What is meant by thermal penetration depth? What is meant by thermal penetration depth? I am doing a project on Thermoacoustics. while researching I came across about thermal penetration depth.I searched over the net but i didn't get a clear idea so please explain me about this and also give me an insight about what are the other applications of this.  
 A: As you understand from the term itself it has to do with the penetration of heat into a material.
Suppose you have a sufficiently thick material (size $D$) of uniform temperature ($T_0$), where you apply a constant (different) temperature ($T_1$) at one side. Eventually, your whole material will be at this new temperature $T_1$. But before this happens, that is, as long as the temperature of the other side of the block is still $T_0$, we can talk about penetration.
The penetration depth is the depth to which the temperature has significantly changed, often, this is approximated with
$$\sqrt{\pi a t}$$
where $a$ is the thermal diffusivity coefficient, and $t$ is time.
In this context, also the Fourier number is relevant, as it relates the penetration depth with the domain length scale, i.e.
$$ Fo=\frac{a t}{D^2}$$
For penetration theory to be applicable (initial stage), $Fo<1$.
A: In an unbound fluid it is sufficient to presume the adiabatic behavior (i.e. no heat transfer and "conservation of enthropy"). BUT! When we examine the flow in the nearby of walls and other real solid boundaries there is a significant energy dissipation due to viscosity, friction etc. etc. connected with thermoacoustical effects. E.g. if we have a duct wide enough, than along its axes the field will be (almost) adiabatic but the boundary layer (neighborhood of walls) will be more complicated. The penetration depth then tells what is the distance from a wall enough to presume the flow to be adiabatic.
A: I think the answer from Bernard seems correct, but I seem to remember a formula for penetration velocity.  Pira appears to confuse boundary layer thickness with penetration depth, which to my memory is only for solid heat conduction.
Good luck, Tom in Lyons, CO
