Predicting the thermal distribution in a convective wavy fin using a novel training physics-informed neural network method.

Fins are widely used in many industrial applications, including heat exchangers. They benefit from a relatively economical design cost, are lightweight, and are quite miniature. Thus, this study investigates the influence of a wavy fin structure subjected to convective effects with internal heat generation. The thermal distribution, considered a steady condition in one dimension, is described by a unique implementation of a physics-informed neural network (PINN) as part of machine-learning intelligent strategies for analyzing heat transfer in a convective wavy fin. This novel research explores the use of PINNs to examine the effect of the nonlinearity of temperature equation and boundary conditions by altering the hyperparameters of the architecture. The non-linear ordinary differential equation (ODE) involved with heat transfer is reduced into a dimensionless form utilizing the non-dimensional variables to simplify the problem. Furthermore, Runge-Kutta Fehlberg's fourth-fifth order (RKF-45) approach is implemented to evaluate the simplified equations numerically. To predict the wavy fin's heat transfer properties, an advanced neural network model is created without using a traditional data-driven approach, the ability to solve ODEs explicitly by incorporating a mean squared error-based loss function. The obtained results divulge that an increase in the thermal conductivity variable upsurges the thermal distribution. In contrast, a decrease in temperature profile is caused due to the augmentation in the convective-conductive variable values.

Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study.

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing the Fractional Euler Method, we were able to simulate the dynamics of the fractional visceral leishmaniasis model, evaluate the stability of the equilibrium point, and devise a treatment strategy for the disease. The endemic and disease-free equilibrium points are studied as symmetrical components of the proposed dynamical model, together with their stabilities. It was shown that the fractional calculus model was more accurate in representing the situation under investigation than the classical framework at α = 0.99 and α = 0.98. We provide justification for the usage of fractional models in mathematical modeling by comparing results to real-world data and finding that the new fractional formalism more accurately mimics reality than did the classical framework. Additional research in the future into the fractional model and the impact of vaccinations and medications is necessary to discover the most effective methods of disease control.

Modified conformable double Laplace-Sumudu approach with applications.

In this study, we combine two novel methods, the conformable double Laplace-Sumudu transform (CDLST) and the modified decomposition technique. We use the new approach called conformable double Laplace-Sumudu modified decomposition (CDLSMD) method, to solve some nonlinear fractional partial differential equations. We present the essential properties of the CDLST and produce new results. Furthermore, five interesting examples are discussed and analyzed to show the efficiency and applicability of the presented method. The results obtained show the strength of the proposed method in solving different types of problems.