The study of blood flow through arteries has been a significant area of research in biomedical engineering, physics, and applied mathematics. Understanding the dynamics of blood flow is essential for diagnosing and treating various cardiovascular diseases. Recently, there has been a growing interest in computational studies of mathematical models that describe blood flow, especially in the presence of nanoparticles and heat transfer through porous arteries [1,2]. Such studies can provide insights into the behavior of blood as it interacts with artificial nanoparticles, which are increasingly used in medical applications like drug delivery and imaging [3,4].  In the human circulatory system, blood flow through arteries is influenced by various factors, including blood viscosity, pressure, and temperature. The incorporation of nanoparticles-tiny particles typically smaller than 100 nanometers into the bloodstream can alter the physical properties of blood, particularly in microcirculatory systems [5]. Nanoparticles are often used for targeted drug delivery or as agents for improving the efficacy of diagnostic techniques [6]. The heat transfer mechanism within arteries, particularly in conditions like hyperthermia or thermotherapy, further complicates the blood flow dynamics by introducing thermal effects, which can influence particle behavior and enhance therapeutic outcomes [7].  Porous media models are crucial in simulating complex biological environments, as they can mimic the intricate structures of blood vessel walls and tissues, which are not entirely rigid but allow some flow of fluids through the porous spaces [8]. Therefore, studying the blood flow and nanoparticle transport in these porous arteries, combined with heat transfer, is critical for improving clinical applications like localized drug delivery systems, cancer treatment, and enhanced imaging techniques [2, 6]. This research is essential because it contributes to a deeper understanding of how nanoparticles interact with biological fluids and tissues, improving therapeutic interventions and the design of medical devices [1,3]. Additionally, computational studies provide a cost-effective way to simulate and predict real-life scenarios in the human body, reducing the need for expensive or invasive experiments [4,9]. The mathematical modeling of blood flow with nanoparticles and heat transfer in porous arteries can serve as a foundation for the development of more efficient medical treatments and technologies, making it an area of paramount importance in both theoretical and practical applications in medical science and engineering [5,7,9].

Building upon the established studies, it is imperative to mention that this paper aimed at developing a mathematical model that describes blood flow through porous arteries in the presence of nanoparticles and heat transfer. By applying computational and analytical techniques, the study seeks to understand how nanoparticles influence blood flow dynamics, thermal effects, and their interactions with biological tissues. The findings will provide insights into optimizing medical applications such as targeted drug delivery, hyperthermia treatments, and diagnostic imaging, ultimately contributing to the advancement of biomedical engineering and clinical therapies.