Laminar heat transfer to non-Newtonian fluids in pipes with abrupt changes in diameter

In this thesis the results of experimental work performed to determine local heat transfer coefficients for non-Newtonian fluids in laminar flow through pipes with abrupt discontinuities are reported. The fluids investigated were water-based polymeric solutiorrs of time-indpendent, pseudoplastic materials, with flow indices "n" ranging from 0.39 to 0.9.The tube configurations were a 3.3 :1 sudden convergence, and a 1: 3.3 sudden divergence.The condition of a prescribed uniform wall heat flux was considered, with both upstream and downstream tube sections heated. Radial temperature traverses were also under­ taken primarily to justify the procedures used in estimating the tube wall and bulk fluid temperatures and secondly to give further insight into the mechanism of heat transfer beyond a sudden tube expansion. A theoretical assessment of the influence of viscous dissipation on a non-Newtonian pseudoplastic fluid of' arbitrary index "n" was carried out. The effects of other secondary factors such as free convection and temperature-dependent consistency were evaluated empirically. In the present investigations, the test conditions were chosen to minimise the effects of natural convection and the estimates of viscous heat generation showed the effect to be insignificant with the polymeric concentrations tested here. The final results have been presented as the relationships between local heat transfer coef'ficient and axial distance downstream of the discontinuities and relationships between dimensionless wall temperature and reduced radius. The influence of Reynolds number, Prandtl number, non-Newtonian index and heat flux have been indicated.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Analogue simulation of heat transfer in the thermal processing of food

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Uniform design for the optimization of Al2O3 nanofilms produced by electrophoretic deposition

Surface modification by means of nanostructures is of interest to enhance boiling heat transfer in various applications including the organic Rankine cycle (ORC). With the goal of obtaining rough and dense aluminum oxide (Al2O3) nanofilms, the optimal combination of process parameters for electrophoretic deposition (EPD) based on the uniform design (UD) method is explored in this paper. The detailed procedures for the EPD process and UD method are presented. Four main influencing conditions controlling the EPD process were identified as nanofluid concentration, deposition time, applied voltage and suspension pH. A series of tests were carried out based on the UD experimental design. A regression model and statistical analysis were applied to the results. Sensitivity analyses of the effect of the four main parameters on the roughness and deposited mass of Al2O3 films were also carried out. The results showed that Al2O3 nanofilms were deposited compactly and uniformly on the substrate. Within the range of the experiments, the preferred combination of process parameters was determined to be nanofluid concentration of 2 wt.%, deposition time of 15 min, applied voltage of 23 V and suspension pH of 3, yielding roughness and deposited mass of 520.9 nm and 161.6 × 10− 4 g/cm2, respectively. A verification experiment was carried out at these conditions and gave values of roughness and deposited mass within 8% error of the expected ones as determined from the UD approach. It is concluded that uniform design is useful for the optimization of electrophoretic deposition requiring only 7 tests compared to 49 using the orthogonal design method.

Shell-side transfer in shell-and-tube heat exchangers

Local mass transfer coefficients were determined by using the electrochemical technique. A simple model of a heat exchanger with segmental nickel tube joined to p.v.c. rods replaced the exchanger tubes. Measurements were made for both no-Ieakage, semi-leakage and total leakage configurations. Baffle-spacings of 47.6 mm, 66.6 mm, 97 mm and 149.2 mm wer studied. Also studied were the overall exchanger pressure drops for each configuration. The comparison of the heat transfer data with this work showed good agreement at high flow rates for the no-leakage case, but the agreement became poor for lower flow rates and leakage configurations. This disagreement was explained by non-analogous driving forces existing in the two systems. The no-leakage data showed length-wise variation of transfer coefficients along the exchanger length. The end compartments showing transfer coefficients inferior by up to 26% compared to tbe internal compartments, depending on Reynolds number. With the introduction of leakage streams this variation however became smaller than the experimental accuracy. A model is outlined to show the characteristic behaviour of individual electrode segments within the compartment. This was able to discriminate between cross and window zones for the no- leakage case, but no such distinction could be made for the leakage case. A flow area was found which, when incorporated in the Reynolds number, enabled the correlation of baffle-cut and baffle-spacing parameters for the no-leakage case . This area is the free flow area determined at the baffle edge. Addition of the leakage area to this flow area resulted in correlation of all commercial leakage geometrical parameters. The procedures used to correlate the pressure drop data from a total of eighteen different configurations on a single curve are also outlined.

Heat and mass transfer in membrane distillation used for desalination with slip flow

A theoretical model for the transport phenomena in an air gap membrane distillation is presented. The model is based on the conservation equations for the mass, momentum, energy and species within the feed water solution as well as on the mass and energy balances on the membrane sides. The slip flow occurs due to the hydrophobic properties of the membrane. The slip boundary condition applied on the feed saline solution-membrane interface is taken into consideration showing its effects on process parameters particularly permeate flow, heat transfer coefficient and thermal efficiency. The theoretical model was validated with available experimental data and was found to be in good agreement especially when the slip condition is introduced. Increasing slip length from zero to 200 μm was found to increase the permeate flux and the thermal efficiency by 33% and 1.7% respectively.

Velocity distributions in a plate heat exchanger channel

The development of a Laser Doppler Anemometer technique to measure the velocity distribution in a commercial plate heat exchanger is described. Detailed velocity profiles are presented and a preliminary investigation is reported on flow behaviour through a single cell in the channel matrix. The objective of the study was to extend previous investigations of plate heat exchanger flow patterns in the laminar range with the eventual aim of establishing the effect of flow patterns on heat transfer performance, thus leading to improved plate heat exchanger design and design methods. Accurate point velocities were obtained by Laser Anemometry in a perspex replica of the metal channel. Oil was used as a circulating liquid with a refractive index matched to that of the perspex so that the laser beams were not distorted. Cell-by-cell velocity measurements over a range of Reynolds number up to ten showed significant liquid mal-distribution. Local cell velocities were found to be as high as twenty seven times average velocity, contrary to the previously held belief of four times. The degree of mal-distribution varied across the channel as well as in the vertical direction, and depended on the upward or downward direction of flow. At Reynolds numbers less than one, flow zig-zagged from one side of the channel to the other in wave form, but increases in Reynolds number improved liquid distribution. A detailed examination of selected cells showed velocity variations in different directions, together with variation within individual cells. Experimental results are also reported on the flow split when passing through a single cell in a section of a channel . These observations were used to explain mal-distribution in the perspex channel itself.

Local shell-side coefficients in shell and tube exchanges the use of a mass transfer technique

A diffusion-controlled electrochemical mass transfer technique has been employed in making local measurements of shell-side coefficients in segmentally baffled shell and tube heat exchangers. Corresponding heat transfer data are predicted through the Chilton and Colburn heat and mass transfer analogy. Mass transfer coefficients were measured for baffle spacing lengths of individual tubes in an internal baffle compartment. Shell-side pressure measurements were also made. Baffle compartment average coefficients derived from individual tube coefficients are shown to be in good agreement with reported experimental bundle average heat transfer data for a heat exchanger model of similar geometry. Mass transfer coefficients of individual tubes compare favourably with those obtained previously by another mass transfer technique. Experimental data are reported for a variety of segmental baffle configurations over the shell-side Reynolds number range 100 to 42 000. Baffles with zero clearances were studied at three baffle cuts and two baffle spacings. Baffle geometry is shown to have a large effect on the distribution of tube coefficients within the baffle compartment. Fluid "jetting" is identified with some baffle configurations. No simple characteristic velocity is found to correlate zonal or baffle compartment average mass transfer data for the effect of both baffle cut and baffle spacing. Experiments with baffle clearances typical of commercial heat exchangers are also reported. The effect of leakage streams associated with these baffles is identified. Investigations were extended to double segmental baffles for which no data had previously been published. The similarity in the shell-side characteristics of this baffle arrangement and two parallel single segmental baffle arrangements is demonstrated. A general relationship between the shell-side mass transfer performance and pressure drop was indicated by the data for all the baffle configurations examined.

CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors. Part B: Heat, momentum and mass transport in bubbling fluidised beds

The fluid–particle interaction inside a 150 g/h fluidised bed reactor is modelled. The biomass particle is injected into the fluidised bed and the heat, momentum and mass transport from the fluidising gas and fluidised sand is modelled. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Heat transfer from the bubbling bed to the discrete biomass particle, as well as biomass reaction kinetics are modelled according to the literature. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of user-defined function (UDF). The study completes the fast pyrolysis modelling in bubbling fluidised bed reactors.

Flow and pressure drop on the shellside of cylindrical heat exchangers

This work presents pressure distributions and fluid flow patterns on the shellside of a cylindrical shell-and-tube heat exchanger. The apparatus used was constructed from glass enabling direct observation of the flow using a dye release technique and had ten traversable pressure instrumented tubes permitting detailed pressure distributions to be obtained. The `exchanger' had a large tube bundle (278 tubes) and main flow areas typical of practical designs. Six geometries were studied: three baffle spacings both with and without baffle leakage. Results are also presented of three-dimensional modelling of shellside flows using the Harwell Laboratory's FLOW3D code. Flow visualisation provided flow patterns in the central plane of the bundle and adjacent to the shell wall. Comparison of these high-lighted significant radial flow variations. In particular, separated regions, originating from the baffle tips, were observed. The size of these regions was small in the bundle central plane but large adjacent to the shell wall and extended into the bypass lane. This appeared to reduce the bypass flow area and hence the bypass flow fraction. The three-dimensional flow modelling results were presented as velocity vector and isobar maps. The vector maps illustrated regions of high and low velocity which could be prone to tube vibration and fouling. Separated regions were also in evidence. A non-uniform crossflow was discovered with, in general, higher velocities in the central plane of the bundle than near the shell wall._The form of the isobar maps calculated by FLOW3D was in good agreement with experimental results. In particular, larger pressure drops occurred across the inlet than outlet of a crossflow region and were higher near the upstream than downstream baffle face. The effect of baffle spacing and baffle leakage on crossflow and window pressure drop measurements was identified. Agreement between the current measurements, previously obtained data and commonly used design correlations/models was, in general, poor. This was explained in terms of the increased understanding of shellside flow. The bulk of previous data, which dervies from small-scale rigs with few tubes, have been shown to be unrepresentative of typical commerical units. The Heat Transfer and Fluid Flow Service design program TASC provided the best predictions of the current pressure drop results. However, a number of simple one-dimensional models in TASC are, individually, questionable. Some revised models have been proposed.

Transfer coefficients over inclined tube banks

The thesis presents experimental results for shell-side transfer coefficients and pressure drops across four different tube banks, using small-scale models, with yawed tubes, as found in many types of heat exchangers, boilers and nuclear reactors. The tube banks investigated have a staggered tube layout on a rotated square pitch, with a 1.25 pitch-to-diameter ratio. The angle of attack was varied between 45o and 90o. An extensive range of Reynolds number, i.e. 0.5. to 12,600, covering so-called laminar, transition and turbulent flows, was investigated. A diffusion-controlled electrochemical mass transfer technique has been employed to measure mass transfer coefficients. The heat transfer coefficients may be then readily obtained from the mass transfer values by applying the well-established Chilton-Colburn analogy. The results for the normal tube bank, which forms the base case for the study on inclined tube banks, show close agreement with previous work. The transfer coefficients and pressure drops of the inclined tube banks are compared with results from the ideal normal tube bank to examine the effect of inclination angle on heat transfer and pressure drop variations. The variation of the transfer coefficients row-by-row and the entrance and exit effects have also been investigated. An auxilary investigation has been carried out on the role of natural convection. A preliminary correlation of transfer coefficients and pressure drops against the variation in the yaw angle has been attempted. The results are discussed in the light of the few existing theoretical treatments and experimental data for these situations, and recommendations made for future work.

Fin spacing interaction in fluidized bed heat exchangers

The work presented in this thesis is concerned with the heat transfer performance of a single horizontal bare tube and a variety of finned tubes immersed in a shallow air fluidized bed. Results of experimental investigations with the bare tube indicate that the tube position in the bed influences its performance narticularly where fine bed materials are used. In some cases the maximum heat transfer is obtained with the tube in the particle cloud just above the dense phase fluidized bed - a phenomenon that has not been previously observed. This was attributed to the unusual particle circulation in shallow beds. The data is also presented in dimensionless correlations which may be useful for design purposes. A close approximation to the bare tube data can be obtained by using thetransient heating of a spherical robe and this provides a valuable way of accumulating a lot of data very rapidly. The experimental data on finned tubes shows that a fin spacing less than twenty times the average particle diameter can cause a significant reduction in heat transfer due to the interaction which takes place between the particles and the surface of the fins. Furthermore, evidence is provided to show that particle shape plays an important part in the interaction with spherical particles being superior to angular particles at low fin spacing/particle diameter ratio. The finned tube data is less sensitive to tube position in the bed than bare tubes and the best performance is when the tube is positioned at the distributor.A reduction in bed depth decreases the thermal performance of the finned tube but in many practical installations the reduction in pressure drop might more than comnensate for the reduced heat flux. Information is also provided on the theoretical uerformance of fins and the effect of the root contact area between the fins and the tube was investigated.