Asymptotic analysis of the thermomicropolar fluid flow through a thin channel with cooling

Abstract

In this paper, we consider a steady-state flow the thermomicropolar fluid through a thin straight channel. The flow is governed by the prescribed pressure drop between channel's ends. The heat exchange between the fluid inside the channel and the exterior medium is allowed through the upper wall, whereas the lower wall is insulated. Using the asymptotic analysis with respect to the thickness of the channel, we derive a first-order asymptotic solution acknowledging the effects of the fluid's microstructure. A rigorous justification of the proposed effective model is provided by proving the error estimates in suitable norms.

Keywords:

• Thermomicropolar fluid
• cooling condition
• thin channel
• asymptotic model
• rigorous justification

2010 Mathematics Subject Classifications:

• 35C20
• 35Q35
• 76M45

Acknowledgments

The first author of this work has been supported by the National Science Center (NCN) of Poland under project No. DEC-2017/25/B/ST1/00302. The second author of this work has been supported by the Croatia Science Foundation under the project Multiscale problems in fluid mechanics – MultiFM (IP-2019-04-1140). The third author has been supported by the Croatian Science Foundation under the project Asymptotic analysis of boundary value problems in continuum mechanics – AsAn (IP-2018-01-2735). We thank the Reviewer for his/her valuable remarks and comments that helped to correct and improve our paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author of this work has been supported by the National Science Center (NCN) of Poland under project No. DEC-2017/25/B/ST1/00302. The second author of this work has been supported by the Croatia Science Foundation under the project Multiscale problems in fluid mechanics – MultiFM (IP-2019-04-1140). The third author has been supported by the Croatian Science Foundation under the project Asymptotic analysis of boundary value problems in continuum mechanics – AsAn (IP-2018-01-2735).