Theoretical analysis of thermal entrance problem for blood flow: An extension of classical Graetz problem for Casson fluid model using generalized orthogonality relations

摘要

An analysis of classical Graetz problem is carried out for the case of fluid obeying the Casson constitutive equation. The considered model physically corresponds to the thermal entry flow of blood in a duct. The governing equation for the premeditated problem is investigated by employing the separation of variables approach in conjunction with the MATLAB built in package bvp4c for the calculation of the eigenvalues and related numerical solution of the eigenvalue problem. The solution is computed for the case of uniform surface temperature boundary condition for both flat and circular geometries. The axial diffusion and viscous dissipation effects on temperature field are also taken into account. The expressions of bulk mean temperature and Nusselt number are presented and discussed in terms of the main effect brought by the yield stress parameter, Peclet number and Brinkman number. It is found that both local and mean Nusselt numbers for blood enhance considerably with the increase of dimensionless plug radius and Brinkman number. In contrast, the thermal entrance length reduces with the rise of Peclet number. The results of present analysis have potential applications in development of nano fluidic, microfluidic and bio-medical devices used in haemodialysis and oxygenation.