Mathematical Modelling of Blood Flow and Heat Transfer in the Human Cardiovascular System

Abstract

This work investigates how variations in blood viscosity and thermal conductivity—when influenced by a porous environment and an externally applied magnetic field—affect blood flow and heat distribution within the human circulatory system. The fluid is modelled as flowing through a porous structure, with viscosity assumed to change in relation to hematocrit concentration. Additionally, the thermal conductivity of the blood is treated as temperature-dependent to simulate physiological realism.The unsteady-state governing equations for heat and momentum transfer, considering the flow of an incompressible, laminar, and Newtonian fluid, are addressed using the Generalized Polynomial Approximation Method (GPAM). Solutions were obtained for both velocity and temperature distributions across blood and tissue regions. All mathematical computations were carried out using MAPLE 17, a symbolic computation platform, and the results are displayed through graphical illustrations.The analysis reveals that changes in hematocrit levels, magnetic field strength (quantified by the Hartmann number), the medium's permeability, Reynolds number, and imposed pressure gradients all significantly influence the velocity field of blood. Moreover, temperature responses in both blood and surrounding tissues are heavily affected by variations in Peclet number, pressure gradients, and perfusion mass flow rates.Specifically, it was found that flow velocity reached its peak when the condition was satisfied. Similarly, the maximum temperature in the blood was observed under the conditions and . A key finding indicates that as the Hartmann number increases (from an unspecified lower to upper bound), the flow velocity approaches zero , which signifies that the Lorentz force becomes increasingly dominant. This growing electromagnetic resistance effectively slows down the movement of blood, suggesting that magnetic field intensity can serve as a mechanism for regulating arterial blood flow.Additionally, the study found that at a specific temperature ratio , blood temperature was at its lowest, whereas a higher temperature ratio led to a pronounced increase in blood temperature. This observation supports the potential use of temperature-dependent thermal conductivity to amplify heat delivery—an advantage in targeted treatments such as cancer hyperthermia.In conclusion, the study demonstrates that external magnetic control and thermally sensitive blood properties can play a pivotal role in managing blood flow dynamics and enhancing therapeutic heat transfer within biological tissues