This study investigates the flow of a magnetohydrodynamic (MHD) Maxwell fluid over a stretching sheet using a Darcy-Forchheimer (DF) model. We employ numerical analysis with a copper (Cu) nanofluid suspended in water, considering Cattaneo–Christov heat flow, viscous dissipation, and joule heating. Nonlinear ordinary differential equations (ODEs) are solved using the bvp4c method in Matlab and we examine the normalized shear stress, temperature profile, and heat flux rate. Our findings reveal insights for practical applications, showing how parameters such as the relaxation Prandtl number, magnetic parameter, Eckert number parameter, and radiation parameter impact system behaviour.

In the image processing, noise is referred to as the visual distortion. This undesirable by-product may be captured in an image due to unpreventable assorted reasons. The interference of natural phenomena and technical problem, such as small sensor size, long exposure time, low ISO, shadow noise etc., can pollute image. The presence of noise images affects image processing outputs that include segmentation. Segmentation for noisy images is the major concern. To tackle this issue, we propose a modernistic model that is able neutralize the negative effects of outlier using the characteristic of kernel function by different approaches such as linear approach and quadratic approach for global segmentation. Moreover the weight function is used for local segmentation of noisy images. Comparing with classical models, the proposed technique shows robust performance. In comparison with the well-known models such as Chan-Vese (CV) model, Yongfei Wu and Chuanjiang He (Wu-He) model and Chunming Li (Li) model we conclude that performance of our new model is much better.

Intensity inhomogeneity poses a significant obstacle in the process of image segmentation, particularly when employing region-based level set methodologies. This challenge becomes particularly pronounced when dealing with images that exhibit varying intensity values between the background and foreground objects. To mitigate this issue, a novel approach has been introduced, which leverages both global and local statistical information to enhance the accuracy of segmentation outcomes. The proposed model comprises three key components: a regularisation term, a local term, and a global term. The regularisation term facilitates the attainment of smooth and coherent segmented regions, while the local term detects areas of intensity variation by utilizing location-specific statistical data. The global term takes into account the overall intensity characteristics of the image, enabling the differentiation of items with dissimilar intensities. The effectiveness of the proposed model has been meticulously evaluated through comprehensive experimentation, which has demonstrated superior accuracy and efficacy when compared to existing models. These results serve to affirm the efficacy of the methodology and underscore its capacity to effectively address the challenges arising from non-uniform intensity distribution in image segmentation tasks.