An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field
Abstract
:1. Introduction
- To identify the laminar-turbulent transition of the fluid flow in a shallow geometry in the thermo-magnetic convection
- The performing of a traditional visualization of the flow field in the experimental part—to try to visualize the flow changes performing the wavelet transform—a technique not applied to thermo-magnetic convection before
- To provide quantitative information about characteristic frequencies from fast Fourier transform of the temperature and velocity signals
- To deliver a benchmark case for further analysis in the absence of energy spectrum analyses for the experimental and numerical thermo-magnetic convection process in the transitional state
- To describe the evolution and behavior of thermal plumes when under the influence of imposed, strong magnetic gradients.
2. Theoretical Outline
3. Experimental Setup
4. Numerical Procedure
4.1. Magnetic Field Calculations
4.2. Nonisothermal Flow Field
5. Analysis Methodology
6. Results
6.1. Temperature Signals
6.2. Velocities
7. Summary
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
a | base dimension of the experimental enclosure (m) |
a | shape parameter in wavelet function (-) |
b0max | magnetic induction in the center of the magnet (T) |
b | location parameter in wavelet function (-) |
Ca,b | wavelet coefficient (-) |
cp | heat capacity (J/kgK) |
d | height (m) |
fg | gravitational force (N/m3) |
fG | gravitational buoyancy force (N/m3) |
fmg | magnetic force (N/m3) |
fMG | magnetic buoyancy force (N/m3) |
Fn | discrete Fourier function (-) |
g | gravitational acceleration (m2/s) |
H | intensity of a magnetic field (A/m) |
k | wave number (-) |
M | magnetization (A/m) |
n n | length of sequence i (-) normal vector to the sphere surface (-) |
Qnet_cond | net conduction heat flux (W) |
Qnet_conv | net convection heat flux (W) |
t | time (s) |
T | temperature (°C) |
T0 | reference temperature (°C) |
Th | temperature at the heated wall (°C) |
Tc | temperature at the cooled wall (°C) |
xi | sequence length (-) |
Imaginary | imaginary part of transformed data (-) |
Real | real part of transformed data (-) |
α | thermal diffusivity (m2/s) |
β | thermal expansion coefficient (1/K) |
λ | thermal conductivity (W/mK) |
µ0 | magnetic permeability of vacuum (H/m) |
µ | dynamic viscosity (kg/ms) |
ν | kinematic viscosity (m2/s) |
ρ | density (kg/m3) |
χm | mass magnetic susceptibility (m3/kg) |
χ | volume magnetic susceptibility (-) |
Nusselt number (-) | |
thermal Rayleigh number (-) | |
magnetic Rayleigh number (-) | |
thermo-magnetic Rayleigh number (-) | |
magnetization number (-) |
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Property | Value | Unit |
---|---|---|
Heat capacity | 2.92 × 103 | J/kgK |
Thermal diffusivity | 9.13 × 10−8 | m2/s |
Thermal expansion coefficient | 1.21 × 10−5 | 1/K |
Dynamic viscosity | 1.30 × 10−2 | kg/ms |
Thermal conductivity | 0.376 | W/mK |
Kinematic viscosity | 9.25 × 10−6 | m2/s |
Density | 1411 | kg/m3 |
Mass magnetic susceptibility | 2.39 × 10−7 | m3/kg |
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Kraszewska, A.; Donizak, J. An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field. Energies 2021, 14, 7972. https://doi.org/10.3390/en14237972
Kraszewska A, Donizak J. An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field. Energies. 2021; 14(23):7972. https://doi.org/10.3390/en14237972
Chicago/Turabian StyleKraszewska, Anna, and Janusz Donizak. 2021. "An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field" Energies 14, no. 23: 7972. https://doi.org/10.3390/en14237972