Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. (C) 2006 Elsevier. SAS. All rights reserved.

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Laminar flow of soursop juice through concentric annuli: Friction factors and rheology

Laminar axial flow of a pseudoplastic fluid food (soursop, juice) in annular ducts has been experimentally investigated. In the first part of the manuscript, the rheological behavior of soursop juice, being essential for the annular flow analysis, was completely determined from 9.3 to 49.4 degrees Brix and temperatures from 0.4 degrees C to 68.8 degrees C, using a rotational rheometer equipped with coaxial cylinders. In order to test the adequacy of the rheology results, pressure loss data in the laminar pipe flow were collected and then experimental and theoretical friction factors were compared, showing excellent agreement, which indicated the reliability of the Power-Law model for describing the soursop juices. In the second part, pressure loss in annular regions was measured and used to estimate friction factors, which were then compared to those resulted from analytical and semi-analytical equations. The principal contributions of this article are to provide a review on the determination of friction factors-Reynolds number of pseudoplastic fluids in annuli, and also supply extensive new experimental data on the rheological properties and pressure loss of an important shear-thinning fluid food, which is of particular interest for the food engineering process design. (c) 2006 Elsevier Ltd. All rights reserved.

Study on transient ice formation of laminar flow inside externally supercooled rectangular duct

The transient process of solidification of laminar liquid flow (water) submitted to super-cooling was investigated both theoretically and experimentally. In this study an alternative analytical formulation and numerical approach were adopted resulting in the unsteady model with temperature dependent thermophysical properties in the solid region. The proposed model is based upon the fundamental equations of energy balance in the solid and liquid regions as well as across the solidification front. The basic equations and the associated boundary and initial conditions were made dimensionless by using the Landau transformation to immobilize the moving front and render the problem to a fixed plane type problem. A laminar velocity profile is admitted in the liquid domain and the resulting equations were discretized using the finite difference approach. The numerical predictions obtained were compared with the available results based on other models and concepts such as Neumann analytical model, the apparent thermal capacity model due to Bonacina and the conventional fixed grid energy model due to Goodrich. To obtain further comparisons and more validation of the model and the numerical solution, an experimental rig was constructed and instrumented permitting very well controlled experimental measurements. The numerical predictions were compared with the experimental results and the agreement was found satisfactory.

Laminar forced convection to a pseudoplastic fluid food in circular and annular ducts

In this manuscript we investigated experimentally the steady-state heat transfer to an important pseudoplastic fluid food, the soursop juice, flowing in laminar regime through circular and concentric annular ducts. The mean convection heat transfer coefficients, determined by measuring the bulk temperatures before and after the heating sections with constant temperatures of the tube walls, were used to correlate simple new empiric expressions to estimate the average Nusselt number in the thermal entrance of the considered geometries. In addition, the thermophysical properties of the tested fluid food, as well as the rheological behavior, being essential for the heat transfer analyses, were experimentally determined. (c) 2006 Elsevier Ltd. All rights reserved.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

Anomalous flow behaviour of bauxite tailings

This paper deals with the anomalous flow behaviour observed in two bauxite tailings pumping systems, with 450 mm and 680 mm outer diameter. In order to enlarge the pipeline lengths in the field, tests were carried out in a laboratory test-loop in order to try to understand the anomalous (intermittent) flow behaviour and to solve the problem. Based on data obtained from these laboratory tests and using a generalized REYNOLDS number it was possible to obtain results that fit the MOODY ROUSE diagram.

Coeficientes de perda de carga em valvulas e acessorios no escoamento laminar de fluidos nao-Newtonianos

Friction loss coefficients for laminar flow of xantan gum solutions (concentrations in the range of 0.1-0.5% by weight) through valves and fittings were experimentally determined. The rheological behavior, studied by means of a concentric cylinder rheometer, was pseudoplastic, being well described by the Ostwald-De Waele model with non-linear correlation coefficients (r) between 0.998 and 0.999. In the pressure drop measurements the following fittings were employed: completely open and half way open ball valve, completely open and half way open angle valve, tee used like coupling, tee used like a 90° elbow, short radius 90° elbow and coupling. The results showed that the friction loss coefficients increased with decreasing generalized Reynolds number. The friction loss coefficients could be well adjusted by a potential model, suggested by Kittredge & Rowley (1957) for Newtonian fluids, K f = A(Re g) -B, with correlation coefficients between 0.837 and 0.999.

Flow evolution of a metallic slurry during thixoextrusion of an automotive valve

The aim of this work is to characterize a metallic slurry (Al-4.5%Cu) flow during thixoforming of an automotive valve. The necessary globular structure was obtained by first inoculating the alloy with TIBAL (5%Ti, 1%B, Al - rest) at 750.0°C, and then reheating to a state between liquidus and solidus prior to thixoforming. Two metallic slurries, with a solid phase of approximately 86.1 and 78.2 percent, were used to generate different experimental flow patterns during the thixoforming process. The flow of the material into the die was observed for total, and partial displacement (2.7, 5.4, 7.5mm) of the punch. The first displacement shows formation of the valve rod. The patterns at each step of displacement of the punch were preserved by quenching in water, thus revealing the profile of the die fill and microstructural evolution. Degeneration of the globular phase was observed along the piece thixoextruded. Thixoextrusion forces versus time curves were generated for partial and full displacement of the punch. Porosity was visible along the billet prior to thixoforming. However, some areas show that the porosity gradually decreased to zero as the thixoextrusion pressure increased. Turbulent, transient and laminar flow are analyzed in this work.

Evaluation of strip rolling directly from the semi-solid state

defect metal alloy strip when thixorolling directly from the semi-solid state. To facilitate the study lead/tin alloys were chosen for their relatively low operating temperature. The objective is to extrapolate these findings to the higher temperature aluminium, alloys. Three alloys (70%Pb30%Sn, 60%Pb-40%Sn, 50%Pb-50%wtSn) were used particularly to study the influence of the solidification interval. The equipment consists of a two roll mill arranged as an upper and lower roller, where both rollers are driven at a controlled speed. The lower roller is fed with semi solid alloy through a ceramic nozzle attached to the lower end of a cooling slope. Several types of nozzle and their position at the roller were tested. This produced different solidifications and consequently different finished strip. The alloys were first cast and then poured onto the cooling slope through a tundish in order to create a continuous laminar flow of slurry and uniformity of metal strip quality. The pouring was tested at different positions along the slope. The cooling slope was coated with colloidal graphite to promote a smooth slurry flow and avoid the problem of adherence and premature solidification. The metallic slurry not only cools along the slope but is also initially super-cooled to a mush by the lower roller whilst at room temperatures, thus enabling thixorolling. It was also found that the nozzle position could be adjusted to enable the upper roller to also contribute to the solidification of the metallic slurry. However the rollers and the cooling slope naturally heat up. Temperature distribution in these zones was analysed by means of three thermocouples positioned along the cooling slope and a fourth in the base of the semi solid pool within the nozzle. The objective being to design an optimum pouring and cooling system. The formed strip was cooled down to room temperature with a shower of water. Microstructures of the thixorolling process were analysed. The differences in solidification conditions resulted in differing qualities of finished strip and corresponding defect types, all of which are a serious quality issue for the rolled product.

Uso de antibióticos para o controle de bactérias endógenas visando à micropropagação da figueira

A descontaminação dos explantes é um dos princípios básicos para o sucesso da cultura de tecidos. Um dos problemas diagnosticados na propagação in vitro da figueira, através de gemas apicais, é a contaminação endógena dos explantes por bactérias. Este trabalho teve como objetivo avaliar a eficiência de alguns antibióticos em meio de cultura para o controle de bactérias endógenas em gemas apicais de figueira. Foram avaliados os seguintes tratamentos: T1(sem adição de antibiótico); T2 (30 mg L-1 de cloranfenicol); T3 (250 mg L-1 de ampicilina sódica); T4 (500 mg L-1 de ácido nalidícico); T5 (150 mg L-1 de cefalotina sódica); T6 (500 mg L-1 de tetraciclina), e T7 (400 mg L-1 de norfloxacina). Após coletados em campo, os segmentos de ramos contendo as gemas foram colocados em recipiente com água corrente. Posteriormente, as gemas apicais foram imersas em álcool etílico a 70% e hipoclorito de sódio a 2,5%. Todo procedimento de desinfestação externa dos explantes foi realizado em câmara de fluxo laminar. Os explantes foram inoculados em tubos de ensaio contendo 15 mL de meio básico MS suplementado, após a autoclavagem, com as doses de antibióticos de acordo com os tratamentos estabelecidos. Após a inoculação, os explantes foram mantidos em sala de crescimento por quatro dias no escuro e, em seguida, sob fotoperíodo de 16 horas de luz branca fria e irradiância de 25 µmol m s-1, na temperatura de 22 ± 3ºC. A assepsia realizada externamente nos explantes foi suficiente para o controle de contaminação fúngica, e a adição de antibióticos ao meio, após autoclavagem, foi eficiente para o controle de bactérias endógenas, cujo antibiótico ampicilina sódica proporcionou mais de 90% de explantes sobreviventes.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Rheological and thermophysical properties of blackberry juice

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Friction factors, convective heat transfer coefficients and the Colburn analogy for industrial sugarcane juices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Friction losses in valves and fittings for liquid food products

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)