# Thermal Penetration Depth discrepancy

I've been working on a project that involves thermoacoustics, and one of the commonly-used values in this field is know as the thermal penetration depth. It is calculated as follows:

$$\delta_k = \sqrt{2K / (C_p 2 \pi f \rho)}$$

where $K$ is the thermal conductivity of the fluid in question (helium) $C_p$ is the isobaric specific heat of the fluid $f$ is the frequency of vibration $\rho$ is the density of the fluid

For my project, I've been using this document as a reference guide

In it, the given $\delta_k$ is 0.1 millimeters. The given frequency is 400 $Hz$. The fluid is helium at 10 bar.

Based on this information, I found the density of helium (~1.6 $g/mL$), the thermal conductivity of helium (~0.15 $W/mK$), and its isobaric specific heat (5.193 $J/gK$).

However, when I plug these values into the equation, I get delta_k = 0.00379 mm, which is considerably off.

Am I doing something wrong here? Is this widely-cited paper incorrect on such a basic fact?

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A small mistake while substituting helium specific heat is being done. While calculating the delta_k, a consistency in units has to be there. Using cp = 5193 J/kgK would yield the correct result. The paper you've cited is a well known article

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