This investigation explored the many-sided features of mild intensity movement and an incompressible magnetohydrodynamic (MHD) Poiseuille stream in a permeable fine cylinder, focusing on the characteristics of viscous blood. This review investigated the effects of temperature-subordinate thickness and fluctuating strain inclination on blood behavior. These discoveries offer little knowledge of advancing intensity moves and stream qualities in the blood through permeable small frameworks and are urgently needed for applications in biomedical and medical service settings. This review presents an extensive assessment of the overseeing Brinkman equation and energy equation, unraveling the complicated interaction of factors. By utilizing Galerkin’s finite element method, exploration has explored the nuanced connections between boundaries, such as suction/injection, the Darcy number, the consistency boundary, the Prandtl number, and time. Remarkably, the outcomes feature the enormous impact of these elements on the speed and temperature profiles of the blood. The volumetric stream rate was increased, the suction/injection boundary was decreased, and the Prandtl number was increased. Additionally, the Nusselt number increases when the suction/injection boundary and Prandtl number decrease. These findings coincide with the existing information.