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Many real-world problems have been modeled via delay differential equations. The pantograph delay differential equation y ′ (t) = a y (t) + b y c t belongs to such a set of delay differential equations. To the authors' knowledge, there are no standard methods to solve the delay differential equations, i.e., unlike the ordinary differential equations, for which numerous and standard methods are well-known. In this paper, the Adomian decomposition method is suggested to analyze the pantograph delay differential equation utilizing two different canonical forms. A power series solution is obtained through the first canonical form, while the second canonical form leads to the exponential function solution. The obtained power series solution coincides with the corresponding ones in the literature for special cases. Moreover, several exact solutions are derived from the present power series solution at a specific restriction of the proportional delay parameter c in terms of the parameters a and b. The exponential function solution is successfully obtained in a closed form and then compared with the available exact solutions (derived from the power series solution). The obtained results reveal that the present analysis is efficient and effective in dealing with pantograph delay differential equations. [ABSTRACT FROM AUTHOR]

The present study numerically simulates a new circular micro heat sink (HS) used to cool electronic equipment (i.e., CPU). The HS contained Al2O3-water nanofluid (NF) at the concentration of 0–1%. The HS had a diameter and a thickness of 7.6 and 0.5 mm, respectively. It included two separate inlets with a 6 mm-diameter middle section subjected to a fixed heat flux of 100 W/cm2. NF flows were employed to cool the HS at the Reynolds numbers of 500–1500. The FVM-based SIMPLE algorithm was developed to obtain the entropy generation, thermal efficiency, and pressure drop. The results revealed that a rise in Re number and NF concentration enhanced Nu and head loss, while reduced the maximum and average temperatures of the electronic device. The best figure of merit (FOM) of the HS was found to be 1.12. A raise in the fluid velocity and NF concentration increased the pumping power but reduced thermal resistance. [ABSTRACT FROM AUTHOR]

This investigation peruses the features of temperature and mass transport of the non-Newtonian third-order liquid over an absorbent convective temperature shrinking sheet. The sheet is packed with silver nanoparticles. The Buongiornos modelling uses a particular non-Newtonian third-order liquid with the Brownian movement and the thermophoresis consequences using the non-linear radiation. The non-linear partial differential equations are changed to the ordinary differential equations with similarity transformations. The changed system of equations is then resolved using the numerical Shooting method and the sixth-order Runge-Kutta's method. The numerically obtained solutions of the velocity profiles, temperature distributions, and concentrations of nanoparticles are discussed graphically. Also, the non-Newtonian parameter reduced the velocity of the liquid, increased the temperature and the concentration profiles throughout the fluid. Ultimately, the qualified systematic analysis is built by the preceding study in restrictive cases and displaingy the best correlation. [ABSTRACT FROM AUTHOR]

In this paper, thermal conductivity prediction of nanofluids is discussed by the RSM and ANN models. The nanofluids contain SiO2 nanoparticles, and their thermal conductivity is measured in the temperature range of 30–60 °C. The effect of SiO2 nanoparticles on thermal conductivity depends on the type of base fluid. For the ethylene glycol (EG) base fluid, SiO2 nanoparticles improve the thermal conductivity by 12%. For glycerol base fluid, thermal conductivity is increased by 6%. The thermal conductivity of both nanofluids depends on temperature and volume fraction so that as the volume fraction and temperature increase, their positive effect on thermal conductivity is enhanced. ANN and RSM models are used to estimate the thermal conductivity ratio of nanofluid to base fluid, i.e., TCR = k nf k bf . Both techniques are well able to predict the amount of TCR for both nanofluids. A cubic function with R 2 = 0.997 and 0.994 is proposed for SiO2-EG and SiO2-G nanofluids, respectively. It is found by trial and error that the neural network with 8 neurons is suitable for both nanofluids. For Ann statistical calculations demonstrate that the R 2 for SiO2-EG nanofluid is 0.995 and for SiO2-G nanofluid is 0.994. The error of both methods is less than 0.3%, which indicates that both methods can well estimate TCR value. [ABSTRACT FROM AUTHOR]

Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwidth device it would seem natural therefore to utilize resonators that span a range of length scales. In this article, we derive a mathematical model to predict the dynamics of a fractal ultrasound transducer; the fractal in this case being the Sierpinski gasket. Expressions for the electrical and mechanical fields that are contained within this structure are expressed in terms of a finite element basis. The propagation of an ultrasonic wave in this transducer is then analysed and used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the driving frequency. Comparing these key performance measures to an equivalent standard (Euclidean) design shows some benefits of these fractal designs. [ABSTRACT FROM AUTHOR]

The COVID-19 is an epidemic that causes respiratory infection. The forecasted data will help the policy makers to take precautionary measures and to control the epidemic spread. The two models were adopted for forecasting the daily newly registered cases of COVID-19 namely 'earlyR' epidemic model and ARIMA model. In earlyR epidemic model, the reported values of serial interval of COVID-19 with gamma distribution have been used to estimate the value of R 0 and 'projections' package is used to obtain epidemic trajectories by fitting the existing COVID-19 India data, serial interval distribution, and obtained R0 value of respective states. The ARIMA model is developed by using the 'auto.arima' function to evaluate the values of (p, d, q) and 'forecast' package is used to predict the new infected cases. The methodology evaluation shows that ARIMA model gives the better accuracy compared to earlyR epidemic model., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Emerging Trends in Materials Science, Technology and Engineering.)