https://doi.org/10.1140/epjp/s13360-022-02671-1
Letter to the Editor
A note on classical Graetz problem based on Cattaneo–Christov heat flux model
Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan
Received:
15
June
2021
Accepted:
31
March
2022
Published online:
9
April
2022
The classical Graetz problem of fluid concerning with the thermally developing temperature profile inside a channel is elaborated here under the influence of the relaxation time of heat flux via the use of Cattaneo–Christov heat flux law. Assuming a uniform velocity (slug flow) across the channel, the energy equation for the said problem is modelled by taking into account the effects of axial conduction. The developed energy equation is analytically solved for uniform wall temperature boundary condition by using an efficient integral transform technique. The graphical representations of mean temperature and Nusselt number (local and mean) are presented and elaborated on in detail. This study is the first of its kind and would serve as a baseline for further research in the realm of thermal entry flows based on the Cattaneo–Christov heat flux model. The analysis reveals that both mean temperature and Nusselt numbers escalate in the presence of thermal relaxation time and axial conduction. As a consequence of that an enhancement in the thermal entrance length is observed.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
