Thermal entrance problem for blood flow inside an axisymmetric tube: the classical Graetz problem extended for Quemada’s bio-rheological fluid with axial conduction

Khan, MWS; Ali, N; Beg, OA

Abstract

The heat-conducting nature of blood is critical in the human circulatory system and
features also in important thermal regulation and blood processing systems in biomedicine.
Motivated by these applications, in the present investigation, the classical Graetz problem in
heat transfer is extended to the case of a bio-rheological fluid model. The Quemada biorheological fluid model is selected since it has been shown to be accurate in mimicking
physiological flows (blood) at different shear rates and hematocrits. The two-dimensional
energy equation is tackled via a separation of variables approach for the uniform surface
temperature case. Following the introduction of transformation variables, the ensuing
dimensionless boundary value problem is solved numerically via MATLAB based algorithm
known as Bvp5c (a finite difference code that implements the four-stage Lobatto IIIa
collocation formula). Numerical validation is also presented against two analytical approaches
namely, series solutions and Kummer function techniques. Axial conduction in terms of Péclet
number is also considered. Typical values of Reynolds number and Prandtl number are used to
categorize the vascular regions. The graphical representation of mean temperature, temperature
gradient and Nusselt numbers along with detail discussions are presented for the effects of
Quemada non-Newtonian parameters and Péclet number. The current analysis may also have
potential applications for the development of microfluidic and biofluidic devices particularly
which are used in the diagnosis of disease in addition to blood oxygenation technologies.

Citation

Khan, M., Ali, N., & Beg, O. (in press). Thermal entrance problem for blood flow inside an axisymmetric tube: the classical Graetz problem extended for Quemada’s bio-rheological fluid with axial conduction. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, https://doi.org/10.1177/09544119221086479

• Journal Article Type: Article
• Acceptance Date: Apr 10, 2022
• Online Publication Date: Apr 4, 2022
• Deposit Date: Apr 20, 2022
• Publicly Available Date: Jun 21, 2022
• Journal: Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine
• Print ISSN: 0954-4119
• Electronic ISSN: 2041-3033
• Publisher: SAGE Publications
• DOI: https://doi.org/10.1177/09544119221086479
• Publisher URL: https://doi.org/10.1177/09544119221086479