Abstarct: The erosion of rotating industrial devices due to lubrication problems stands as a critical engineering concern, shaping the design imperative for optimal, efficient, and reliable systems capable of functioning across diverse conditions, particularly for bearings. A foundational requirement for accurate bearing design lies in understanding the hydrodynamic behavior of bearings under various conditions. Many engineering applications necessitate the simultaneous support of radial and axial loads, a demand effectively met by tapered bearings. These bearings exhibit the capacity to bear both types of loads concurrently, offering ease of assembly alongside their applicability in diverse scenarios, including high-speed rotating systems. Another pivotal parameter influencing bearing design is the choice of lubricant. Acknowledging the defects and damages arising from inappropriate lubricant selection, the spotlight is increasingly on employing controlled lubricants that exhibit desired behavior according to specific conditions. Recent advancements in lubricant production technology underscore the need for a more scientific and extensive study of the effects of these lubricants on lubricated components. The proliferation of smart fluids and their manifold applications in engineering and medical systems has made their integration into bearings an enticing topic for lubrication science engineers. Smart fluids, such as magnetorheological fluids, enable precise control of lubricant properties, preventing the occurrence of various defects in bearings. The use of magnetorheological fluids proves instrumental in controlling slack, increasing load capacity, and reducing losses in bearings. Hence, this research delves into the phenomenon of lubrication in conical magnetorheological bearings. The Bingham-Papanastasiou constitutive model serves as the constitutive equation for magnetorheological fluids. The study involves the simulation of flow, magnetic field, and heat transfer equations for the given problem in three dimensions, with solutions obtained using the finite element method. Additionally, the research explores the effects of magnetic field strength, eccentricity, heat loss, friction coefficient, and load capacity for various values of bearing geometric quantities. Furthermore, the Reynolds equation for the given problem is analytically derived, considering the magnetorheological fluid as a lubricant. This comprehensive investigation aims to enhance our understanding of the intricate interplay of factors influencing lubrication in conical magnetorheological bearings.