Heat transfer in a continuous bloomcaster

Four approaches to detecting disruptions to the primary cooling process in the continuous bloomcaster at BHP's Rod and Bar Division in Newcastle are investigated. Three of these are based on heat conduction models of the mould. A one-dimensional steady-state formulation leads to the conclusion that it may not be possible to detect changes in the length of the lubricating flux layer between the solidifying steel strand and the mould from data collected at thermocouples in the mould. Two two-dimensional models give formal procedures for determining either the heat input to the mould or the presence of hot spots in the strand from the thermocouple data. The final approach suggests the use of time-series analysis to detect changes in the heat transfer process

Cooling of jarred cheese spreads

An overall heat balance and a model for the cooling of an individual jar are derived for glass jars of cheese spread on Kraft's production line. Good agreement is found between the model predictions and temperature data collected by Kraft. A possible cause of boiling in the cheese is proposed and steps for its prevention are suggested

Reduction behaviour in Fastmet(TM) pellets

Fastmet (TM), a process developed by the Midrex Corporation, produces iron for steelmaking by heating pellets composed of iron oxide and coal. Here we develop several simple models of the reduction process and confirm claims made by the manufacturer about the conversion time. These models can also be used to investigate the dependence of the conversion time on controlling parameters

Moisture movement in bulk stockpiles

Both drainage and evaporation are possible mechanisms for moisture loss in iron-ore and coal stockpiles. Some simple models are used to study both these mechanisms for various stages of stockpiling. The process of segregation of different particle sizes of the ore as it is stockpiled is also considered and this may have important implications for both drainage and evaporative moisture loss

Corrosion and wear in moulding boxes

We assess the potential causes of damage to mould box ends and find that both HOT corrosion, due to burning of emitted volatiles, and COLD corrosion, due to the presence of high humidity (and possibly high chloride ion concentration), are likely to contribute to the damage. We suggest strategies to minimise the damage, including venting of the volatiles, ventilation of the pallet grooves during cooling and minimisation of brushing effects during cleaning. Some calculations are described in an attempt to quantify the various effects discussed, but we are unable to accurately estimate their significance

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A two-compartment mechanochemical model of the roles of\ud transforming growth factor β and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor−β (TGFβ) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGFβ and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGFβ in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGFβ significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures

Wound healing angiogenesis the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly-formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds