P. J. Heggs

Improved formulations for the analysis of convecting and radiating finned surfaces

The study of the heat flow within finned surfaces involving combined convective and radiative heat dissipation is conventionally based upon unidirectional analyses with attention restricted solely to the fin side. In this study the heat conduction within the interface to which the fins are attached, and the heat transfer from the unfinned side of this interface are also considered. The general situation in which the fins and the base surface have different thermal conductivities and different surface emissivities is examined. Fin-to-base-surface, fin-toenvironment, fin-to-fin, and base-surface-to-environment radiant interactions are all accounted for, but the convective fluids are assumed to be radiatively transparent. Oneand two-dimensional formulations are developed for analyzing the heat flow. These represent a major extension of the previously employed formulations. The results obtained indicate, in particular, that the previously employed formulations are inadequate for the effective design of finned heat exchangers.

Boundary Integral Equation Analysis of Transmission-Line Singularities

The TEM line analysis of microstrips and coaxial lines generally involves boundary singularities which cause slow convergence of solutions computed by standard numencal techniques. In this study, the singularities occurring at the ends of the inner conductor in an unsymmetric closed microstrip containing a dielectric substrate, are treated by a modified boundary integral equation method. This method is shown to be successful in reducing the error due to the presence of the singularities.

Prediction of flow distributions and pressure changes in multi-layered annular packed beds

Annular packed bed configurations are used in many different systems and the radial packing region is not always composed of a single layer of material. This work is based on a commercial air filter which was found to have several different layers within the radially packed region, comprising a particulate filter and an activated carbon layer as the main flow resistances. To enable modelling of such a filter, an existing model has been extended to predict flow distributions and pressure profiles for annular packed bed systems. The enhanced model predicts the trends and orders of magnitude of experimentally obtained pressure profiles and overall pressure drops for three air flow rates through a commercial air filter.

PARAMETER IDENTIFICATION IN TWO-DIMENSIONAL FINS USING THE BOUNDARY ELEMENT METHOD

The identification of the ratio of the convective heat transfer coefficient and the thermal conductivity of two-dimensional polygonal fins on square and hexagonal (equilateral-triangular) pitches and the equivalent radial rectangular fin from a single additional boundary or internal temperature measurement is investigated. This problem is motivated by the facilities available at the University of Manchester, which at the moment make possible only a single temperature measurement, and is approached by combining the boundary element method (BEM) with a constrained nonlinear minimization technique. The accuracy, convergence, and stability of the proposed numerical method with respect to the level of noise added into the temperature measurement are carefully analyzed. The inaccuracy in the numerical results obtained using the combined BEM–constrained nonlinear minimization technique is around three and nine times less than the level of noise added into the extra temperature measurements located in the domain and on the boundary, respectively. The sensitivity analysis with respect to the location of the extra temperature measurement suggests that more accurate numerical approximates for the ratio of the convective heat transfer coefficient and the thermal conductivity of the fins investigated are retrieved for one additional boundary temperature measurement than for one extra internal temperature measurement. Furthermore, the BEM–constrained nonlinear minimization technique is also robust with respect to the initial guess for the minimization process. In addition, the inaccuracy in the prediction of the average of the space-dependent coefficient for only one additional internal or boundary temperature measurement ranges from 5.33% to 25.35%.

Evaluation of pressure profiles and overall pressure drop for flow through annular packed bed configurations

A recently published model for the prediction of flow distributions in annular packed bed systems has been extended to provide pressure maps throughout the system and overall pressure drop. For a particular fixed filter design, the analysis shows that the best flow distribution (0.58% average deviation from uniform flow) and least overall pressure drop (7% less than the maximum) is obtained from a U-type flow arrangement with inward radial flow across the annular bed. A sensitivity analysis has revealed that the lowest overall pressure drop is obtained when flow maldistribution is minimal.

Parameter identification in Helmholtz-type equations with a variable coefficient using a regularized DRBEM

The identification of the space-dependent coefficient in two-dimensional Helmholtz-type equations from a complete knowledge of the field modelled by these equations and its normal derivative on the boundary and additional internal measurements of the field is investigated. This problem is approached by combining a regularized dual reciprocity boundary element method (DRBEM) with a constrained non-linear minimisation technique. The optimal regularization parameter is chosen according to Morozovs discrepancy principle. The accuracy, convergence and stability of the proposed numerical method are carefully analysed and a sensitivity analysis with respect to the initial guess for the minimisation process is also performed. The numerical results obtained show that the combined regularized DRBEM-constrained non-linear minimisation technique is accurate, convergent, stable and robust.

The Evaluation of a Vent Condenser by the Film and Equilibrium Methods for Steam/Air Mixtures

The current design and performance evaluation methods for vent and reflux condensers include minimum safety factors of 30% or more. These oversized condensers incur high capital and operational costs. Experimental data are fundamental in order to evaluate these design methodologies. This paper presents a new set of experiments performed in a steam/air vent condenser at subatmospheric pressures. The experimental apparatus consists of a vertical, double-pipe condenser with a length of 3 m and inner diameter of 0.028 m. The produced experimental data allow the evaluation of the local heat transfer coefficients and the heat-flux profile on the coolant side. After comparing the predictions of the two main methods for the design of vent and reflux condensers, that is, the film method and the equilibrium method as modified by Webb et al. (1996), it becomes apparent that the film method is always better and should be always preferred when diffusive data are available. The equilibrium method error in predicting the heat transfer area is shown to be a function of the Lewis number. Further valuable observations are noted regarding the calculation procedures of the two mentioned methods and the risks of using the equilibrium method.

Reflux Condensation under Vacuum of a Methanol/Water Mixture with Plain Tube and Tube Inserts

This paper presents preliminary observations and calculations obtained for the reflux condensation of a water–methanol vapor mixture in a plain tube and a tube fitted with inserts. It is an attempt to present findings that resolve the reflux condenser controllability and operability, which has always been a major issue in the industry. A modification to the experimental apparatus has improved pressure measurement and aided in determining mass and heat balance information, thus giving greater confidence in the operation of the reflux condenser. Tube inserts are installed in the condenser tube in two different arrangements. The tube inserts are called HiTRAN® and are manufactured by Cal Gavin Ltd. (UK). This work describes some of the behaviors observed in the reflux condenser both with and without tube inserts. The dynamic temperature and pressure trends are notable. The inserts threshold length is the length where the reflux condensation process avoids flooding and has a recovery of heavier and lighter components.

A New Method to Quantify the Swelling Properties of Polymer Beads Used in Solid Phase Peptide Synthesis (SPPS)

The swelling properties of cross-linked polymer beads used as supports in solid phase peptide synthesis (SPPS) are important to the efficiency of the process and the purity of the product. Two of the important swelling properties are the volume to which the solid support will swell when contacted with solvent and how long the process requires to reach equilibrium [1]. If the swelling properties change at any stage, the reaction rate and ability to access every reactive site could be hampered. The swelling properties of the solid support are known to change throughout the synthesis, but an exact correlation is unknown. The technique highlighted here could be used to determine the effect of a change in the solvent concentration and the addition of an amino acid to the solid support on the swollen volume. The most obvious physical property of the solid support is the volume to which it swells when contacted with solvent. When the solid support is contacted with solvent, the solid support will swell to produce a gel phase made up of individual swollen beads. The swelling properties of the gel phase must be determined to be able to understand the process of SPPS. The gel phase must be maintained in a highly swollen state to allow the active species to diffuse to the reactive sites within the bead and to remove the by-products and excess reagents within the swollen bead [2].