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Advection–diffusion–reaction equations are widely used in applied science, since they are able to describe real-life phenomena in which transport phenomena and chemical reactions take place. Here, they are used to predict the amount of extracted substances during the percolation of espresso coffee. The corresponding initial-boundary value problem is solved by the Crank–Nicolson scheme and a nested fixed-point iteration. The reliability of the model and the solving strategy is assessed experimentally, by comparing the amount of chemical substances in real and simulated extractions performed under different extractive conditions. [ABSTRACT FROM AUTHOR]

In this study, we propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier–Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger. [ABSTRACT FROM AUTHOR]

Geothermal heat exchanger fields are complex systems that exploit the soil as a heat reservoir for space heating and cooling. They consist of several heat exchangers conveniently arranged in a given soil portion. The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task requires modelling the relevant processes in the system, i.e., the heat transfer within and outside the exchangers. We propose a mathematical model for the study of the heat conduction into the soil that considers the presence of the exchangers. This problem is formulated and solved with an analytical approach. Some numerical experiments are used to show the effectiveness of the proposed method through a comparison with a reference approximation procedure, based on a finite difference method. Moreover, the obtained analytical solution is used in an optimisation procedure to compute the best position of the exchangers by minimising the adverse effect of neighbouring devices. The obtained results are promising and show that the proposed procedure can be exploited as an effective tool in the design of geothermal systems. • An efficient optimisation method to design an optimised geothermal field. • Analytical solution of the heat transfer problem in a solid–fluid system. • An inverse source problem to effectively mimic the thermal effect of an exchanger. • An inverse conduction problem for the optimal position of the exchangers. [ABSTRACT FROM AUTHOR]

• Use of the FFT for fast numerical derivative computation. • Use of the SVE of the integral kernel associated to derivative operator of a generic order. • Proof of the order of convergence of the proposed method. • Development of a robust algorithm for first order derivative. • Generalization of the algorithm to higher order derivatives. • Generalization of the algorithm to derivatives of multivariate functions. We consider the numerical differentiation of a function tabulated at equidistant points. The proposed method is based on the Fast Fourier Transform (FFT) and the singular value expansion of a proper Volterra integral operator that reformulates the derivative operator. We provide the convergence analysis of the proposed method and the results of a numerical experiment conducted for comparing the proposed method performance with that of the Neville Algorithm implemented in the NAG library. [ABSTRACT FROM AUTHOR]

• Physico-chemical modelling of coffee extraction. • Fluid flow in porous media. • Transport of solutes and particles in porous media. • In-silico coffee extraction. Brewing coffee is primarily considered an art rather than a business. Drinking coffee is a practice spread worldwide irrespective of race, age, and social extraction, making coffee the leading commodity in the fair trade movement. Its daily consumption has scientifically proven health benefits. Thus, such interesting features of coffee have stimulated a wide coffee-oriented scientific research addressing health, social and economical aspects. An important component of this research is an in-depth knowledge of the physico-chemical processes occurring in the coffee preparation. In this paper, we propose a mathematical model for describing the percolation processes occurring during the espresso coffee extraction by exploiting fluid-dynamics components. The validity of this water percolation model into porous media is demonstrated on an experimental basis, exploiting chemical laboratory analyses of espresso coffee samples extracted under different conditions. [ABSTRACT FROM AUTHOR]