Powder flow and temperature distribution are recognized as essential factors in the laser melting deposition (LMD) process, which affect not only the layer formation but also its characteristics. In this study, two mathematical models were developed. Initially, the three-jet powder flow in the Gaussian shape was simulated for the LMD process. Next, the Gaussian powder flow was coaxially added along with the moving laser beam to investigate the effect of powder flow on temperature distribution at the substrate. The powder particles’ inflight and within melt-pool heating times were controlled to avoid vapors or plasma formation due to excessive heat. Computations were carried out via MATLAB software. A high-speed imaging camera was used to monitor the powder stream distribution, experimentally, while temperature distribution results were compared with finite element simulations and experimental analyses. A close correlation was observed among analytical computation, numerical simulations, and experimental results. An investigation was conducted to investigate the effect of the focal point position on powder stream distribution. It was found that the focal point position plays a key role in determining the shape of the powder stream, such that an increment in the distance from the focus point will gradually transform the powder stream from the Gaussian to Transition, and from the Transition to Annular streams. By raising the powder flow rate, the attenuation ratio prevails in the LMD process, hence, decreasing the laser energy density arriving at the substrate. The computations indicate that, if the particle’s heating temperature surpasses the boiling point, a strong possibility exists for vapors and plasma formation. Consequently, an excessive amount of laser energy is absorbed by the produced vapors and plasma, thus impeding the deposition process.

Heat equations can estimate the thermal distribution and phase transformation in real-time based on the operating conditions and material properties. Such wonderful features have enabled heat equations in various fields, including laser and electron beam processing. The integral transform technique (ITT) is a powerful general-purpose semi-analytical/numerical method that transforms partial differential equations into a coupled system of ordinary differential equations. Under this category, Fourier and non-Fourier heat equations can be implemented on both equilibrium and non-equilibrium thermo-dynamical processes, including a wide range of processes such as the Two-Temperature Model, ultra-fast laser irradiation, and biological processes. This review article focuses on heat equation models, including Fourier and non-Fourier heat equations. A comparison between Fourier and non-Fourier heat equations and their generalized solutions have been discussed. Various components of heat equations and their implementation in multiple processes have been illustrated. Besides, literature has been collected based on ITT implementation in various materials. Furthermore, a future outlook has been provided for Fourier and non-Fourier heat equations. It was found that the Fourier heat equation is simple to use but involves infinite speed heat propagation in comparison to the non-Fourier heat equation and can be linked with the Two-Temperature Model in a natural way. On the other hand, the non-Fourier heat equation is complex and involves various unknowns compared to the Fourier heat equation. Fourier and Non-Fourier heat equations have proved their reliability in the case of laser–metallic materials, electron beam–biological and –inorganic materials, laser–semiconducting materials, and laser–graphene material interactions. It has been identified that the material properties, electron–phonon relaxation time, and Eigen Values play an essential role in defining the precise results of Fourier and non-Fourier heat equations. In the case of laser–graphene interaction, a restriction has been identified from ITT. When computations are carried out for attosecond pulse durations, the laser wavelength approaches the nucleus-first electron separation distance, resulting in meaningless results.

The interest in ultrathin silver (Ag) films has increased due to their high surface plasmon resonance for coatings of only a few nm. Low roughness ultrathin films of 1 to 9 nm have been deposited on different substrates, such as polyethylene terephthalate (PET) and optical glass, using radio frequency (RF) magnetron sputtering. Films show good surface plasmon resonance up to 7 nm thickness, as revealed by the ultraviolet-visible (UV-Vis) spectra. The roughness of the films, investigated by Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM), is small, and one can conclude that depositions are smooth and homogeneous. The bandgap values decrease with film thickness. The refractive index of the films, calculated from ellipsometry measurements, leads to values of under 1 visible domain, with minima in the wavelength range of 400–600 nm. The results are useful for obtaining lower roughness ultrathin Ag films with good surface plasmon resonance for photonic applications.

This work is devoted to the electron temperature variation in metals through interaction with femtosecond laser pulses. Our study was inspired by the last mathematical breakthroughs regarding the exact analytical solutions of the heat equation in the case of flash laser-matter interaction. To this purpose, the classical Anisimov’s two temperature model was extended via the 3D telegraph Zhukovsky equation. Based upon this new approach, the computational plots of electron thermal fields during the first laser pulse interaction with a gold surface were inferred. It is shown that relaxation times and coupling factors over electron thermal conductivities (g/K) govern the interaction between the laser pulse and metal sample during the first picoseconds. The lower the factor g/K, the higher the electron temperature becomes. In contrast, the lower the relaxation time, the lower the electron temperature.

A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.

IV-VI semiconductor quantum dots embedded into an inorganic matrix represent nanostructured composite materials with potential application in temperature sensor systems. This study explores the optical, structural, and morphological properties of a novel PbS quantum dots (QDs)-doped inorganic thin film belonging to the Al₂O₃-SiO₂-P₂O₅ system. The film was synthesized by the sol-gel method, spin coating technique, starting from a precursor solution deposited on a glass substrate in a multilayer process, followed by drying of each deposited layer. Crystalline PbS QDs embedded in the inorganic vitreous host matrix formed a nanocomposite material. Specific investigations such as X-ray diffraction (XRD), optical absorbance in the ultraviolet (UV)-visible (Vis)-near infrared (NIR) domain, NIR luminescence, Raman spectroscopy, scanning electron microscopy–energy dispersive X-ray (SEM-EDX), and atomic force microscopy (AFM) were used to obtain a comprehensive characterization of the deposited film. The dimensions of the PbS nanocrystallite phase were corroborated by XRD, SEM-EDX, and AFM results. The luminescence band from 1400 nm follows the luminescence peak of the precursor solution and that of the dopant solution. The emission of the PbS-doped film in the NIR domain is a premise for potential application in temperature sensing systems.