Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Comparison among monitoring strategies to assess water flow dynamic and soil hydraulic properties in agricultural soils

Irrigated agriculture is usually performed in semi-arid regions despite scarcity of water resources. Therefore, optimal irrigation management by monitoring the soil is essential, and assessing soil hydraulic properties and water flow dynamics is presented as a first measure. For this purpose, the control of volumetric water content, θ, and pressure head, h, is required. This study adopted two types of monitoring strategies in the same experimental plot to control θ and h in the vadose zone: i) non-automatic and more time-consuming; ii) automatic connected to a datalogger. Water flux was modelled with Hydrus-1D using the data collected from both acquisition strategies independently (3820 daily values for the automatic; less than 1000 for the non-automatic). Goodness-of-fit results reported a better adjustment in case of automatic sensors. Both model outputs adequately predicted the general trend of θ and h, but with slight differences in computed annual drainage (711 mm and 774 mm). Soil hydraulic properties were inversely estimated from both data acquisition systems. Major differences were obtained in the saturated volumetric water content, θs, and the n and α van Genuchten model shape parameters. Saturated hydraulic conductivity, Ks, shown lower variability with a coefficient of variation range from 0.13 to 0.24 for the soil layers defined. Soil hydraulic properties were better assessed through automatic data acquisition as data variability was lower and accuracy was higher.