Sample Solutions

This page lists all sample solutions, gives the governing equations they solve, shows which unknowns you need to provide initial guesses for, and lays out all the parameters they need to be initialized. Some solutions have "log variants" that only allow the logs of the unknowns to be varied during the fitting process. You can use these variants by simply using the alternative name and replacing the unknown fields with their alternatives. For more details on how to use these sample solutions, please consult the Solver section of the Basic Usage page.

Lopez-Baeza's Solution for Short Samples

Name

'lopez-baeza'

Governing Equations

Symbol	Meaning
	time
	distance from heat source
	temperature
	length
	cross-sectional area
	perimeter
	angular frequency
	thermal conductivity
	thermal diffusivity
	convective heat transfer coefficient

Unknowns

thermal_diffusivity_m2__s : float

• The rate of heat transfer inside the material sample.

convective_heat_transfer_coefficient_W__m2_K : float

• The rate of heat transfer between the material sample and the fluid surrounding it.

Parameters

r_meters : float

• Effective radius of the material sample. Use geometric radius for circular cross sections and ab/(a + b) for rectangular cross sections of side lengths a and b.

length_meters : float

• Total length of the material sample along the direction of heat flow.

Log Variant

Name

'log_lopez-baeza'

Unknowns

thermal_diffusivity_log10_m2__s : float

• The order of magnitude of the thermal diffusivity.

convective_heat_transfer_coefficient_log10_W__m2_K : float

• The order of magnitude of the convective heat transfer coefficient.

Parameters

(Same as original)

Paper Referenced

Lopez-Baeza, Ernesto & Rubia, J & Goldsmid, Hiroshi. (1987). Angstrom's thermal diffusivity method for short samples. Journal of Physics D Applied Physics. 20. 1156. 10.1088/0022-3727/20/9/011.

Kil's 1D Solution for Cylindrical Coordinates

Name

'kil'

Governing Equations

Symbol	Meaning
	time
	distance from heat source
	temperature
	inner radius
	outer radius
	sample thickness
	angular frequency
	thermal conductivity
	thermal diffusivity
	convective heat transfer coefficient

Unknowns

thermal_diffusivity_m2__s : float

• The rate of heat transfer inside the material sample.

convective_heat_transfer_coefficient_W__m2_K : float

• The rate of heat transfer between the material sample and the fluid surrounding it.

Parameters

sample_thickness_meters : float

• Thickness of the material sample.

heating_source_radius_meters : float

• Minimum radius of steady sinusoidal temperature oscillations.

outer_boundary_radius_meters : float

• Outer radius at which semi-infinite assumption holds.

Log Variant

Name

'log_kil'

Unknowns

thermal_diffusivity_log10_m2__s : float

• The order of magnitude of the thermal diffusivity.

convective_heat_transfer_coefficient_log10_W__m2_K : float

• The order of magnitude of the convective heat transfer coefficient.

Parameters

(Same as original)