International Journal of Computational Materials Science and Engineering

Thermal management in the looming world of electronic packaging system is the most prior and conspicuous issue as far as the working efficiency of the system is concerned. The cooling in such systems can be achieved by impinging air jet over the heat sink as jet impingement cooling is one of the cooling technologies which are widely studied now. Here the modulation in impinging and geometric parameters results in the establishment of the characteristic cooling rate over the target surface. The characteristic cooling curve actually resembles non-uniformity in cooling rate. This non-uniformity favors the area average heat dissipation rate. In order to study the non-uniformity in cooling characteristic, the present study takes an initiative in plotting the local Nusselt number magnitude against the non-dimensional radial distance of the different thickness of target surfaces. For this, the steady temperature distribution over the target surface under the impingement of air jet is being determined numerically. The work is completely inclined towards the determination of critical value of geometric thickness below which the non-uniformity in the Nusselt profile starts. This is done by numerically examining different target surfaces under constant Reynolds number and nozzle-target spacing. The occurrences of non-uniformity in Nusselt profile contributes to over a 42% enhancement in area average Nusselt magnitude. The critical value of characteristic thickness (t/d) reported in the present investigation approximate to 0.05. Below this value, the impingement of air jet generates a discrete pressure zones over the target surface in the form of pressure spots. As a result of this, the air flowing in contact with the target surface experiences a damping potential, in due of which it gets more time and contact with the surface to dissipate heat.

The graphene-on-substrates breaks the sub-lattice symmetry leading to the opening of a small gap. The small band gaps can be enhanced by electron–phonon interactions by keeping strongly polarized superstrate on graphene. To describe the band gap opening in graphene, we propose a tight-binding model Hamiltonian taking into account of third-nearest-neighbor electron-hoppings. We introduce repulsive Coulomb interaction at two sub-lattices of graphene. Further, we consider phonon coupling to the electron densities centered at two sub-lattices in the presence of phonon vibration with a single frequency. For high frequency phonons, the present interaction represents the Holstein interaction. Applying Lang–Firsov canonical transformation in the high phonon-frequency limit, we calculate the modified Coulomb interaction and the effective hopping integral which are functions of electron–phonon coupling, phonon-frequency and nearest-neighbor electron-hopping integral. The electron Green’s functions are calculated by Zubarevs technique. The electron occupancies at two sub-lattices for up and down spins are calculated and computed self-consistently. Finally, we calculate the modulated substrate induced gap of graphene-on-substrate, which is computed numerically for $100\times 100$ grid points for electron momentum. We have studied the interplay of Coulomb interaction, electron–phonon interaction in high phonon-frequency limit. The maximum band gap achieved due to the interplay is nearly 67% more than the substrate induced gap. To achieve this condition, one requires low Coulomb energy for low frequency phonon, while one needs high Coulomb interaction and high electron–phonon interaction of a given lattice vibration frequency. For given electron–phonon interaction and phonon-frequency, the modified gap is enhanced throughout the temperature range with increase of Coulomb interaction.

Graded finite elements (GFEs) provide a promising way for simulating functionally graded materials. Nevertheless, the existing GFE method takes the conventional isoparametric transform functions as a unified representation for the material non-homogeneity in each element regardless of the practical global distribution forms of material properties. This inevitably leads to a certain difference between the local formulation of material property variation in the elements and the corresponding global gradation patterns. In order to eliminate this difference, an improved GFE algorithm is proposed in the present article. The property distribution in the element is formulated by substituting the isoparametric transform of the coordinates directly into the corresponding global gradation functions. Therefore, the local property distribution is always consistent with the global one. Both the improved six-node triangular elements (T6) and eight-node quadrilateral elements (Q8) are developed for non-homogeneous elastic, piezoelectric and magneto-electro-elastic materials, respectively. Exact solutions in three special cases are presented to make comparison with the numerical results, and the accuracy of the proposed algorithm is verified. It is demonstrated that the improved GFE is an effective method for the numerical simulation of functionally graded materials.

We studied the geometric effects on the charge transfer through the anthracenedithiol (ADT) molecular junction using density functional theory combined with the non-equilibrium Green’s function approach. Two major geometric aspects, bond length and bond angle, were moderated to optimize the electrical conduction. From the results established in this paper, we found that the electrical conduction can be tuned from 0.2 $G_0$ to 0.9 $G_0$ by varying the Au–S bond length, whereas the moderation of bonding angle assayed a minor change from 0.37 $G_0$ to 0.47 $G_0$. We attributed this escalating zero bias conductance to the increasing charge on the terminal sulfur atom of the ADT molecule, which increased the energy of the HOMO orbital towards Fermi level and exhibited a semi-metallic behaviour. Therefore, geometry plays a critical role in deciding the charge transport through the metal/molecule interface.

Wavelet analysis is a recently developed mathematical tool for many problems. One of its main attractive features is the ability to accurately represent general functions with small number of adaptively chosen wavelet coefficients. In this paper, the Legendre wavelet collocation method (LWCM) for the numerical solution of differential equations is presented. The proposed method gives better results than the existing ones. Some of the illustrative examples are included to observe the performance of the proposed scheme.

The two-dimensional space fractional dispersion equation (SFDE) is obtained from the standard dispersion equation by replacing the two second-order space derivatives by the Riemann–Liouville fractional derivatives. A numerical analysis of the two-dimensional SFDE is presented based on the reproducing kernel particle method (RKPM). The final algebraic equation system is obtained by employing Galerkin weak form and functional minimization procedure. The Riemann–Liouville operator is discretized by the shifted Grünwald formula. The fully-discrete approximation schemes for SFDE are established using center difference method and RKPM and the shifted Grünwald formula. Numerical simulations for SFDE with known exact solution were presented in the format of the tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error estimate of RKPM for SFDE has been analyzed, which shows that this method has reasonable convergence rates in spatial and temporal discretizations.

In this paper, a generalized wavelet collocation operational matrix method based on Haar wavelets is proposed to solve fractional relaxation–oscillation equation arising in fluid mechanics. Contrary to wavelet operational methods accessible in the literature, we derive an explicit form for the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

The effect of doping on the electron transport of molecular junctions is analyzed in this paper. The doped fullerene molecules are stringed to two semi-infinite gold electrodes and analyzed at equilibrium and nonequilibrium conditions of these device configurations. The contemplation is done using nonequilibrium Green’s function (NEGF)-density functional theory (DFT) to evaluate its density of states (DOS), transmission coefficient, molecular orbitals, electron density, charge transfer, current, and conductance. We conclude from the elucidated results that Au–C${}_{16}$Li₄–Au and Au–C${}_{16}$Ne₄–Au devices behave as an ordinary p–n junction diode and a Zener diode, respectively. Moreover, these doped fullerene molecules do not lose their metallic nature when sandwiched between the pair of gold electrodes.