The effect of thermal radiation on the three-dimensional magnetized rotating flow of a hybrid nanofluid has been numerically investigated. Enhancing heat transmission is a contemporary engineering challenge in a range of sectors, including heat exchangers, electronics, chemical and biological reactors, and medical detectors. The main goal of the current study is to investigate the effect of magnetic parameter, solid volume fraction of copper, Eckert number, and radiation parameter on velocity and temperature distributions, and the consequence of solid volume fraction on declined skin friction and heat transfer against suction and a stretching/shrinking surface. A hybrid nanofluid is a contemporary type of nanofluid that is used to increase heat transfer performance. A linear similarity variable is−applied to convert the governing partial differential equations (PDEs) into corresponding ordinary differential equations (ODEs). Using the three-stage Labatto III-A method included in the MATLAB software’s bvp4c solver, the ODE system is solved numerically. In certain ranges of involved parameters, two solutions are received. The temperature profile θη upsurges in both solutions with growing values of EC and Rd. Moreover, the conclusion is that solution duality exists when the suction parameter S≥Sci, while no flow of fluid is possible when S
Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3-Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%-10% copper nanoparticles and 1%-500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f ″ ( 0 ) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport - θ ' ( 0 ) decreases. As heat generation/absorption increases 1%-500%, - θ ' ( 0 ) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S ≥ S c i in assisting flow case, while no fluid flow is possible when S < S c i .
Current breast cancer diagnosis methods often face limitations such as high cost, time consumption, and inter-observer variability. To address these challenges, this research proposes a novel deep learning framework that leverages generative adversarial networks (GANs) for data augmentation and transfer learning to enhance breast cancer classification using convolutional neural networks (CNNs). The framework uses a two-stage augmentation approach. First, a conditional Wasserstein GAN (cWGAN) generates synthetic breast cancer images based on clinical data, enhancing training stability and enabling targeted feature incorporation. Second, traditional augmentation techniques (e.g., rotation, flipping, cropping) are applied to both original and synthetic images. A multi-scale transfer learning technique is also employed, integrating three pre-trained CNNs (DenseNet-201, NasNetMobile, ResNet-101) with a multi-scale feature enrichment scheme, allowing the model to capture features at various scales. The framework was evaluated on the BreakHis dataset, achieving an accuracy of 99.2% for binary classification and 98.5% for multi-class classification, significantly outperforming existing methods. This framework offers a more efficient, cost-effective, and accurate approach for breast cancer diagnosis. Future work will focus on generalizing the framework to clinical datasets and integrating it into diagnostic workflows.