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Abstract. When a hazardous chemical agent has soaked into a porous medium, such as concrete, 4it can be difficult to neutralise. One removal method is chemical decontamination, where a cleanser 5 is applied to react with and neutralise the agent, forming less harmful reaction products. There are 6 often several cleansers that could be used to neutralise the same agent, so it is important to identify 7 the cleanser features associated with fast and effective decontamination. As many cleansers are 8 aqueous solutions while many agents are immiscible with water, the decontamination reaction often 9 takes place at the interface between two phases. In this paper, we develop and analyse a mathematical 10 model of a decontamination reaction between a neat agent and an immiscible cleanser solution. We 11 assume that the reaction product is soluble in both the cleanser phase and the agent phase. At the 12 moving boundary between the two phases, we obtain coupling conditions from mass conservation 13 arguments and the oil-water partition coefficient of the product. We analyse our model using both 14 asymptotic and numerical methods, and investigate how different features of a cleanser affect the time 15 taken to remove the agent. Our results reveal the existence of two regimes characterised by different 16 rate-limiting transport processes, and we identify the key parameters that control the removal time 17 in each regime. In particular, we find that the oil-water partition coefficient of the reaction product 18 is significantly more important in determining the removal time than the effective reaction rate. 19

Motivated by convection of planetary mantles, we consider a mathematical model for Rayleigh-Bénard convection in a basally heated layer of a fluid whose viscosity depends strongly on temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and steady solutions for temperature, isotherms, and streamlines are obtained. To improve the efficiency of numerical computation, we introduce a modified viscosity law with a low temperature cutoff. We demonstrate that this simplification results in markedly improved numerical convergence without compromising accuracy. Continued numerical experiments suggest that narrow cells are preferred at extreme viscosity contrasts, and this conclusion is supported by a linear stability analysis. C 2015 AIP Publishing LLC. [http://dx

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This article investigates the influence of variable heat flux on the problem of steady two dimensional MHD flow and heat transfer of an electrically conducting fluid along a semi-infinite vertical plate taking into account the effect of viscous dissipation. The governing equations are converted into a system of nonlinear ordinary differential equations via a similarity variable. The resulting system of equations is then solved numerically by using Natchsheim Swigert shooting iteration technique together with sixth order RungeKutta integration scheme. Boundary layer velocity and temperature profiles are determined numerically for various values of the ratio of free stream velocity and stretching velocity, the magnetic field parameter, suction/blowing parameter, Brinkman number. Regardless of the flow conditions, the flow velocity and temperature is found significantly affected by the flow parameters.