Transportation of water-based slurry in an open furrow, launder or stream

The transport of large boulders in a furrow from a mining area to a nearby pond was considered. The furrow is filled with a mixture of water and soil particles flowing down to the pond at a very high velocity. Due to operating constraints, the slope of the furrow is reduced progressively. A formula is derived, relating the slope of the furrow and the composition of the fluid to the maximum size and shape of the transported boulders. The characteristics of the boulders carried all the way down to the pond may then be determined

Modelling surface heat exchanges from a concrete block to the environment

The presented problem was to determine an appropriate heat transfer boundary condition at the surface of a concrete slab exposed to the environment. The condition obtained involves solar radiation and convective heat transfer, other terms were shown to be small compared to these. It is shown that this boundary condition leads to a temperature variation that has qualitative agreement with experiments carried out by the Cement and Concrete Institute

Fracturing rock with ultra high pressure water

Modelling issues are considered for the process of cracking rock in mines using ultra high pressure water. The elevated pressures are caused by the ignition of a propellant and may be as large as 1000MPa. We first consider time, length and pressure scales and then derive a model for the propagation of a two-dimensional crack. A number of aspects of this model are considered and similarity solutions and behaviour near the crack tip are investigated. Consideration is given to a simplified model where the elastic component of the interaction between the rock and the fluid is handled using an elementary closure law: in this case much progress may be made and closed-form solutions may be determined. Conditions are also identified where a model based on “impulsive” lubrication theory is appropriate. However, this leads to a very challenging problem. Finally, some other ways of extending the model to include (for example) fluid leak-off into the rock are discussed

Modelling the cooling of concreate by piped water

Large concrete structures are usually made sequentially in a series of blocks. After each block is poured it must be left to cool and shrink for a period depending on its size, but typically for around 1 week, before the next block is poured. The reason for the delay is that the mixture of cement and water, which constitute the binding agent of the concrete, results in a series of hydration reactions that generate heat.Piped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generation model. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems

Modelling the cooling of concrete by piped water

Large concrete structures are usually made sequentially in a series of blocks. After each block is poured it must be left to cool and shrink for a period depending on its size, but typically for around 1 week, before the next block is poured. The reason for the delay is that the mixture of cement and water, which constitute the binding agent of the concrete, results in a series of hydration reactions that generate heat.The chemical reaction can lead to temperature rises in excess of 50 K and it can take a number of years before the concrete cools to the ambient temperature. Prior to construction of the Hoover dam engineers at the U.S. Bureau of Reclamation estimated that if the dam were built in a single continuous pour the concrete would require 125 years to cool to the ambient temperature and that the resulting stresses would have caused the dam to crack and fail (U.S. Bureau of Reclamation 2005)

Modeling the cooling of concrete by piped water.

Accepted ManuscriptPiped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generation model. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems.MvdH2016http://ascelibrary.org/journal/jenmd

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close