The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

The purpose of this work is to present the model of a Parabolic Trough Solar Collector (PTC) using the Finite Element Method to predict the thermal behavior of the working fluid along the collector receiver tube. The thermal efficiency is estimated based on the governing equations involved in the heat transfer processes. To validate the model results, a thermal simulation of the fluid was performed using Solidworks software. The maximum error obtained from the comparison of the modeling with the simulation was 7.6% at a flow rate of 1 L/min. According to the results obtained from the statistical errors, the method can effectively predict the fluid temperature at high flow rates. The developed model can be useful as a design tool, in the optimization of the time spent in the simulations generated by the software and in the minimization of the manufacturing costs related to Parabolic Trough Solar Collectors.

Broad-spectrum antibiotics, such as tetracyclines, are used to treat and manage a range of infectious disorders. Since the kidneys are the primary organs responsible for excreting tetracyclines, clinicians should refrain from prescribing them to patients who have renal failure. Tetracyclines are one of the clinical waste products of today. One of the biggest problems in the field of pollution of the environment today is the persistence of different pharmaceutical residues, drug residues, pesticides, and metal ion species of the new-generation pollutants in surfaces and groundwater. In the present work, carboxymethyl cellulose (CMC)-CuO nanoparticles (CMC-CuO NPs) were synthesized using CuO NPs within different amounts of CMC (0.5, 1.0, 1.5 and 2.0 g) at 85 °C. The synthesized nanoparticles were characterized by XRD, FT IR, SEM, and TG-DTA analysis. According to XRD and SEM, the crystallize size and morphology influenced the dosage of CMC. FT-IR analysis confines the layer of CMC to the CuO nanoparticle surface. TG-DTA results indicated that the CMC content of CMC-CuO NPs was between the range of 69% and 75% by weight. The effects of some parameters such as initial concentration, pH, adsorbent dosage, and contact time on the adsorption of tetracycline from aqueous model solutions on CMC-CuO NPs were investigated with batch studies. It was found that the removal of tetracycline was obtained about 80% with optimized parameters of 10 mg/L concentration, 180 min contact time, 5 pH, and 0.3 g/25 mL dose. The synthesized CMC-CuO NPs nanocomposite may be a promising material for the removal of tetracycline in environmental pollution and toxicology.

Heat removal has become an increasingly crucial issue for microelectronic chips due to increasingly high speed and high performance. One solution is to increase the thermal conductivity of the corresponding dielectrics. However, traditional approach to adding solid heat conductive nanoparticles to polymer dielectrics led to a significant weight increase. Here we propose a dielectric polymer filled with heat conductive hollow nanoparticles to mitigate the weight gain. Our mesoscale simulation of heat conduction through this dielectric polymer composite microstructure using the phase-field spectral iterative perturbation method demonstrates the simultaneous achievement of enhanced effective thermal conductivity and the low density. It is shown that additional heat conductivity enhancement can be achieved by wrapping the hollow nanoparticles with graphene layers. The underlying mesoscale mechanism of such a microstructure design and the quantitative effect of interfacial thermal resistance will be discussed. This work is expected to stimulate future efforts to develop light-weight thermal conductive polymer nanocomposites.