The popularity of the internet, smartphones, and social networks has contributed to the proliferation of misleading information like fake news and fake reviews on news blogs, online newspapers, and e-commerce applications. Fake news has a worldwide impact and potential to change political scenarios, deceive people into increasing product sales, defaming politicians or celebrities, and misguiding visitors to stop visiting a place or country. Therefore, it is vital to find automatic methods to detect fake news online. In several past studies, the focus was the English language, but the resource-poor languages have been completely ignored because of the scarcity of labeled corpus. In this study, we investigate this issue in the Urdu language. Our contribution is threefold. First, we design an annotated corpus of Urdu news articles for the fake news detection tasks. Second, we explore three individual machine learning models to detect fake news. Third, we use five ensemble learning methods to ensemble the base-predictors’ predictions to improve the fake news detection system’s overall performance. Our experiment results on two Urdu news corpora show the superiority of ensemble models over individual machine learning models. Three performance metrics balanced accuracy, the area under the curve, and mean absolute error used to find that Ensemble Selection and Vote models outperform the other machine learning and ensemble learning models.

In this article, we demonstrate the closed formulas for atom-bond connectivity index, geometric arithmetic index, first K Banhatti index, second K Banhatti index, first K hyper Banhatti index, second K hyper Banhatti index, modified first K Banhatti index, modified second K Banhatti index and harmonic K Banhatti index via M-polynomial. We recover these topological indices for H-Naphtalenic nanotube.

Nanofluids and nanotechnology are very important in enhancing heat transfer due to the thermal conductivity of their nanoparticles, which play a vital role in heat transfer applications. Researchers have used cavities filled with nanofluids for two decades to increase the heat-transfer rate. This review also highlights a variety of theoretical and experimentally measured cavities by exploring the following parameters: the significance of cavities in nanofluids, the effects of nanoparticle concentration and nanoparticle material, the influence of the inclination angle of cavities, heater and cooler effects, and magnetic field effects in cavities. The different shapes of the cavities have several advantages in multiple applications, e.g., L-shaped cavities used in the cooling systems of nuclear and chemical reactors and electronic components. Open cavities such as ellipsoidal, triangular, trapezoidal, and hexagonal are applied in electronic equipment cooling, building heating and cooling, and automotive applications. Appropriate cavity design conserves energy and produces attractive heat-transfer rates. Circular microchannel heat exchangers perform best. Despite the high performance of circular cavities in micro heat exchangers, square cavities have more applications. The use of nanofluids has been found to improve thermal performance in all the cavities studied. According to the experimental data, nanofluid use has been proven to be a dependable solution for enhancing thermal efficiency. To improve performance, it is suggested that research focus on different shapes of nanoparticles less than 10 nm with the same design of the cavities in microchannel heat exchangers and solar collectors.

The rapid changes in nanotechnology over the last ten years have given scientists and engineers a lot of new things to study. The nanofluid constitutes one of the most significant advantages that has come out of all these improvements. Nanofluids, colloid suspensions of metallic and nonmetallic nanoparticles in common base fluids, are known for their astonishing ability to transfer heat. Previous research has focused on developing mathematical models and using varied geometries in nanofluids to boost heat transfer rates. However, an accurate mathematical model is another important factor that must be considered because it dramatically affects how heat flows. As a result, before using nanofluids for real-world heat transfer applications, a mathematical model should be used. This article provides a brief overview of the Tiwari and Das nanofluid models. Moreover, the effects of different geometries, nanoparticles, and their physical properties, such as viscosity, thermal conductivity, and heat capacity, as well as the role of cavities in entropy generation, are studied. The review also discusses the correlations used to predict nanofluids’ thermophysical properties. The main goal of this review was to look at the different shapes used in convective heat transfer in more detail. It is observed that aluminium and copper nanoparticles provide better heat transfer rates in the cavity using the Tiwari and the Das nanofluid model. When compared to the base fluid, the Al₂O₃/water nanofluid’s performance is improved by 6.09%. The inclination angle of the cavity as well as the periodic thermal boundary conditions can be used to effectively manage the parameters for heat and fluid flow inside the cavity.

Chemical graph theory is a branch of mathematical chemistry which has an important outcome on the development of the chemical sciences. A chemical graph is a graph which is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with M-polynomials is a new idea and the M-polynomial of different molecular structures supports us to calculate many topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and supports to understand its physical features, chemical reactivates and boiling activities. In this paper, we compute M-polynomial and topological indices of tadpole graph, then we recover numerous topological indices using the M-polynomial.