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• # How is Tp* selected/computed

Posted by on August 10, 2023 at 7:56 pm

Hello! From lesson 16 where it was explained the ways of linearizing source terms, on the examples were added the term Tp* along with Tp (Temperature)… where S was a curve, and the method of the derivative was used… what is Tp* and what is finally Tp? can you make an example where we can difference the value of each one? Thank you

2 Members · 3 Replies
• 3 Replies
• ### Sujith FTL

Member
August 11, 2023 at 1:16 pm

Hello Maria,

Can you confirm if this is from CFD Foundation-Lesson 16?

Regards,

Sujith P Joseph

• ### MarÃ­a Manuela

Member
August 12, 2023 at 8:29 pm

I’m sorry, my mistake, lesson is 18 part 2, around min 15:10.

• ### Sujith FTL

Member
August 17, 2023 at 2:19 pm

Dear Maria,

Tp represents the original temperature, and Tp* represents an adjusted temperature used in the linearized expression of the source term.

Example:

Let’s consider a simple example where the source term S is a quadratic function of temperature:

S(T) = T^2

Let’s assume the reference temperature Tp is 100Â°C. We want to linearize the source term around this reference temperature.

Linearization:

S(T) â‰ˆ S(Tp) + (T – Tp) * dS/dT

S(T) â‰ˆ 100^2 + (T – 100) * 2T

Let’s say we choose an adjusted reference temperature Tp* as 110Â°C.

Linearized source term at Tp*:

S*(T) â‰ˆ 110^2 + (T – 110) * 2T

Now, we can evaluate the values of the original source term S(T) and the linearized source term S*(T) for different temperature values, say T = 105Â°C:

Original Source Term:

S(105) = 105^2 = 11025

Linearized Source Term with Adjusted Reference Temperature:

S*(105) â‰ˆ 110^2 + (105 – 110) * 2 * 105 = 11025

In this example, you can see that both the original and linearized source terms yield the same result for the chosen temperature value. This might not always be the case, especially for more complex source term functions and adjustments, but the linearization process allows us to simplify calculations around a chosen reference temperature.

Regards,

Sujith P Joseph