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Thermal Gradient-Mediated Instability in a Bilayer Flow Over a Porous Medium

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Fluid Mechanics and Fluid Power, Volume 2 (FMFP 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

In the current work, we explore the noticeable features of thermal gradient-triggered instability of a bilayer placed over a porous media. A comprehensive Orr-Sommerfield (OS) analysis is used to inspect the instability of a bilayer flow narrowed between a Darcy-Brinkman porous medium and a rigid plate. The OS equations are then numerically solved by implying suitable boundary conditions to get the length and time scales of instability aroused in the system. The parametric analysis gives the critical conditions at which the system becomes unstable and causes one of the layers in the bilayer to rupture, leading to the formation of micro-scale shapes. The predicted length scale at which the interface is highly unstable is in good agreement with the existing works. Interestingly, the length scale of the instability after film ruptures is identical to the most catastrophic wavelength of the system and with the available literature.

Saurabh Dubey and Vinod B. Vanarse: Equal contribution by both the authors.

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Abbreviations

μr:

Viscosity ratio

ρr:

Density ratio

kth:

Thermal conductivity

ψ:

Stream function

ξ:

Stress jump coefficient

γ:

Surface tension

b:

Porosity

κ:

Permeability

ω:

Growth coefficient

k:

Wavenumber

ωm:

Maximum growth coefficient

Pr:

Prandtl number for polymer film

Preff:

Prandtl number for porous layer

Da:

Darcy number

λr:

Thermal conductivity ratio top to bottom layer

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Acknowledgements

We are grateful for the support from the Department of Chemical Engineering and Centre for Nanotechnology, IIT Guwahati. V.B.V. and S.D. thank Dr. Siddharth Thakur for their insightful suggestions. S. D. and V.B.V. are grateful to MHRD, the Government of India, for financial support.

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Authors and Affiliations

  1. Centre for Nanotechnology, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Saurabh Dubey & Dipankar Bandyopadhyay

  2. Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Vinod B. Vanarse, Prathu Raja Parmar, Omkar S. Deshmukh & Dipankar Bandyopadhyay

  3. Jyoti and Bhupat Mehta School of Health Sciences and Technology, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Dipankar Bandyopadhyay

Authors
  1. Saurabh Dubey
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  2. Vinod B. Vanarse
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  3. Prathu Raja Parmar
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  4. Omkar S. Deshmukh
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  5. Dipankar Bandyopadhyay
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Corresponding author

Correspondence to Dipankar Bandyopadhyay .

Editor information

Editors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Krishna Mohan Singh

  2. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sushanta Dutta

  3. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sudhakar Subudhi

  4. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Nikhil Kumar Singh

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Dubey, S., Vanarse, V.B., Parmar, P.R., Deshmukh, O.S., Bandyopadhyay, D. (2024). Thermal Gradient-Mediated Instability in a Bilayer Flow Over a Porous Medium. In: Singh, K.M., Dutta, S., Subudhi, S., Singh, N.K. (eds) Fluid Mechanics and Fluid Power, Volume 2. FMFP 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-5752-1_13

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  • DOI: https://doi.org/10.1007/978-981-99-5752-1_13

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5751-4

  • Online ISBN: 978-981-99-5752-1

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