The objective of this paper comprises two key aspects: to establish descriptive mathematical models for constant and variable fluid flows over a variable thickness sheet by inducting applied electric and magnetic fields, porosity, radiative heat transfer, and heat generation/absorption, and to seek their solution by constructing a novel numerical method, the Simplified Finite Difference Method (SFDM). We resort to similarity transformations to implicate partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). Optimal results for a pair of ODEs obtained from SFDM are assessed by drawing a comparison with bvp4c and existing literature values. SFDM has been implemented in MATLAB for both constant and variable fluid properties. Tabulated numerical values of the skin friction coefficient and local Nusselt and Sherwood numbers are measured and analyzed against different parameters. The influence of distinct parameters on velocity, temperature, and nanoparticle volume fraction are explained in great detail via diagrams. The skin friction coefficient for variable fluid properties is greater than for constant fluid properties. However, the local Nusselt number is lower for variable fluid properties than with constant fluid properties. Surprisingly, high-precision computational results are achieved from the SFDM.

Marfan syndrome (MS) is a genetic disorder often associated with the development of aortic aneurysms, leading to severe vascular complications. The progression of this condition is intricately linked to hemodynamic factors such as wall shear stress (WSS) and von Mises stress, as abnormal distributions can contribute to thrombus formation, endothelial damage, and the worsening of aneurysmal conditions. In this study, six vascular models were analyzed: four representing diseased aortas with Marfan syndrome aneurysms and two healthy aortic models for comparison. The models were sourced from Vascular Model Repository, and computational fluid dynamics (CFD) simulations were conducted using a Newtonian fluid model and the shear stress transport (SST) k–ω turbulent transitional model to evaluate WSS and von Mises stress. Fluid–structure interaction was employed to incorporate vessel wall interaction, and pulsatile inlet velocity profiles were used to simulate physiological blood flow, capturing time-dependent hemodynamic variations. The results revealed significant differences between healthy and diseased aortic models. In healthy models, WSS was uniformly distributed, with values consistently below 40 Pa, reflecting stable vascular conditions. Conversely, the diseased models exhibited highly non-uniform WSS distributions, with notably lower values in aneurysmal regions, contributing to thrombus formation, with elevated WSS in areas like the carotid and subclavian arteries due to geometric and hemodynamic complexities. The von Mises stress analysis identified regions of heightened rupture risk, particularly on the superior side of case MS1, where both von Mises stress and WSS reached their highest values among all cases. Physics-informed neural networks demonstrated strong agreement with CFD results while significantly reducing computational cost, highlighting their potential for real-time clinical applications. These findings underscore the critical role of hemodynamic factors in aneurysm progression and rupture risk, offering valuable insights for optimizing diagnostic and therapeutic strategies in vascular diseases.

In this paper, we present an innovative mechanism for image restoration problems in which the image is corrupted by a mixture of additive white Gaussian noise (AWGN) and impulse noise (IN). Mixed noise removal is much more challenging problem in contrast to the problems where either only one type of noise model (either Gaussian or impulse) is involved. Several well-known and efficient algorithms exist to effectively remove either Gaussian noise or Impulse noise, independently. However, in practice, noise may occur as a mixture of such noise models. Thus, the existing techniques devised to handle individual types of noise may not perform well. Moreover, the complexity of the problem hinges on the fact that the removal of either type of noise from the given image affects the noise statistics in the residual image. Therefore, a rigorous mechanism is required which not only infers altered noise statistics but also removes the residual noise in an effective manner. In this regard, an innovative approach is introduced to restore the underlying image in three key steps. Firstly, the intensity values, affected by impulsive noise, are identified by analyzing noise statistics with the help of adaptive median filtering. The identified intensity values are then aggregated by exploiting nonlocal data redundancy prior. Thus the first step enables the remaining noise to follow the zero mean Gaussian distribution in the median filtered image. Secondly, we estimate Gaussian noise in the resulting image, which acts as a key parameter in the subsequent singular value thresholding process for rank minimization. Finally, a reduced rank optimization applied to the pre-processed image obtained in the first step. The experimental results indicate that the proposed AMNLRA (Adaptive Median based Non-local Low Rank Approximation) approach can effectively tackle mixed noise complexity as compared to numerous state of the art algorithms.

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter , magnetic parameter , and porosity parameter . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number and Peclet number and decreases with the increasing values of an unsteady parameter .