Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.

Heat transfer from molten materials to liquids

An apparatus was designed and constructed which enabled material to be melted and heated to a maximum temperature of 1000C and then flooded with a pre-heated liquid. A series of experiments to investigate the thermal interaction between molten metals (aluminium, lead and tin) and sub-cooled water were conducted. The cooling rates of the molten materials under conditions of flooding were measured with a high speed-thermocouple and recorded with a transient recorder. A simplified model for calculating heat fluxes and metal surface temperatures was developed and used. Experimental results yielded boiling heat transfer in the transition film and stable film regions of the classic boiling curve. Maximum and minimum heat fluxes were observed at nucleate boiling crisis and the Leidenfrost point respectively. Results indicate that heat transfer from molten metals to sub-cooled water is a function of temperature and coolant depth and not a direct function of the physical properties of the metals. Heat transfer in the unstable transition film boiling region suggests that boiling dynamics in this region where a stationary molten metal is under pool boiling conditions at atmospheric pressure would not initiate a fuel-coolant interaction. Low heat fluxes around the Leidenfrost point would provide efficient fuel-coolant decoupling by a stable vapour blanket to enable coarse mixing of the fuel and coolant to occur without appreciable loss of thermal energy from the fuel. The research was conducted by Gareph Boxley and was submitted for the degree of PhD at the University of Aston in Birmingham in 1980.

Variations of local heat transfer coefficient in piped flow of viscous liquids

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

Local heat transfer coefficient in a baffled shell and tube heat exchanger

Local shell side coefficient measurements in the end conpartments of a model shell and tube heat exchanger have been made using an electrochemical technique. Limited data are also reported far the second compartment. The end compartment average coefficients have been found to be smaller than reported data for a corresponding internal conpartment. The second compartment data. have been shown to lie between those for the end compartments and the reported internal compartment data. Experimental data are reported fcr two port types and two baffle orientations. with data for the case of an inlet compartment impingement baffle also being given . Port type is shown to have a small effect on compartment coefficients, these being largely unaffected. Likewise, the outlet compartment average coefficients are slightly snaller than those for the inlet compartment, with the distribution of individual tube coefficients being similar. Baffle orientation has been shown to have no effect on average coefficients, but the distribution of the data is substantially affected. The use of an impingement baffle in the inlet compartment lessens the efect of baffle orientation on distribution . Recommendations are made for future work.

CFD modelling of the fast pyrolysis of an in-flight cellulosic particle subjected to convective heat transfer

The pyrolysis of a freely moving cellulosic particle inside a 41.7mgs -1 source continuously fed fluid bed reactor subjected to convective heat transfer is modelled. The Lagrangian approach is adopted for the particle tracking inside the reactor, while the flow of the inert gas is treated with the standard Eulerian method for gases. The model incorporates the thermal degradation of cellulose to char with simultaneous evolution of gases and vapours from discrete cellulosic particles. The reaction kinetics is represented according to the Broido–Shafizadeh scheme. The convective heat transfer to the surface of the particle is solved by two means, namely the Ranz–Marshall correlation and the limit case of infinitely fast external heat transfer rates. The results from both approaches are compared and discussed. The effect of the different heat transfer rates on the discrete phase trajectory is also considered.

Computational modelling of the impact of particle size to the heat transfer coefficient between biomass particles and a fluidised bed

The fluid–particle interaction and the impact of different heat transfer conditions on pyrolysis of biomass inside a 150 g/h fluidised bed reactor are modelled. Two different size biomass particles (350 µm and 550 µm in diameter) are injected into the fluidised bed. The different biomass particle sizes result in different heat transfer conditions. This is due to the fact that the 350 µm diameter particle is smaller than the sand particles of the reactor (440 µm), while the 550 µm one is larger. The bed-to-particle heat transfer for both cases is calculated according to the literature. Conductive heat transfer is assumed for the larger biomass particle (550 µm) inside the bed, while biomass–sand contacts for the smaller biomass particle (350 µm) were considered unimportant. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Biomass reaction kinetics is modelled according to the literature using a two-stage, semi-global model which takes into account secondary reactions. 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).

Extended surface fluidized bed heat transfer

Experirnental data and theoretical calculation on the heat transfer performance of extended surface submerged: in shallow air fluidized beds ~ less than 150 mm, are presented. Energy t;ransferrence from the bed material was effected by water cooled tubes passing through the fins. The extended surface tested was either manufactured from square or radial copper fins silver soldered to a circular basic tube or commercially supplied, being of the crimped or extruded helical fin type. Performances are compared, for a wide range of geometric variables, bed configurations and fluidized materials, with plain and oval tubes operating under similar experimental conditions. A statistical analysis of all results, using a regression technique, has shown the relative importance of each significant variable. The bed to surface heat transfer coefficients are higher than those reported in earlier published work using finned tubes in much deeper beds and the heat transfer to the whole of the extended surface is at least as good as that previously reported for un-finned tubes. The improved performance is attributed partly to the absence of large bubbles in shallow beds and it is suggested that the improved circulation of the solids when constrained in the narrow passages between adjacent fins may be a contributory factor. Flow visualisation studies between a perspex extended surface and a fluidized bed using air at ambient temperatures, have demonstrated the effect of too small a fin spacing. Fin material and the bonding to the basic tube are more important in the optimisation of performance than in conventional convective applications because of the very much larger heat fluxes involved. A theoretical model of heat flow for a radial fin surface, provides data concerning the maximum heat transfer and minimum metal required to fulfil a given heat exchange duty. Results plotted in a series of charts aim at assisting the designer of shalJow fluidized beds.