Impact of couple stress and variable viscosity on heat transfer and flow between two parallel plates in conducting field

Geetika Saini; B. N. Hanumagowda; S. V. K. Varma; Jasgurpreet Singh Chohan; Nehad Ali Shah; Yongseok Jeon; Geetika Saini; B. N. Hanumagowda; S. V. K. Varma; Jasgurpreet Singh Chohan; Nehad Ali Shah; Yongseok Jeon

doi:10.3934/math.2023858

AIMS Mathematics

2023, Volume 8, Issue 7: 16773-16789. doi: 10.3934/math.2023858

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Research article Special Issues

Impact of couple stress and variable viscosity on heat transfer and flow between two parallel plates in conducting field

1.
Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru, Karnataka, India
2.
Department of Mechanical Engineering and University Centre for Research & Development, Chandigarh University, Mohali-140413, Punjab
3.
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
4.
Interdisciplinary Major of Maritime AI Convergence, Department of Mechanical Engineering, Korea Maritime & Ocean University, Busan 49112, Korea
^† These authors contributed equally to this work and are co-first authors.

Received: 19 February 2023 Revised: 13 April 2023 Accepted: 23 April 2023 Published: 12 May 2023
MSC : 35Q79, 93C20

This study explores the flow properties of a couple stress fluid with the consideration of variable viscosity and a uniform transverse magnetic field. Under the effect of irreversible heat transfer, a steady fluid flow has taken place between two parallel inclined plates. The fluid flows due to gravity and the constant pressure gradient force. The plates are fixed and isothermal. The governing equations have been solved analytically for velocity and temperature fields. The total rate of heat flow and volume flow across the channel, skin friction, and Nusselt number at both plates are calculated and represent the impacts of relevant parameters through tables and graphs. The findings show that velocity, temperature, and the total rate of heat flow across the channel are enhanced by increasing the couple stress parameter and the viscosity variation parameter, while increasing the values of the Hartmann number reduces them.
- magnetic field,
- couple stress fluid,
- viscous dissipation,
- heat transfer,
- Lorentz force,
- variable viscosity
Citation: Geetika Saini, B. N. Hanumagowda, S. V. K. Varma, Jasgurpreet Singh Chohan, Nehad Ali Shah, Yongseok Jeon. Impact of couple stress and variable viscosity on heat transfer and flow between two parallel plates in conducting field[J]. AIMS Mathematics, 2023, 8(7): 16773-16789. doi: 10.3934/math.2023858

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Abstract

This study explores the flow properties of a couple stress fluid with the consideration of variable viscosity and a uniform transverse magnetic field. Under the effect of irreversible heat transfer, a steady fluid flow has taken place between two parallel inclined plates. The fluid flows due to gravity and the constant pressure gradient force. The plates are fixed and isothermal. The governing equations have been solved analytically for velocity and temperature fields. The total rate of heat flow and volume flow across the channel, skin friction, and Nusselt number at both plates are calculated and represent the impacts of relevant parameters through tables and graphs. The findings show that velocity, temperature, and the total rate of heat flow across the channel are enhanced by increasing the couple stress parameter and the viscosity variation parameter, while increasing the values of the Hartmann number reduces them.

References

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