Mathematical Technique for Predicting Thermal Exchange Dynamics in the Circulatory System

Abstract

Mathematical methods were employed to study and forecast heat transfer patterns that occur in the human circulatory system. The research establishes a blood flow model which treats blood as a Newtonian fluid that flows through a porous medium while its viscosity changes with hematocrit levels. The research assumes that thermal conductivity shows temperature-dependent behavior. The study uses the parameter expansion method together with the eigenfunction technique to solve the governing equations which describe the fluid flow and thermal interactions. The research presents analytical solutions which explain both blood flow velocity distribution and temperature distribution throughout blood and adjacent tissue. The research uses Computer Symbolic Algebra system MAPLE 17 as its computational tool and displays the results through graphical representations which help users understand the data. The study demonstrates that velocity profiles depend on multiple factors which include hematocrit level magnetic field strength permeability Reynolds number and pressure gradient. Temperature changes in tissue and blood result from three key elements which include Peclet number pressure gradient and perfusion rate. The results show that the flow velocity achieves its maximum value at   ( , ) 3.1 t = when  = 0 while blood temperature attained maximum values when  = 0 andt = 0.5. The research revealed that the blood flow velocity tends to zero (  ( , 0 t) → ) as the Hartmann number varies from 0 to 4.0 . This implies that the strength of Lorentz force produced become stronger with an increase in Hartmann number that leads to retardation on the blood’s motion and this indicates that to ensure the flow along the artery region is properly controlled, a certain strength of magnetic intensity is required. The research also revealed that at a temperature ratio, ( = 0) the blood temperature was minimal while the temperature ratio (  = − = 1.0, 1.0) resulted in a maximal high blood temperature.