 1 1 Parts I and II of this work have appeared in Chem. Engng Sci. on the flow of temperature dependent power-law fluids in channels is here extended to take account of heat generation. It is found that the steady unidirectional flow solution, for the case of flat plates forming a channel of uniform length, leads to a relation between pressure drop P and mean velocity V that can display two ranges of V for which d P/d V < 0. One of these is associated with the physical mechanisms investigated earlier, that of initially hot fluid flowing into a cold channel where generation is unimportant; the second, and often distinct, range relates to the interaction between heat generation and heat transfer and is relevant at much larger values of V. The stability of this unidirectional flow to small disturbances is then investigated. Once again it is found that all regions for which d P/d V < 0 lie within the unstable part of operating space. In particular, this means that whatever the inlet temperature of the fluid, and whatever the channel wall temperature, there will always be some value of V above which the unidirectional flow is unstable.

Stability of non-isothermal flow in channels—II: Temperature dependent power-law fluids without heat generation

The simplified lubrication type model used in earlier work on temperature dependent Newtonian fluid flow in a cooled channel is here extended to take account of shear dependent viscosity and is applied not only to plane channel flow but also to radial flow between parallel circular discs. Two additional dimensionless parameters are thereby introduced: m, a power-law index, and R, a geometrical variable based on the inlet and exit radii of the discs. The results are unsurprising: symmetrical flow curves of pressure P vs flow rate V are found to be multi-valued if B, the dimensionless inlet temperature, is large enough; the minimum value of B for which this occurs decreases as the fluid becomes more pseudoplastic, but is only weakly dependent upon the disc geometry, R, until the inner radius is a very small fraction of the outer radius. Linearized stability analysis for the flow is carried out in the same way as before: this shows that all symmetrical flow regimes for which d P/d V ⩽ 0 are unstable to small perturbations and so in practice steady flows showing less symmetry than the boundary conditions are to be expected. Entrance and exit pressure losses are shown to lead to greater stability.

Stability of non-isothermal flow in channels—I. Temperature dependent Newtonian fluid without heat generation

We study here stability of non-isothermal flow between two closely spaced, heat conducting, parallel flat plates forming a channel of length l, uniform depth h and infinite width. Very viscous fluid enters along x = 0 at temperature t 1⪢ w the plate temperature. We look for flow nonuniformity caused by coupling between the energy equation, which describes the heat transfer mechanism between fluid and channel walls, and the flow equation which includes the (exponential) temperature dependence of viscosity. The simplified model chosen for the flow assumes similarity profiles for velocity and temperature in the flow direction. The velocities are assumed non-zero in both directions parallel to the bounding plates and negligible in the direction perpendicular to the plates ( h ⪡ l). This is analogous to lubrication theory. The governing equations are taken to be ▪ where v is a two-dimensional mean velocity in the ( x, y)-plane, p( x,y) is pressure and T( x, y) temperature; H is a thermal transfer coefficient; C and b are rheological parameters of the fluid; p(0, y) and p( l,y) are constant, their difference being the relevant pressure drop. We show first that the system can be described in terms of two dimensionless parameters B = b( T 1− T w ) and Gz = V| Hl, V being the mean velocity, and that for steady flow (independent of y, with v = ( V, 0)) a plot of inlet pressure P vs V is multivalued for B sufficiently large. We then investigate the stability of this unidirectional flow to small disturbances of the form fn(x) exp ( iλ y+ω t), λ real. The resulting eigen-value problem for λ ( B, Gz, ω) is solved numerically. Results indicate that a unique neutral stability curve in the plane of ( B, Gz) can be obtained for ω = 0. This stability curve indicates that for B < 2·4, flow instability will not be observed for any Gz. A comparison between the multivalued curve in V( P) obtained for a unidirectional solution and the neutral stability curve is also presented.

On the stability of non-isothermal flow in channels

When polymer melts flow through narrow channel or small-orifice dies, highly unsteady or irregular flow have sometimes been observed even when the imposed boundary conditions are steady and uniform (Pearson, 1969).