Mathematical modelling and analysis of thermoregulation effects on blood viscosity under magnetic effects and thermal radiation in a permeable stretching capillary.

The current study deals with the mathematical modelling and analysis of the effects of thermoregulation on blood viscosity under magnetic and thermal radiation effects on a permeable, stretching blood capillary. The model comprises the governing equations of the resulting boundary layer problem, which is a set of nonlinear partial differential equations, and this is transformed into a coupled system of nonlinear differential equations using similarity transformation. The numerical solution of the problem is attained by the fourth-order Runge Kutta method with the shooting method. The current work examines the velocity and temperature profile of blood flow with the impact of varying temperature-dependent blood viscosity, involving the variation of several physical parameters such as magnetic field, radiation parameter, permeability parameter, Prandtl number, and surface temperature, as well as their physical interpretation. During certain therapies, the thermoregulation mechanism in humans causes a change in blood flow behaviour. Also, blood flow must be regulated during pathological conditions with the help of radiation, heat, or magnetic effects. It is found that, due to the varying viscosity parameter, the magnetic field effect inhibits heat transport in the body. It has also been found that increasing the permeability parameter enhances mass and heat transfer. The results of this paper could be important in analysing and regulating blood flow and body temperature during hypothermia and hyperthermia therapies.