Thermal Diffusion Ratio Research Articles

Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers

Spatial variations of concentrations and temperature across exothermic chemical fronts can initiate buoyancy-driven convection. We investigate here theoretically the spatiotemporal dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows when an exothermic autocatalytic front travels perpendicularly to the gravity field in a thin solution layer. To do so, we numerically integrate the incompressible Stokes equations coupled to evolution equations for the concentration of the autocatalytic product and temperature through buoyancy terms proportional to, respectively, a solutal R(C) and a thermal R(T) Rayleigh number. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection with regard to the isothermal system. In the cooperative case (R(C) and R(T) are of the same sign), the dynamics asymptotes to one vortex surrounding, deforming, and accelerating the front much like in the isothermal case. However, persistent local stratification of heavy zones over light ones can be observed at the rear of the front when the Lewis number Le (ratio of thermal diffusivity over molecular diffusion) is nonzero. When the solutal and thermal effects are antagonistic (R(C) and R(T) of opposite sign), temporal oscillations of the concentration, temperature, and velocity fields can, in some cases, be observed in a reference frame moving with the front. The various dynamical regimes are discussed as a function of R(C), R(T), and Le.

Influence of non-uniform activity and conductivity on stationary and moving patterns in catalytic reactors

Abstract We examine pattern formation in a two-phase system consisting of a catalytic wire or ribbon or a string of catalyst particles suspended in a well-mixed fluid phase in an adiabatic reactor. We assume that a single exothermic reaction of the type A → B occurs in the solid phase and account for the variation in the interphase heat and mass transfer coefficients with the flow rate of the reactants. First, we examine the case of uniform activity, conductivity and diffusivity in the solid phase and use linear stability theory to show that steady non-uniform patterned states emerge from the unstable middle branch of the spatially uniform state. Unlike the Turing patterns, these transport limited patterns exist only in the region of multiple homogeneous (uniform) states. They always emerge as unstable branches but may gain stability through a limit point bifurcation when the fluid Lewis number (ratio of fluid thermal diffusivity to the mass diffusivity of the reacting species) Le f 1 but the solid phase Lewis number (ratio of solid thermal diffusivity to the effective species diffusivity in the solid) can be larger than unity. For a fixed set of kinetic constants, the range of Damkohler numbers or residence times over which stable patterned states exist increases with increased interphase heat and mass transfer resistances and with decreased intraphase conduction in the solid. Local bifurcation analysis and transient simulations show that when the activity, conductivity and diffusivity in the solid phase are constant, only moving temperature and concentration fronts exist when Le f ≥ 1 , while both stationary and moving fronts exist when Le f 1 for the practical range of other parameters. Next, we examine pattern formation with non-uniform activity but uniform conductivity and diffusivity within the solid and show that both stationary and moving patterns can exist for any value of Le f . We also determine the influence of the length scale and magnitude of the heterogeneity in activity on pattern formation. The last case examined is that of non-uniform activity, conductivity and diffusivity within the solid phase with profiles of these corresponding to the case of discrete particles in a string with point contacts. In this case, we show that stationary patterns can exist for any Le f and realistic values of all other parameters. This last result explains the differences between various literature results on pattern formation using discrete and continuum models with uniform properties. It also shows that one of main reasons for stationary pattern formation in catalytic packed-bed reactors is the spatial non-uniformity in activity and conductivity caused due to discrete nature of the solid phase (particles) with point contacts.

Turbulent diffusion and turbulent thermal diffusion of aerosols in stratified atmospheric flows

The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion, and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10 years ago and detected recently in the laboratory experiments. This effect causes a nondiffusive flux of aerosols in the direction of the heat flux and results in formation of long‐living aerosol layers in the vicinity of temperature inversions. We applied the theory of turbulent thermal diffusion to the Global Ozone Monitoring by Occultation of Stars (GOMOS) aerosol observations near the tropopause in order to explain the shape of aerosol vertical profiles with elevated concentrations located almost symmetrically with respect to temperature profile. We demonstrate that this theory is in good agreement with the observed profiles of aerosol concentration and temperature in the vicinity of the tropopause. In combination with the derived expression for the dependence of the turbulent thermal diffusion ratio on the turbulent diffusion, these measurements yield an independent method for determining the coefficient of turbulent diffusion at the tropopause. We also derived a practically applicable formulation for dispersion of atmospheric trace species which takes into account the phenomenon of turbulent thermal diffusion. We evaluated the impact of turbulent thermal diffusion to the lower troposphere vertical profiles of aerosol concentration by means of numerical dispersion modeling and found a regular upward forcing of aerosols with coarse particles affected more strongly than fine aerosols.

Traveling Fronts for the Thermo-Diffusive System with Arbitrary Lewis Numbers

We consider KPP-type systems in a cylinder with an arbitrary Lewis number (the ratio of thermal and material diffusivities) in the presence of a shear flow. We show that traveling fronts solutions exist for all Lewis numbers and approach uniform limits at the two ends of the cylinder.

Stability of Thermosolutal Natural Convection in Superposed Fluid and Porous Layers

This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers.

The kinetic theory of partially ionized reactive gas mixtures II

We investigate the kinetic theory of partially ionized reactive gas mixtures in strong magnetic fields following Giovangigli et al (2003 Physica A 327 313–48). A new tensor basis is introduced for expanding the perturbed distribution functions associated with the viscous tensor. New symmetry properties of transport coefficients are established as well as simplified bracket expressions. A variational framework is introduced for a direct evaluation of the thermal conductivity and the thermal diffusion ratios. The transport linear systems corresponding to the usual Sonine/Wang–Chang Uhlenbeck polynomial expansions are evaluated. The behavior of transport coefficients and transport fluxes for vanishing magnetic fields is investigated using series expansions. Practical implementation of iterative algorithms for solving the resulting complex symmetric constrained singular linear systems is discussed as well as various approximations of the transport coefficients.

Thermal convection in mixtures with an inversion of the separation ratio

We have numerically investigated Rayleigh-Bénard convection in binary mixtures assuming a thermal diffusion ratio that depends on the local temperature and changes its sign within the cell. The stationary instability has been found to precede the oscillatory one for a wide range of negative mean psi values. The bifurcation diagram for stationary rolls turns out to be qualitatively different from that for constant Soret effect. Nevertheless, it can be mapped onto this special case by using a scaling argument, taking into account the fact that for small convection amplitudes the rolls are restricted to parts of the cell where the sign of the Soret coefficient favors instability.

Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium

Adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM) proposed by Nield and Kuznetsov (2008), the classical steady, mixed convection boundary layer flow about a horizontal, isothermal circular cylinder embedded in a porous medium has been theoretically studied in this article. It is shown that the boundary layer analysis leads to expressions for the flow and heat transfer characteristics in terms of an inter-phase momentum parameter, a thermal diffusivity ratio, a thermal conductivity ratio, a permeability ratio, a modified thermal capacity ratio, and a buoyancy or mixed convection parameter. The transformed partial differential equations governing the flow and heat transfer in the f-phase (the macro-pores) and the p-phase (the remainder of the structure) are solved numerically using a very efficient implicit finite-difference technique known as Keller-box method. A good agreement is observed between the present results and those known from the open literature in the special case of a traditional Darcy formulation (monodisperse system).

A Practical Verification of Ambient Temperature Slide Method (ATS Method) during Retort Sterilization

In our previous report, we have proposed the Ambient Temperature Slide Method (ATS Method) as a rational way to estimate the central temperature of individually packed foods during retort sterilization. In this paper, we aimed to get new knowledge by specifically comparing ATS Method with simple One-Dimensional Finite-Difference Method (s-OFD Method) that was improved for the practical use of a conventional method using numerical calculation in order to solve the heat conduction equation (One-Dimensional Finite-Difference Method (OFD Method)). From the results of the experiments, it was clear that the Outside Film Heat-Transfer Coefficient h showed a smaller value than the expected one in the OFD Method and so surface heat transfer resistance is so large that it cannot be ignored. Because of this reason, it was thought to have been the obstacle for accurate estimating of the central temperature of foods. When we did parameter-fitting, ATS Method proved to be more than twice as good as the s-OFD Method in convergent accuracy and it was also good in convective foods as well as conductive foods. And, the F-value errors in simulation by using parameters obtained by parameter-fitting in the case of 4 food samples showed only one fifth of the value calculated on the s-OFD Method, it means that the convergent accuracy of ATS Method is five times better than the s-OFD Method. ATS Method showed approximately '1' in the ratio of thermal diffusivity for conductive foods. This result may indicate the possibility in simple theoretical calculation of parameter of heat transfer tau. From these results, ATS Method was thought to be several times better than the s-OFD method that is a conventional method and an improving one of OFD Method in estimating for the central temperature of foods.

One‐dimensional analysis of a poroelastic medium during freezing

AbstractA solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley & Sons, Ltd.

Tricritical Dynamics at the Demixing-λ-Transition in 3He-4He Mixtures

We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in 3He-4He mixtures. Model F′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(tX)∼tX1/2 (tX is the relative temperature distance at constant concentration) and the thermal diffusion ratio kT∼tX−1 diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.

Unsteady conjugate problem of a dissipative fluid in a horizontal channel with a periodic variation temperature

The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness, Peclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary, while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or integrated transport variables at any point or section of the medium.

Thermal diffusion analysis for LED module

AbstractAn experimental investigation of the thermal characteristic of the LED chip and the sensitivity of illumination with thermal substrate is discussed in this study. An optimum thermal diffusion area to the heat flux of LED system is also conducted. Results show that a red LED chip has lower electrical resistance, and therefore has lower power consumption than that of green and blue LED chips. Given these three colors of lighting LEDs, the red LED chip is more sensitive to the thermal environment. A red LED's lighting illumination is decreased almost 12% when the substrate temperature difference is increased to 25°C. Under the same condition, an LED's illumination experiences only a 2 to 2.5% reduction for the green and blue LED chip. Copyright © 2004 Wiley Periodicals, Inc.Thermal diffusion area results show a close correlation between thermal diffusion ratio and LED substrate temperature. If the upper limit LED substrate temperature is set at 50°C and the thermal diffusion ratio approximates 72 cm2/w, for a 500 cm2 thermal diffusion area, it can sustain an optimum heat flux at 7 watts. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 449–458, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20182

Natural convection about a vertical plate embedded in a bidisperse porous medium

The classical Cheng–Minkowycz study of convection past a vertical plate embedded in a porous medium has been extended to the case of a bidisperse porous medium (BDPM). The boundary layer analysis leads to expressions for the velocity and temperature fields in terms of a geometrical parameter, an inter-phase momentum transfer parameter, a thermal diffusivity ratio, a permeability ratio, a thermal conductivity ratio, and an inter-phase heat transfer parameter. For the leading edge region, and for an inner layer, a similarity solution is obtained numerically. This involves the first four parameters, each of which is a characteristic of the BDPM.

Studies on piston and soret effects in a binary mixture supercritical fluid

Heat and mass transport phenomena in a binary mixture compressible supercritical fluid around the pseudo-critical line were investigated theoretically and numerically. In this study, we focused on supercritical artificial air with a composition of 79% nitrogen and 21% oxygen, and investigated the piston effect, the soret effect, and the interactions between these effects. We derived thermo-fluid dynamic equations, in which the compressibility of the fluid, the temperature, the pressure, and the concentration dependences of the entropy were taken into account. The governing equations were solved numerically by using the finite difference method. We could verify that the thermal energy was propagated by the piston effect in a binary mixture supercritical fluid, and the concentration change certainly occurred due to the soret effect. Moreover, we could also estimate the thermal diffusion ratio, which made a direct correlation between the temperature gradient and the concentration gradient.

On pattern formation in ferrocolloid convection

Experimental studies and numerical simulations of stability of buoyancy-driven flows in a ferrocolloid for the cases of horizontal and inclined vertical orientation of a thin cylindrical cavity are performed. The influence of a homogeneous longitudinal magnetic field on convective instability and spatio-temporal patterns were also investigated. In the case of ferrocolloids the gradients of magnetic permeability may arise due to both temperature and particle concentration gradients. The particle mass flux in a classical form is summarized from the translation diffusion coefficient and the thermal diffusion ratio. However, the explanation for the observed self-oscillation regimes in magnetic fluid for the cavities of sufficiently large thickness is conditioned by the competition of density variations originating from the fluid thermal expansion and barometric sedimentation. The results prove that a uniform longitudinal magnetic field allows to control the stability and the shape of secondary convection motions at inclined orientation of layer. In a ferrocolloid the repeated transients involving localized roll convection and pure shear flow took place. Under action of uniform longitudinal magnetic field orientated perpendicular to flux velocity of shear motion on such long-wave transients can lead to complicated types of chaotic localized states or solitary vortices.

Entropy generation in double diffusive convection in presence of the Soret effect

Influence of the Soret effect on entropy generation in a square cavity filled with a binary gas mixture in double diffusive convection is numerically studied. It was found that entropy generation increases with the increase of thermal diffusion and buoyancy ratios for fixed thermal Grashof number. Total irreversibility takes a minimum value at a special buoyancy ratio ranging between 1 and 0. Soret effect causes the increase of total irreversibility by more than 50% at higher values of thermal Grashof number and buoyancy ratio. More details of the irreversibilities localisation are discussed.

Critical Rayleigh Number of Natural Convection in an Anisotropic Horizontal Porous Layer with High Porosity

Linear stability analysis was applied to obtain the critical Rayleigh number Rac at the onset of natural convection for horizontal anisotropic porous fluid layers with vertical thin circular cylinders inserted by variational method with the consideration of non-Darcy viscous flow assumption. The permeability ratio of x-direction to z-direction is 0.5 and the effective thermal diffusivity ratio ξ of x-direction to z-direction for the anisotropic porous fluid layer is less than unity for any circular cylinders with high or low thermal conductivity. The analytical results show that Rac is the highest for the case of ξ=1 and decreases with the decrease in ξ. It decreases with the increase in Darcy number Da and asymptotically approaches to a constant value for Da→∞. The constant value of Rac for Da→∞ is the smallest to be 690.8 for ξ→0. The analytical results were compared with experimental results performed with silicon oil and plastic resin as a working fluid and circular cylinders respectively for ξ=1. The experiment agreed well with the analysis based on non-Darcy viscous flow assumption. The analysis showed that Darcy flow assumption is applied for small Da dependent on ξ.

Thermal Diffusivity Variation Study of Cold Stored Malaysian Pangasius Sutchi at 10°C

This paper presents the use of thermal diffusivity-variation of Malaysian Pangasius Sutchi freshwater fish as a criterion to estimate the freshness in fish marketing. A homogenous specified area of a fresh fish body was cut into slices which were wrapped and preserved in a cold store of 10°C for a period of 28 days. Ansari's approach has been found earlier as an appropriate one to measure the thermal diffusivity of fish through transient cooling. The daily measurement of those slices (samples) along the muscle orientation revealed that thermal diffusivity increased up to 3 days then stayed approximately constant up to the end of the preservation period (28 days). In the literature the shelf life was also found 3 days at 10°C, which in turn agreed with the present investigation. Regression analysis was made to develop an empirical correlation between thermal diffusivity ratio and preservation time of the fish under study. This correlation could be used by food technologists as an index of deterioration of freshness or consumer acceptance

Stability of Natural Convection in Superposed Fluid and Porous Layers Using Integral Transforms

A stability analysis of thermal natural convection in superposed fluid and porous layers is carried out. The two-layer system is described using a one-domain formulation, and the eigenvalue problem resulting from the stability analysis is solved using the generalized integral transform technique (GITT). The numerical results confirm that the onset of convection can have a bimodal nature depending on the depth ratio. The influence of the dimensionless permeability and thermal diffusivity ratio are investigated.