Constant Fluid Properties Research Articles

Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel Free Stream

The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite‐difference scheme known as Keller‐box method. Numerical results for the flow and the thermal fields for both cases are obtained for various values of the free stream parameter and the Prandtl number. It is found that dual solutions exist for both cases when the fluid and the plate move in the opposite directions. Moreover, fluid with constant properties shows drag reduction characteristics compared to fluid with variable viscosity.

Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers

This work extends an existing analytical solution for pressure buildup because of CO2 injection in brine aquifers by incorporating effects associated with partial miscibility. These include evaporation of water into the CO2 rich phase and dissolution of CO2 into brine and salt precipitation. The resulting equations are closed‐form, including the locations of the associated leading and trailing shock fronts. Derivation of the analytical solution involves making a number of simplifying assumptions including: vertical pressure equilibrium, negligible capillary pressure, and constant fluid properties. The analytical solution is compared to results from TOUGH2 and found to accurately approximate the extent of the dry‐out zone around the well, the resulting permeability enhancement due to residual brine evaporation, the volumetric saturation of precipitated salt, and the vertically averaged pressure distribution in both space and time for the four scenarios studied. While brine evaporation is found to have a considerable effect on pressure, the effect of CO2 dissolution is found to be small. The resulting equations remain simple to evaluate in spreadsheet software and represent a significant improvement on current methods for estimating pressure‐limited CO2 storage capacity.

Combined influences of viscous dissipation, non-uniform Joule heating and variable thermophysical properties on convective heat transfer in microtubes

This study presents a comprehensive investigation on hydrodynamic and thermal transport properties of mixed electroosmotically and pressure driven flow in microtubes. Particular emphasis is given to investigating the combined consequences of viscous dissipation, non-uniform Joule heating, and variable thermophysical properties. Analytical solutions are obtained using the Debye–Hückel linearization and constant fluid properties assumption, while a numerical solution is presented for variable fluid properties and non-uniform distribution of Joule heating. The results indicate that, viscous heating effect is pronounced significantly when a favorable pressure gradient exists and cannot be neglected at low values of the dimensionless Debye–Hückel parameter. Moreover, uniform Joule heating assumption, even at low zeta potentials, may reduce the accuracy of the predicted thermal features considerably. The wall shear stress is found to be strongly dependent upon the zeta potential, which is underestimated by the Debye–Hückel linearization. Compared with the constant fluid properties case, decreasing electrical resistivity of the fluid by increasing temperature, amplifies the total energy generation due to the Joule heating and reduces the Nusselt number.

Confined thermocapillary motion of a three-dimensional deformable drop

In this paper, simulations are performed of the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus. The refined level-set grid method is used to track the interface and resolve very small deformations. We compare our results to theoretically predicted thermocapillary migration velocities of drops and to experimentally measured migration velocities in microgravity experiments. The motivation of the present work is to address four important questions surrounding thermocapillary migration. These are as follows. (1) What is the impact of initial conditions on both the initial transient and steady state drop behavior? (2) What is the impact of the domain geometry on drop behavior? (3) Do drops deform for intermediate Marangoni numbers and are those deformations axisymmetric? (4) Can the assumption of constant temperature fluid properties be used when simulating physical experiments? To answer the first question, we explore the parameter space of initial drop temperature distribution and drop holding time. We find that in lower Marangoni number regimes, the drop rapidly settles to a quasisteady state. For larger Marangoni numbers, the initial conditions dominate the drop behavior. To address the second and third questions, we look at the spatial distribution of tangential temperature gradients on the surface of the drop as well as drop deformations and migration velocities. The domain geometry induces nonaxisymmetric deformations and temperature distributions. The results of several axisymmetric runs with realistic physical properties are examined to answer the fourth question. It is found that the variation of material properties influences the drop migration behavior in a nontrivial way.

The developing heat transfer and fluid flow in micro-channel heat sink with viscous heating effect

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper, considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered: water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with Dh = 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered: heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains the fully developed value as the external heating is equal with the internal viscous heating.

Effect of surface radiation on the breakdown of steady natural convection flows in a square, air-filled cavity containing a centered inner body

The physical model considered in the present numerical work is a square air-filled cavity cooled from below and above, with a heated square body located at the cavity center. The aim is to establish the effects of radiation interchanges amongst surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flows. Owing to the low temperature differences involved (1 K ≤ ΔT ≤ 5 K), the two-dimensional model is based on the Boussinesq approximation and constant thermophysical fluid properties at room temperature. The cavity walls are assumed gray and diffuse. The flow structure is investigated for various Rayleigh numbers, emissivities of the wall surfaces and sizes of the inner body. The results clearly establish the influence of surface radiation, both for steady and unsteady flows. For the geometry and thermal boundary conditions considered, the Rayleigh number for the transition to unsteady flows is considerably increased under the influence of radiation. This work underlines the difficulties in comparing experimental data and numerical solutions for gas-filled cavities partly subjected to wall heat flux boundary conditions.

Convective slip flow of rarefied fluids over a wedge with thermal jump and variable transport properties

Convective slip flow of slightly rarefied fluids over a wedge with thermal jump and temperature dependent transport properties such as fluid viscosity and thermal conductivity is studied numerically. Due to the appearance of a slip condition at the surface of the boundary no self similar solution can be found. Locally similar solutions are obtained numerically by using the widely used and very robust computer algebra software Maple. The nondimensional velocity, temperature, Prandtl number, hydrodynamic boundary layer thickness, displacement thickness, momentum thickness, and thermal boundary layer thickness are displayed graphically for various values of the pertinent parameters. The results show that strong rarefaction and increased angle of wedge significantly controls the growth of the hydrodynamic and thermal boundary layers thickness, which are found to be lower for the flow of constant fluid properties than for the flow of variable fluid properties.

Exact solution for the conjugate fluid–fluid problem in the thermal entrance region of laminar counterflow heat exchangers

A generalized Lévêque solution is presented for the conjugate fluid–fluid problem that arises in the thermal entrance region of laminar counterflow heat exchangers. The analysis, carried out for constant property fluids, assumes that the Prandtl and Peclet numbers are both large compared to unity, and neglects axial conduction both in the fluids and in the plate, assumed to be thermally thin. Under these conditions, the thermal entrance region admits an asymptotic self-similar description where the temperature varies as a power j of the axial distance, with the particularity that the self-similarity exponent must be determined as an eigenvalue by solving a transcendental equation arising from the requirement of continuity of heat fluxes at the heat conducting wall. Specifically, the analysis reveals that j depends only on the lumped parameter k ˆ = ( A 2 / A 1 ) 1 / 3 ( α 1 / α 2 ) 1 / 3 ( k 2 / k 1 ) , defined in terms of the ratios of the wall velocity gradients, A i , thermal diffusivities, α i , and thermal conductivities, k i , of the fluids entering, 1, and exiting, 2, the heat exchanger. Moreover, it is shown that for large (small) values of k ˆ the solution reduces to the classical first (second) Lévêque solution. Closed-form analytical expressions for the asymptotic temperature distributions and local heat-transfer rate in the thermal entrance region are given and compared with numerical results in the counterflow parallel-plate configuration, showing very good agreement in all cases.

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Local and average heat transfer in the thermally developing region of an asymmetrically heated channel

Forced convection heat transfer between parallel plates kept at unequal wall temperatures has been studied assuming laminar, incompressible, steady flow of a Newtonian fluid of constant thermophysical properties. Unequal wall temperatures have been characterized by an asymmetry parameter. It has been shown that the heat transferred from the walls monotonically varies with the axial distance even though the Nusselt number (at one of the walls) does not vary continuously due to asymmetry. It has been found that a modified Nusselt number varies continuously with the asymmetry parameter. Plots to obtain heat transferred from each wall have been presented which serve the purpose of mean Nusselt number. Non-dimensional heat transferred from the two walls is independent of the asymmetry parameter. The down stream boundary condition applicable for the thermal field when the walls are kept at unequal temperatures has been brought out which becomes necessary when solving elliptic form of conservation of thermal energy equation, say, when axial conduction is included.

A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity

This article presents a numerical simulation of combined radiation and natural convection in a three-dimensional differentially heated rectangular cavity with two opposite side walls kept at a temperature ratio Th/Tc=2.0 and Tc=500 K, with others walls insulated. A non-Boussinesq variable density approach is used to incorporate density changes due to temperature variation. The Navier–Stokes (NSE), temperature, as well as the radiative transfer (RTE) equations are solved numerically by a finite volume method, with constant thermophysical fluid properties (except density) for Rayleigh number Ra=105 and Prandtl number Pr=0.71. The convective, radiative, and total heat transfer on the isothermal and adiabatic walls is studied along with the flow phenomena. The results reveal an extraordinarily complex flow field, wherein, along with the main flow, many secondary flow regions and singular points exist at the different planes and are affected by the optical properties of the fluid. The heat transfer decreases with increase in optical thickness and the pure convection Nusselt number is approached as the optical thickness τ>100, but with substantially different velocity field. The wall emissivity has a strong influence on the heat transfer but the scattering albedo does not.

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.

Numerical analysis of laminar flow in micro-tubes with a slip boundary

Investigated numerically are the effects of slip and viscous heat dissipation on the friction number of thermally developing laminar water flow in micro-tubes. Also investigated are the effects of the micro-tube diameter, D, aspect ratio, L/ D, and Reynolds number on the friction number. The decrease in the dynamic viscosity slightly decreases the friction number below that of the Hagen–Poiseuille, determined from the solution of the Navier–Stokes equations assuming thermally and hydro-dynamically fully developed flow and constant fluid properties. A slip at the wall decreases the friction number with increased L/ D and decreased D. Results confirmed that the flow in micro-tubes is never thermally developed, significantly increasing the friction number with increased Reynolds number beyond critical values. Below the critical Reynolds numbers, the effect of the thermally developing flow is negligible and the friction numbers in micro-tubes is almost identical to those of the Hagen–Poiseuille, with and without slip at the wall. The comparison with reported experimental data confirmed the results of the present analysis.

Coherent anti-Stokes Raman scattering microscopy for quantitative characterization of mixing and flow in microfluidics

We present an optical, noninvasive and label-free approach to characterize flow profiles in microfluidic devices. Coherent anti-Stokes Raman scattering signals were used to map the mass transport in a microfluidic device that was then related back to the local flow rate of dilute solutes having constant fluid properties. Flow characterization was demonstrated in two common types of microfluidic devices, polydimethylsiloxane/glass square channels and wet-etched glass tapered channels.

Thermal Transport Characteristics of Mixed Pressure and Electro-Osmotically Driven Flow in Micro- and Nanochannels With Joule Heating

This study investigates convective transport phenomena of combined electro-osmotic and pressure-driven flow in a microchannel subject to constant surface heat flux, with Joule heating effect taken into account. The governing system of equations includes the electric potential field, flow field, and energy equations. Analytical solutions are obtained for constant fluid properties, while numerical solutions are presented for variable fluid properties. For constant properties, the problem is found to be governed by three ratios: the length scale ratio (the ratio of Debye length to half channel height), the velocity scale ratio (the ratio of pressure-driven velocity to electro-osmotic velocity), and the ratio of Joule heating to surface heat flux. A small length scale ratio corresponds to a microchannel, while finite length scale ratio represents a nanochannel. For electro-osmotic flow only, the momentum transport is solely a function of the length scale ratio. For combined electro-osmotic and pressure-driven flow, the velocity profile and therefore the friction factor depend on both the length scale ratio and the velocity scale ratio. Assuming a thermally fully developed flow, analytical expressions for the normalized temperature profile and Nusselt number are developed. The representative results for the friction factor, normalized temperature profile, and Nusselt number are illustrated for some typical values of the three ratios. For purely electro-osmotic flow, it is found that the Nusselt number increases with decreasing ε, approaching the value for slug flow as the length scale ratio approaches zero. For mixed flow with a given length scale ratio, the results show that the Nusselt number decreases with the velocity scale ratio, approaching the classical Poiseuille flow as the velocity scale ratio approaches infinite. When the effects of variable fluid properties are included in the analysis, numerical solutions are generated to explore the influence of thermal conductivity and viscosity variations with local temperature on the hydrodynamic and thermal characteristics of the fluid. These temperature-dependent property variations would initially develop pressure-driven flow, and correspondingly the dimensionless velocity and volume flow rate increase to account for such variations. The friction factor reduces considerably with viscosity variation, while the Nusselt number increases gently. Although the influence of thermal conductivity variation on the hydrodynamic characteristics is not impressive, it has certain impact on the heat transfer results; more specifically, increasing the conductivity variation will produce a sensible increase in Nusselt number but a small decrease in the normalized temperature.

Drag force acting on a neuromast in the fish lateral line trunk canal. II. Analytical modelling of parameter dependencies

In Part I of this two-part study, the coupled flows external and internal to the fish lateral line trunk canal were consecutively calculated by solving the Navier-Stokes (N-S) equations numerically in each domain. With the external flow known, the solution for the internal flow was obtained using a parallelepiped to simulate the neuromast cupula present between a pair of consecutive pores, allowing the calculation of the drag force acting on the neuromast cupula. While physically rigorous and accurate, the numerical approach is tedious and inefficient since it does not readily reveal the parameter dependencies of the drag force. In Part II of this work we present an analytically based physical-mathematical model for rapidly calculating the drag force acting on a neuromast cupula. The cupula is well approximated as an immobile sphere located inside a tube-shaped canal segment of circular cross section containing a constant property fluid in a steady-periodic oscillating state of motion. The analytical expression derived for the dimensionless drag force is of the form |F(N)/(|P(L) - P(R)|pi(D/2)(2) = f(d/D, L(t)/D, omega(*)(D), where |F(N)| is the amplitude of the drag force; |P(L)-P(R)| is the amplitude of the pressure difference driving the flow in the interpore tube segment; d/D is the ratio of sphere diameter to tube diameter; L(t)/D is the ratio of interpore tube segment length to tube diameter; and omega(*)(D) = omega(D/2)(2) /v is the oscillating flow kinetic Reynolds number (a dimensionless frequency). Present results show that the dimensionless drag force amplitude increases with decreasing L(t)/D and maximizes in the range 0.65< or =d/D< or =0.85, depending on the values of L(t)/D and omega(*)(D). It is also found that in the biologically relevant range of dimensionless frequencies 1< or = omega(*)(D) < or =20 and segment lengths 4< or =L(t)/D< or =16, the sphere tube (neuromast-canal) system acts as a low-pass filter for values d/D< or =0.75, approximately. For larger values of d/D the system is equally sensitive to all frequencies, but the drag force is significantly decreased. Comparisons with N-S calculations of the drag force show good agreement with the analytical model results. By revealing the parameter dependencies of the drag force, the model serves to guide biological understanding and the optimized design of corresponding bioinspired artificial sensors.

Analysis of single side ventilated and cross ventilated rooms by varying the width of the window opening using CFD

Natural ventilation contributes to the improvement of thermal comfort and quality conditions of the internal air and at the same time it is recognized very effective technique when applied properly. The present project refers to the numerical predictions of air velocities in cross and single-sided naturally ventilated rooms which are considered along with atmospheric zone. This is done for different sizes of the opening at particular height of the wall. Continuity and Momentum equations have been solved by control volume method. SIMPLE and SIMPLEC algorithm are used to solve these equations. Steady, k- ε turbulence model and incompressible flow of a constant property fluid under Boussinesq’s approximation have been considered. Air velocities were taken at various heights from middle of the opening and compared for single side ventilated and cross ventilated rooms. Air flow rate increases with increase of width of the opening.

Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties

A theoretical study of the effect of variable fluid properties on the Blasius and Sakiadis flow with uniform suction at the asymptotic state is presented in this paper. The investigation concerns air and water taking into account the variation of their physical properties with temperature. Velocity and temperature profiles are presented as well as values of the displacement thickness, momentum thickness, shape factor, wall shear stress and Nusselt number for different temperatures of the plate and the ambient fluid. It is found that the nondimensional displacement thickness, momentum thickness, shape factor, absolute wall shear stress and Nusselt number are identical in both Blasius and Sakiadib flow at the asymptotic state for a fluid with constant properties. The same is valid for any fluid with variable properties if the temperature boundary conditions are the same in Blasius and Sakiadis flow.

A two-dimensional simulation of developing laminar heat and mass transfer in fuel cell channels with uniform suction of O2 and H2

A numerical model was developed to simulate the momentum, heat, and mass transfer in the fuel cell channels at steady state and developing laminar flow with constant fluid properties. The continuity, momentum, energy, and species equations were solved for humidified air and humidified H2 with constant mass flux suction boundary condition for O2 in the cathode and H2 in the anode channels. A finite-volume method was used to solve the equations in two-dimensional cases. Friction coefficient was related to the flowrate, whereas Nusselt and Sherwood numbers were, respectively, related to the heat and mass transfer in the flow channels. The distribution of local Nu and Sh numbers and their average values were obtained on the porous walls of the channels (electrodes). The local Nu and Sh numbers were increased with increasing the pressure and Reynolds numbers, whereas the coefficient of friction and the average Nu and Sh numbers were decreased when the pressure and Re number are increased. The mass fraction of O2 and H2 were decreased along the channel, except at the entrance regions, whereas the mass fraction of water vapour increased along the channel, especially on the porous wall. Solving the species equations gave: (a) the distribution of mass concentration of O2 and H2 and other species in the channels and on the electrode surfaces for several stochiometric ratios and different current densities; (b) the local and average Sherwood numbers in the cathode channels for O2 at different stochiometric ratios, different inlet wall Reynolds numbers, and several inlet pressures; and (c) the water vapour mass fraction in both channels and the mass of liquid water if condensation occurs.

Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection

The paper presents an assessment of the performance of a variety of turbulence models in simulating buoyancy-aided, turbulent mixed convection in vertical pipes. This has been done by comparison of RANS predictions with DNS results already available in the literature. Both the RANS and the DNS studies were conducted for conditions of constant and uniform fluid properties with the influence of buoyancy being accounted for using the Boussinesq approximation. This eliminated effects of non-uniformity of properties other than through the action of buoyancy and enabled its influence to be considered in isolation. In the course of the study, the turbulence models have been classified into two groups, namely, those which were able to capture the main features of buoyancy-influenced heat transfer (Group one) and those that were not able to do so (Group two). Common features in model formulation have been identified for each group. It is shown that the response to buoyancy of commonly-used controlling parameters in turbulence damping functions varies significantly and that the performance of a model can largely be correlated with the type of controlling parameter used. A significant defect of the Group-one models which has been identified is that they continue to predict that the ‘viscous sub-layer’ remains thick as a result of the influence of buoyancy even when the velocity profile has been distorted to an extent that it has become inverted in the core, whereas DNS data clearly show that this is not the case. The use of different methodologies for modelling direct production of turbulence through the direct action of buoyancy has been shown to have little effect on predictions of mixed convection in vertical flows because the effect of buoyancy on turbulence is predominantly due to the indirect effect.