Non-isothermal Channel Flow Research Articles

Nonisothermal Channel Flow of a Non-Newtonian Fluid under the Conditions of Chemical Transformations

Nonisothermal Channel Flow of a Non-Newtonian Fluid under the Conditions of Chemical Transformations

Non-isothermal Bingham fluid flow between two horizontal parallel plates with Ion-slip and Hall currents

This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.

Numerical Analysis of the Transient and Non-Isothermal Channel Flow of a Third-Grade Fluid with Convective Cooling

We investigate the unsteady, non-isothermal, pressure driven channel flow of a third grade liquid subject to exothermic reactions. We assume temperature dependent fluid viscosity and also that the flow is subjected to convective cooling at the channel walls. The exothermic reactions are modelled via Arrhenius kinetics and the convective heat exchange with the ambient at the channel walls follows Newton’s law of cooling. The time-dependent, coupled, and nonlinear partial differential equations governing the flow and heat transfer problem are solved numerically using efficient, semi-implicit finite difference algorithms. The sensitivity of the fluid flow and heat transfer system to the various embedded parameters is explored.

Large eddy simulation of turbulent heat transfer in a non-isothermal channel: Effects of temperature-dependent viscosity and thermal conductivity

In this work, we perform large eddy simulations (LES) to study the influence of variable viscosity and thermal conductivity on forced convection in a non-isothermal channel flow. To prevent thermal dilatational effect, the gas density is assumed to be constant. The temperature ratio T2/T1 is varied from 1.01 to 2.2, where T2 and T1 are the temperatures of hot and cold walls, respectively. The mean turbulent Reynolds number is kept the same at 395. The results indicated that the mean flow fields are significantly affected by the temperature-dependent fluid properties. Despite the modified velocity and temperature profiles, it is interesting to note that the molecular momentum and heat transport across the channel remain unchanged. Meanwhile, pronounced differences are exhibited for various turbulence statistics such as root-mean-square velocity and temperature fluctuations, Reynolds shear stress, and correlation between streamwise velocity and temperature. Compared with the isothermal flows, it is also found that the presence of the temperature gradient tends to diminish heat transfer. With increasing the temperature ratio, the Nusselt numbers for both sides are reduced. Moreover, the hot side has a higher Nusselt number than the one at the cold side.

A Comparison of Theoretical and Empirical Viscosity Models for a Nanofluid in a Non-Isothermal Channel Flow

A Comparison of Theoretical and Empirical Viscosity Models for a Nanofluid in a Non-Isothermal Channel Flow

Chebyshev Approximation for Nanofluid flow of Non-Isothermal Channel Flow under Constant Heat Flux

This paper investigates the Nano-fluid for a non-isothermal channel flow under the effect of a constant pressure gradient acting along the channel axis. Two-dimensional, non-isothermal, steady flow of an incompressible fluid in a channel is taken into consideration. Upper and lower walls of the channel are kept at the same constant heat flux. To consider the effect of conductivity and viscosity, Maxwell and Brinkman’s models are used respectively. The effects of volume fraction, pressure gradient and Reynolds numbers on velocity and temperature profiles are discussed for the Nano-fluid Alumina. Water is used as a base fluid. The comparisons of the flow characteristics, including the distributions of velocity, temperature and volumetric flow rate of aluminum oxide are also given in the paper. Shear stress distribution along the channel axis and pressure gradient for different volume fraction are presented as well. Discretization is performed using a Pseudospectral technique based on Chebyshev polynomial expansions. The resulting nonlinear, coupled boundary value problem is solved iteratively using Chebyshev pseudospectral method.

LES of droplet-laden non-isothermal channel flow

In this paper subgrid models for LES of droplet-laden non-isothermal channel flow are tested and improved for three Reynolds numbers based on friction velocity, Reτ of 150, 395, and 950 with the aim to develop a simulation method for LES of a droplet-laden Ranque-Hilsch vortex tube. A new subgrid model combining the beneficial properties of the dynamic eddy-viscosity model and the approximate deconvolution model is proposed. Furthermore, the subgrid model in the droplet equations based on approximate deconvolution is found to perform well also in non-isothermal channel flow. At the highest Reynolds number in the test the dynamic model yields results with a similar accuracy as the approximate deconvolution model.

Shear flow characteristics and crystallization kinetics during steady non-isothermal flow of Vitreloy-1

The steady non-isothermal channel flow of Vitreloy-1 (Zr 41.25Ti 13.75Cu 12.5Ni 10Be 22.5) is simulated by means of finite element modeling. Non-Newtonian flow behavior is accounted for by employing a self-consistent shear-rate dependent flow law. Transition to non-Newtonian flow and shear localization is obtained by superimposing the computed flow evolution onto an experimentally developed flow diagram. The coordinate points that mark transition to shear localization form a narrow boundary layer ∼23% of the channel thickness. The deformation-induced enhancement of crystallization kinetics is approximately accounted for by utilizing the shear-rate dependent viscosity law to shift the transformation time in the apparent TTT diagram. The kinetics of crystallization during flow are assessed by superimposing the temperature evolution onto the “shifted” TTT diagram. The coordinate points that mark the onset of crystallization form a boundary layer ∼15% of the channel thickness, which are narrower than the shear localization boundary layer suggesting that crystallites will form in the shear-banded region.

The hysteresis phenomenon in nonisothermal channel flow of a non-Newtonian liquid

This paper is concerned with the well-known phenomenon of hysteresis in the pressure drop–flow rate relationship for steady-state nonisothermal pressure-driven flow of a non-Newtonian fluid in a channel. The fluid properties are described by a power law with an exponential temperature dependence of viscosity. Solutions of the motion and energy balance equations have been obtained in terms of two approximations for nonisothermal flow in a finite-length cylindrical channel. The conditions of hysteresis and the related multivalued solution of a nonlinear boundary value problem have been found analytically. As part of the analysis, experimental studies have been carried out to verify the predictions of the analytical treatment.

Nonisothermal flow of a rarefied multiatomic gas in a channel

The authors consider the slow flow of a polyatomic gas in a plane channel, bounded at x = + or - d/2 by two infinite parallel planes. Interest in nonisothermal flow in channels and the thermomolecular pressure difference produced by conductivity, which give experimental data on the total thermal conductivity of polyatomic gas provides an independent source of data on internal energy relation times, which are usually determined by experiments on ultrasound absorption or other methods.

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).