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 and Beg, OA ORCID: https://orcid.org/0000-0001-5925-6711 2022, '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 .

[img]
Preview
PDF - Accepted Version
Download (846kB) | Preview

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.

Item Type: Article
Schools: Schools > School of Computing, Science and Engineering
Journal or Publication Title: Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine
Publisher: Sage
ISSN: 0954-4119
Depositing User: OA Beg
Date Deposited: 20 Apr 2022 13:54
Last Modified: 17 Aug 2022 09:32
URI: http://usir.salford.ac.uk/id/eprint/63606

Actions (login required)

Edit record (repository staff only) Edit record (repository staff only)

Downloads

Downloads per month over past year