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This article aims to present a novel mono-dimensional multilayer mathematical model apt to estimate the temperature of photovoltaic (PV) cells for both monofacial and bifacial PV modules. A dynamic three-layer model (3L-NM) has been developed, in which the contribution of solar radiation that hits the back of the PV module is included. The model is constituted by energy balance equations, one for each layer of the PV module. The input data of the proposed model are the environmental weather conditions as well as the withdrawal electrical power. The outputs are the average temperature of each layer, so it is possible to determine the PV cell temperatures that typically cannot be directly measured. With the purpose to investigate the reliability of the proposed model, the numerical results have been compared with experimental data. Finally, a sensitivity analysis has been performed to evaluate the impact of solar radiation in the back of the PV module considering the different wind speed, as well as the operating electrical points (open circuit and maximum power point). From the statistical analysis, correlation values of 0.993 and 0.990 were obtained, PE values equal to 0.718% and 0.161%, respectively, for the monofacial and bifacial module. The sensitivity study shows that the solar radiation on the backside of the module has a greater impact on the bifacial module, infact, when the contribution of back is included in a model, temperature differences up to 5.2 °C for bifacial and 1.0 °C for monofacial module at 1000 W/m2 were observed.

Low-density lipoprotein (LDL) deposition within the walls of an artery causes the growth of an atherosclerotic plaque, which can cause serious health issues. Various physical phenomena affect this aspect, for example, induced temperature gradients, which cause particle movement due to thermodiffusion. In this work, the effects of hypo-and hyperthermia on a curved artery are investigated. The heat source/sink is applied from the interior side of the artery (the lumen side). The curvature effect of the artery is taken into account through variation of the arterial curvature ratio, while a multilayer model that takes into account the heterogeneity of various layers represents the wall. Navier–Stokes and convection–diffusion equations are employed for the LDL transport through the lumen, while Darcy–Brinkman, Staverman–Kedem–Katchalsky with a reaction term, and the energy equation are used to study the wall layers. Results are presented for shear rates, temperature, and LDL profiles. It is shown that the artery curvature has a negligible effect on LDL deposition when a heat source/sink, under hypo-or hyperthermia conditions is applied from the lumen side.

This work is devoted to the description and comparative study of some methods of mathematical modeling. We consider methods that can be applied for building cyber-physical systems and digital twins. These application areas add to the usual accuracy requirements for a model the need to be adaptable to new data and the small computational complexity allows it to be used in embedded systems. First, we regard the finite element method as one of the “pure” physics-based modeling methods and the general neural network approach as a variant of machine learning modeling with physics-based regularization (or physics-informed neural networks) and their combination. A physics-based network architecture model class has been developed by us on the basis of a modification of classical numerical methods for solving ordinary differential equations. The model problem has a parameter at some values for which the phenomenon of stiffness is observed. We consider a fixed parameter value problem statement and a case when a parameter is one of the input variables. Thus, we obtain a solution for a set of parameter values. The resulting model allows predicting the behavior of an object when its parameters change and identifying its parameters based on observational data.

Objectives. The aim of present work was to carry out mathematical modelling of heat transfer with symmetrical heating in flat channels and round pipes with rough walls. Methods. The calculation was carried out using the L'Hopital-Bernoulli's method. The solution of the problem of intensified heat transfer in a round tube with rough walls was obtained using the Lyon's integral. Results. Different from existing theories, a methodology of theoretical computational heat transfer determination for flat rough channels and round pipes with rough walls is developed on the basis of the principle of full viscosity superposition in a turbulent boundary layer. The analysis of the calculated heat transfer and hydroresistivity values for flat rough channels and round rough pipes shows that the increase in heat transfer is always less than the corresponding increase in hydraulic resistance, which is a disadvantage as compared to channels with turbulators, with all else being equal. The results of calculating the heat transfer for channels with rough walls in an extended range of determinant parameters, which differ significantly from the corresponding data for the channels with turbulators, determine the level of heat exchange intensification. Conclusion. An increase in the calculated values of the relative average heat transfer Nu/NuGL for flat rough channels and rough pipes with very high values of the relative roughness is significantly contributed by both an increase in the relative roughness height and an increase in the Reynolds number Re. In comparison with empirical dependencies, the main advantage of solutions for averaged heat transfer in rough flat channels and round pipes under symmetrical thermal load obtained according to the developed theory is that they allow the calculation of heat exchange in rough pipes to be made in the case of large and very large relative heights of roughness protrusions, including large Reynolds numbers, typical for pipes of small diameters and narrow flat channels. An increase in the relative heat exchange in air due to an increase in the relative height of the roughness or the Reynolds number is accompanied by an even more significant increase in the hydraulic resistance. Calculated data on averaged heat transfer obtained in the work showed that in the range of determinant parameters for flat rough channels with symmetrical thermal loading, the average heat transfer is higher by (4.811.7)% as compared to round rough pipes – all other things being equal.

We present here numerical modelling of granular flows with the rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier–Stokes equations with the rheology through an asymptotic analysis; under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fernández-Nieto et al. (2016) [20]. In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well-balanced property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i.e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient but not with a constant friction coefficient.

The problem of the propagation of acoustic wave disturbance initiated by a boundary condition is used to simulate a disturbance of atmospheric gas caused by a rise of water masses. The boundary condition is a function of a dynamic variable that is defined on the border of the problem domain. In this work, it is chosen in such a way that its parameters and form correspond to disturbances in the gas layer produced by a tsunami wave at the air&ndash, water interface. The atmosphere is approximately described as a 1D multilayer gas media with an exponential structure of density in each layer. The boundary conditions are set at the interface between water&ndash, air and gas layers. These determine the direction of propagation and the ratio of dynamic variables characterizing an acoustic wave. The relationship between such variables (pressure, density, and velocity) is derived by means of projection operators on the subspaces of the z-evolution operator for each layer. The universal formulas for the perturbation of atmospheric variables in an arbitrary layer are obtained in frequency and time domains. As a result, explicit expressions are derived that determine the spectral composition and vertical velocity, by the stationary phase method, of the acoustic disturbance of the atmosphere at an arbitrary height, including the heights of the ionosphere. In return, this can be used to calculate the ionospheric effect. The effect is described by the explicit formula for electron density evolution, which is the solution of the diffusion equation. This forms a quick algorithm for early diagnostics of tsunami waves.

In order to reveal the control of tree transpiration by the leaf ecophysiological traits and the hydraulic processes from the soil to leaves, transpiration rates of the tree species in tropical seasonal forests were monitored and modeled using independently measured leaf photosynthetic traits. Stand-level transpiration rate was modeled for rubber trees in a plantation and alien and native species in a community forest using a multilayer biophysical model that couples the energy balance and leaf ecophysiological processes. Model simulation was carried out on the assumption that leaf gas exchange was not limited by the hydraulic processes from the root to the leaves, while transpiration rates, which were independently monitored using sap flux measurements, were influenced both by the seasonal trends in leaf ecophysiological traits and the hydraulic processes. The modeled transpiration rate (Emodel) successfully captured the diurnal trend of the in situ measured one ( E sap) in most rainy seasons in rubber plantation and in dry season in community forests, suggesting the absence of hydraulic limitation in soil-plant continuum. The decoupling between the E model and E sap was observed in mid dry season in rubber plantation and in a native species of the community forest. The daily-scale E model overestimated E sap by 20-40%, mainly due to the midday depression of E sap. On the other hand, in an alien eucalyptus species in community forest, overestimate of E model was observed in mid rainy season, suggesting the failure of water uptake by the roots under flooding conditions. The seasonal decreases in daily E sap matched the timing of the water transport limitation of soil-plant continuum. Under lowered E sap conditions, as high E model as other seasons was observed in each species but could not be met due to the water supply, suggesting the leaf ecophysiological traits oriented for high leaf water demand and their imbalance with the seasonally decreasing water supply capacity. In conclusion, seasonal trends in transpiration rate were strongly characterized by the limitation in the process of soil-plant water transport, rather than the seasonal trends in the leaf ecophysiological traits.

A multilayer computational model for simulating three-dimensional tidal flows in coastal waters is presented in this paper. A truly meshless numerical scheme based on radial basis functions (RBFs) is employed to obtain an accurate approximation to the solution of the model. For computational efficiency in solving large-scale problems, a noniterative domain decomposition method is combined with the use of the RBFs scheme. To smooth the numerical simulation of the advection across each subdomain, the commonly used upstream technique is also incorporated. Finally, for numerical verification, the proposed multilayer model is successfully used to obtain a stable and convergent simulation of the water flows in the Pearl River Estuary of the South China Sea. The numerical approximations exhibit good agreement with the observed tidal and current data.