# About specific heat Cp and cpTref

**URL:** <https://pyfr.discourse.group/t/about-specific-heat-cp-and-cptref/1099>\
**Category:** Cases\
**Tags:** config, compressible, bcs\
**Created:** [29 May 2024 12:46 UTC](https://pyfr.discourse.group/t/about-specific-heat-cp-and-cptref/1099 "2024-05-29T12:46:19Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![wgbb](https://avatars.discourse-cdn.com/v4/letter/w/6f9a4e/32.png) [@wgbb](https://pyfr.discourse.group/u/wgbb)\
**Post date:** [29 May 2024 12:46 UTC](https://pyfr.discourse.group/t/about-specific-heat-cp-and-cptref/1099/1 "2024-05-29T12:46:19Z")

</div>

Hello, everyone.

Can I ask you a question about specific heat Cp?

When I want to use isothermal wall surfaces I find that Cp confuses me a bit as I am using dimensionless to flow parameters and I don’t understand how Cp should be expressed, for example it is 1005 in room temperature air but this has units.  
Here are my incoming flow parameter settings that I referenced for this condition.

 ![image](https://global.discourse-cdn.com/free1/uploads/pyfr/original/1X/93b5219709b5f1151391f23e5bda6e980e3f1436.png)

```auto
[constants]
M = 2.25
gamma = 1.4
Pr = 0.72
rhoin = 1.0
uin = 1.0
vin = 0.0
win = 0.0
pin = 0.14109347442680775
mu = 4e-05
cpTref = 0.4938271604938272
cpTs = 0.19897797675575454
; cp = 1005 ; J/(kg-K)
; Tw = 322 ; k

```

```auto
[soln-bcs-wall]
type = no-slp-isot-wall
cpTw = cp * Tw

```

It is worth mentioning that cpTref and cpTs I calculated by using the following equations, with 110 and 273 as the reference temperature constants.

```auto
gamma = 1.4
p = 0.14109347442680775
rho = 1
cpTref = gamma/(gamma-1) * p / rho
cpTs = cp_Tref * 110/273

```

Not sure if I understand cpTref and cpTs incorrectly and how cp should be calculated?  
Thank you all very much for your valuable time.

Regards, Wgbb.

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<div class="post-metadata">

**Author:** ![tdzanic](https://avatars.discourse-cdn.com/v4/letter/t/f05b48/32.png) [@tdzanic](https://pyfr.discourse.group/u/tdzanic)\
**Post date:** [29 May 2024 16:07 UTC](https://pyfr.discourse.group/t/about-specific-heat-cp-and-cptref/1099/2 "2024-05-29T16:07:42Z")

</div>

That’s the (mostly) correct way to define `cpTref` and `cpTs`. We use `cpT` since for constant `cp` it’s the non-dimensional form of temperature (it’s the enthalpy), whereas temperature itself is dimensional and dependent on the units of `R`. However, Sutherland’s law is inherently dimensional as it’s a nonlinear relation of the temperature to the Sutherland temperature, so there is a need for a reference physical temperature that `cpTref` and `cpTs` correspond to, where the reference temperature is your freestream temperature (since the enthalpy quantity `h = cpTref = gamma/(gamma-1) * p / rho` you compute corresponds to your freestream enthalpy). However, it seems like your freestream temperature for your problem is 169.44, not 273, so you then need to compute `cpTs` in terms of this as `cpTs = cpTref * Ts/Tref = cpTref * 110/169.44`. You can compute your wall enthalpy in the same way as `cpTw = cpTref * Twall/Tref = cpTref * 322/169.44`.

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<div class="post-metadata">

**Author:** ![wgbb](https://avatars.discourse-cdn.com/v4/letter/w/6f9a4e/32.png) [@wgbb](https://pyfr.discourse.group/u/wgbb)\
**Post date:** [31 May 2024 01:25 UTC](https://pyfr.discourse.group/t/about-specific-heat-cp-and-cptref/1099/3 "2024-05-31T01:25:41Z")

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Thank you very much for your help.

Firstly apologising for my misunderstanding.

I think the entropy filtering algorithm is very good to capture strong excitations effectively.

Again, thank you for your answers.

Regards, Wgbb.