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Velocity measurement on a heated vertical wall under a transverse magnetic field using ultrasonic doppler velocimetry

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Abstract

The velocity boundary layer profile for an electrically conducting liquid over a heated vertical flat plate is measured using Ultrasonic Doppler Velocimetry (UDV) technique under a transverse magnetic field. A strong neodymium permanent magnet (of strength 0.35 Tesla on the surface) is kept on the rear side of the heated wall to produce a transverse magnetic field. The liquid used is the 5% and 10% (by weight) aqueous solutions of table salt. The velocity profile is measured at a fixed position of the plate for varying temperature differences \((\Delta T)\) (\(5, \;10, \;15\; ^\circ {\text{C}}\)) and at different Hartmann numbers (\(Ha\)) (0, 0.086, 0.75, and 0.93) under quasi-static heating condition. In this experimental study, we also demonstrate how to measure the velocity on a plane transverse to the wall by moving the UDV probe. Due to relatively low Hartmann numbers, the effect of Lorentz force in comparison with buoyancy is small; nevertheless, a cumulative volumetric force stretches the velocity boundary layer thickness under the applied external magnetic field. Our technique may be used with other conducting liquids such as liquid metals where the Ha is expected to be much larger.

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Abbreviations

F L :

Lorentz force (N)

Ha :

Hartmann number

Ra :

Rayleigh number

L :

Characteristic length (m)

LHP :

Liter per hour (l/h)

TBL :

Thermal boundary layer

UDV :

Ultrasound doppler velocimetry

VBL :

Velocity boundary layer

B :

Magnetic field (T)

J :

Induced current (A/m2)

u :

Velocity (m/s)

α:

Thermal diffusivity (m2 s− 1)

δ:

Velocity boundary layer thickness (m)

ϵ:

Uncertainty in the measurement

ν:

Kinematic viscosity (m2 s−1)

ρ :

Density of fluids (kg/m3)

σ :

Electrical conductivity (S/m)

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Acknowledgements

The authors thank the Department of Mechanical Engineering, Indian Institute of Technology Bombay (IITB) for letting us use the UDV facility. We also thank IRCC, IITB and Science and Engineering Research Board (SERB), Govt. of India (SRG/2020/001057) for the financial support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Ravi Kant, Avishek Ranjan & Atul Srivastava

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  1. Ravi Kant
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  2. Avishek Ranjan
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  3. Atul Srivastava
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Correspondence to Ravi Kant.

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Kant, R., Ranjan, A. & Srivastava, A. Velocity measurement on a heated vertical wall under a transverse magnetic field using ultrasonic doppler velocimetry. Sādhanā 49, 88 (2024). https://doi.org/10.1007/s12046-023-02389-5

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