This package is no longer supported, please consider using ThinFilmsTools.jl instead.
Simulation of the temperature rise response to the sinusoidal heating excitation through a metallic heater atop a system of thin films multilayer using a matrix formalism. The thermal response is given for a range of frequency which is determined by the electrical current excitation source. We consider a heater placed at the top of the system and a semi-infinite boundary condition on the substrate. For further details see https://arxiv.org/abs/1811.00571.
This package is not yet registered. It can be installed in Julia with the following (see further):
julia> ]
(v1.0) pkg> add https://github.com/lnacquaroli/ThreeOmegaMethod.jlThreeOmegaMethod.jl is compatible with Julia version 1.0 or later, and uses QuadGK.jl to perform numerical integration.
See the examples folder to start using the script.
To call the main program we can do as follow:
ΔT, int_error = ThreeOmegaMatrix(layers, hgeometry, source, thresistances, int_limit=1.0e6)Where ThreeOmegaMatrix is the main function exported from the module ThreeOmegaMethod.jl.
layers::Array{Layer} is an array that contains the sequence of layers that compose the thin film multilayer system. Each layer is constructed using the Layer <: LayerInformation subtype exported from the main module using the required information. For instance, we can construct different layers as follow calling layer1 = Layer(ky, kxy, d, ρC), where the parameters required to calculate the thermal response are explained below.
heater = Layer(ky_1, kxy_1, d_1, ρC_1)
substrate = Layer(ky_2, kxy_2, d_2, ρC_2)
specimen = Layer(ky_3, kxy_3, d_3, ρC_3)
layers = [heater specimen substrate]ky::Float64 is the thermal conductivity of the layer, in units of Watt/meter/Kelvin.
kxy::Float64 is the ratio between the in-plane to cross-plane thermal conductivities. It is a dimenionless number. This is the parameter that accounts for the 2D heat conduction.
d::Float64 defines the physical thickness of the layer in units of meter.
ρC::Float64 is the product of the material density (kg per cubic meter) times the heat capacity (calories per degree).
This type contains the information about the geometry of the heater use to excite the films. The calling structure is hgeometry = HeaterGeometry(b, l, ρh), where HeaterGeometry <: HeaterInformation. The method considers a planar geometry of the heater with defined width and length. The parameters are defined below.
b::Float64 is the heater half-width, in units of meter. The half-width appears naturally in the theory so it is a characteristic parameter instead of the width itself.
l::Float64 is the length of the heater, in units of meter. The length is defined, independently of the number of probes in the system, the distance between the pads used to measure the voltage drop, not those to drive the electrical current.
ρh::Float64 is the product of the heater density (kg per cubic meter) times the heat capacity (calories per degree).
This type wraps the electrical source power and the linear frequency range of the simulation. source = Source(p, f), where Source <: HeaterSource. The parameters are defined below.
p::Float64 is the peak power applied to the heater, in units of Watt. The power is defined as the product of the resistance at the temperature the measurements are taken times the squared electrical current that flows through the pads.
f is the frequency range in units of Hertz. The recommended way to define this parameters is in log-space. An easy way to do this is f = exp10.(LinRange(f_initial, f_final, f_length)). Notice that if you set the range in linear-space and then take a log-plot, results in a less convenient look of the simulation.
The method implemented here allows to input the resistances given by the interfaces between layers. thresistances::Array{Float64,1} sets the resistance for each interface in units of Kelvin*meter/Watt. The parameter is an Array where lastindex(thresistances) == size(layers,2) - 1.
int_limit::Float64 sets the upper integration limit for the numerical integration with QuadGK package. This is an optional parameter with default value of 1.0e6.
ΔT::Array{ComplexF64,1} is the temperature rise response calculated in the 2-omega mode.
int_error::Array{Float64,1} is the error returned from QuadGK process at each frequency.
If you have ideas and suggestions to improve ThreeOmegaMethod.jl in Julia, PRs and issues are welcomed.