Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Viscoelastic behavior of persimmons dried at constant air temperature

The viscoelastic behavior of dried persimmons at different air-drying temperatures and velocities was evaluated. Air temperatures and velocities were varied according to a second-order central composite design, with temperature ranging from 40degreesC to 70degreesC and air velocity from 0.8 to 2.0 m/s. After drying, persimmons were equilibrated at four different water activities: 0.432, 0.576, 0.625 and 0.751. The rheological behavior of dried and conditioned persimmons was studied under uniaxial compression-relaxation tests. Three different rheological models were fitted to the experimental relaxation curves: Maxwell, Generalized Maxwell and Peleg and Normand. Based on the root mean square of residuals, the Generalized Maxwell model showed the best fit and a regression analysis was applied to obtain response surfaces for the model parameters. The dependence of the rheological properties on water activity was also analysed. Results showed that only the linear effect of air temperature was significant at a 5% level on the equilibrium stress and relaxation times. In a general way, these parameters increased with increasing air temperature and decreasing water activity. (C) 2004 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Friction losses of Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to determine, for Newtonian and non-Newtonian fluids, the friction factor (fc) with simultaneous heat transfer, at constant wall temperature as boundary condition, in fully developed laminar flow inside a vertical helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w). The non-Newtonian fluids were aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations of 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations of 0.1% and 0.2% (w/w). According to the rheological study done, the polymer solutions had shear-thinning behavior and different values of viscoelasticity. The helical coil used has an internal diameter, curvature ratio, length and pitch, respectively: 0.00483 m, 0.0263, 5.0 m and 11.34 mm. It was concluded that the friction factors, with simultaneous heat transfer, for Newtonian fluids can be calculated using expressions from literature for isothermal flows. The friction factors for CMC and XG solutions are similar to those for Newtonian fluids when the Dean number, based in a generalized Reynolds number, is less than 80. For Dean numbers higher than 80, the friction factors of the CMC solutions are lower those of the XG solutions and of the Newtonian fluids. In this range the friction factors decrease with the increase of the viscometric component of the solution and increase for increasing elastic component. The change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, is in accordance with the study of Ali [4]. There is a change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, which is in according to previous studies. The data also showed that the use of the bulk temperature or of the film temperature to calculate the physical properties of the fluid has a residual effect in the friction factor values.

Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented.

FORCED CONVECTION TO LAMINAR FLOW OF LIQUID EGG YOLK IN CIRCULAR AND ANNULAR DUCTS

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

LAMINAR THERMALLY DEVELOPING FLOW INSIDE RIGHT-ANGULARLY TRIANGULAR DUCTS

An analytical approach based on the generalized integral transform technique is presented, for the solution of laminar forced convection within the thermal entry region of ducts with arbitrarily shaped cross-sections. The analysis is illustrated through consideration of a right triangular duct subjected to constant wall temperature boundary condition. Critical comparisons are made with results available in the literature, from direct numerical approaches. Numerical results for dimensionless average temperature and Nusselt numbers are presented for different apex angles.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K (r)) and wall heat transfer coefficient (h (w)) were estimated from steady-state data and the characteristic packed bed time constant (tau) from transient data. A new correlation for the K (r) in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

Evaluation of bedbath in critically ill patients: impact of water temperature on the pulse oximetry variation

This is a participant study, quasi-experimental, of a before and after type. A quantitative approach of biophysiological measures was used, represented by the saturation of oxygen measured by pulse oximeter (SpO2), and recorded on three occasions: before, during and after the bedbath in critically ill patients hospitalized at the ICU of a University Hospital in Brazil. Objective: to compare the SpO2 in various stages of the bath, with and without control of water temperature. Data collection was performed between December 2007 and April 2008 on a convenience sample consisting of 30 patients aged over 18 who had classification in TISS-28 from level II. Results show that water temperature control means a lower variation of SpO2 (p<0.05). No marked differences in variation of saturation between men and women or between age groups were established. In conclusion, heated and constant water temperature during the bedbath is able to minimize the fall of SpO2 that occurs while handling patients during procedures.

The effects of static and diurnally-cycling temperature acclimations on thermal tolerances of rainbow trout, Salmo gairdneri

:ofiedian lethal temperatures ( LT50' s ) were determined for rainbow trout, Salmo gairdnerii, acclimated for a minimum of 21 days at 5 c onstant temperatures between 4 and 20 0 C. and 2 diel temperature fluctuations ( sinewave curves of amplitudes ± 4 and ± 7 0 C. about a mean temperature of 12 0 C. ) . Twenty-four-, 48-, and 96-hour LT50 estimates were c alculated f ollowing standard flow-through aquatic bioassay techniques and probi t transformation of mortality data. The phenomenon of delayed thermal mortality was also investigated. Shifts in upper incipient lethal temperature occurred as a result of previous thermal conditioning. It was shown that increases in constant acclimation temperature result in proportional l inear increases in thermal tolerances. The increase i n estimated 96-hour LT50's was approximately 0.13 0 c. X 1 0 C:1 between 8 and 20 0 C. The effect of acclimation to both cyclic temperature regimes was an increase in LT50 to values between the mean and maximum constant equivalent daily temperatures of the cycles. Twenty-four-, 48-, and 96-hour LT50 estimates of both cycles corresponded approximately to the LT50 values of the 16 0 C. c onstant temperature equivalent . This increase i n thermal tolerance was further demonstrated by the delayed thermal mortality experiments . Cycle amplitudes appeared to i nfluence thermal resistance through alterations in initi al mortality since mortality patterns characteristic of base temperature acclimations re-appeared after approximately 68 hours exposure to test temperatures for the 12 + 4 0 C. group, whereas mortality patterns stabilized and remained constant for a period greater than 192 hours with the larger therma l cycle ( 12 + 7 0 C. ). NO s ignificant corre lations between s pecimen weight and time-to-death was apparent. Data are discussed in relation to the establishment of thermal criteria for important commercial and sport fishes , such as the salmonids , as is the question whether previously reported values on lethal temperature s may have been under estimated.

Influence of temperature during grain filling on gluten viscoelastic properties and gluten protein composition

BACKGROUND The aim of this study was to investigate the effects of low to moderate temperatures on gluten functionality and gluten protein composition. Four spring wheat cultivars were grown in climate chambers with three temperature regimes (day/night temperatures of 13/10, 18/15 and 23/20 °C) during grain filling. RESULTS The temperature strongly influenced grain weight and protein content. Gluten quality measured by maximum resistance to extension (Rmax) was highest in three cultivars grown at 13 °C. Rmax was positively correlated with the proportion of sodium dodecyl sulfate-unextractable polymeric proteins (%UPP). The proportions of ω-gliadins and D-type low-molecular-weight glutenin subunits (LMW-GS) increased and the proportions of α- and γ-gliadins and B-type LMW-GS decreased with higher temperature, while the proportion of high-molecular-weight glutenin subunits (HMW-GS) was constant between temperatures. The cultivar Berserk had strong and constant Rmax between the different temperatures. CONCLUSION Constant low temperature, even as low as 13 °C, had no negative effects on gluten quality. The observed variation in Rmax related to temperature could be explained more by %UPP than by changes in the proportions of HMW-GS or other gluten proteins. The four cultivars responded differently to temperature, as gluten from Berserk was stronger and more stable over a wide range of temperature