https://doi.org/10.1140/epjp/s13360-026-07943-8
Regular Article
Effects of velocity and thermal slip conditions on the solutions of a convective porous medium flow inside a channel
1
Department of Applied Mathematics, University of Calcutta, 700009, Kolkata, West Bengal, India
2
Department of Mathematics, Adani University, 382421, Ahmedabad, Gujarat, India
3
Department of Mathematics, Indian Institute of Technology Jodhpur, 342037, Jodhpur, Rajasthan, India
a
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Received:
27
March
2026
Accepted:
7
June
2026
Published online:
6
July
2026
Abstract
This investigation focuses on the solution behavior and dynamics of a forced convective porous medium flow through an isothermal flat channel having the combined effects of wall velocity and thermal slips. The walls of the channel are hydrophobic, and the heat flux at the walls is kept constant. The laminar, steady, and symmetric hydrothermal flow is governed by the Brinkman–Forchheimer momentum equation together with the thermal energy equation. The model equations are solved analytically by using the perturbation technique as well as numerically by applying a shooting algorithm combined with the Runge–Kutta method. Both types of solutions are compared to confirm the validity and accuracy. In addition, this study extends and improves the work of Hooman [1] by developing and analyzing a more general and comprehensive model. Importantly, the analytical solutions derived in the present study show a significantly better match with the numerical results compared to Hooman’s analytical solution, highlighting the enhanced accuracy and improved predictive capability of the proposed model. Further, the analysis established the relation of the Nusselt number with the Darcy and Forchheimer numbers. The obtained solutions highlight a significant impact of velocity and temperature slip on the flow dynamics. It is observed that an increase in velocity slip increases the fluid’s velocity near the wall while decreasing it near the centerline. The results also indicate that the thermal slip has a considerable influence on the flow field by altering the heat flux. Consequently, this study extends existing porous channel slip flow analyses by examining the combined influence of velocity and thermal slip. The resulting model provides a more comprehensive representation of the flow and thermal behavior and shows improved agreement between analytical and numerical solutions. The findings enhance the understanding of heat transfer mechanisms and are expected to support future theoretical and experimental developments in engineering applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
