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Boundary conditions in heat transfer

Topics: Medical Engineering

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Yael Ruschkewitz

Yael Ruschkewitz

December 21, 2009 7:36pm UTC

Boundary conditions in heat transfer

Hi,
I want to model a muscle tissue containing a capillary blood vessel. Now I’m using a simple model for start… My model geometry is in the attached file.
As I want to model heat convection between the tissue and blood I want to use on interior boundaries between the blood vessel the “heat flux discontinuity” boundary condition.

My main question is regarding Tinf: according to comsol help files: “Tinf is the external bulk temperature” and this is from the section of interior boundaries (heat flux discontinuity- interior boundaries only)… I don’t understand which subdomain is considered as having external bulk temperature? The blood vessel or the tissue surrounding it? This is a critical question as the temperature of the blood and the tissue are not equal in my model… I’m modeling the tissue as having 37C and the blood as 35C… Does Tinf belong to the subdomain of the higher temperature? in another case of the model I’m representing both blood and tissue as having 37C, but when the tissue has a higher heat production rate from metabolism…
Also, in my model I am representing heat production from metabolism using the subdomain settings of the bioheat modulo, so I thought of setting q=0… I’m not sure whether I best set q=0 or maybe I should set it’s value as the same value I set the metabolic heat of blood? What do you think?

Attachments:   simple geometry.Png  

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Ivar Kjelberg

Ivar Kjelberg

December 27, 2009 10:35am UTC in response to Yael Ruschkewitz

Re: Boundary conditions in heat transfer

Hi Yeal

You might have found out by now, I hope so, but in anycase, in the boundary condition Heat flux you have 2 variables Q and h, you might either choose one or the other, or both. Now to understand how COMSOL isusing these and how they are related (Tinf is only linked to "h") take a look at the equations:

Once you have selected 2D "htgh" BC's "Heat transfer" and the boundary of interest go to :
Physics - Equation Systems - Boundary Settings

and take alook at i.e. 4th row (for "T" as the 4th dependent variable u,v,p,T,J), you should see something like:

-h_htgh*T+q0_htgh+h_htgh*Tinf_htgh

that once rearranged this means:

h_htgh*(Tinf_htgh-T) + q0_htgh

Hence the Q variable (or q0_htgh internally) enters directly thermal power onto the boundary, while the "h" is proportional to the temperature difference (in K) of (Tinf-T) and T is the temperature you are solving for, so Tinf yould be your constant blood temperature, then h should be scaled to take into account the liquid solid exchange, but perhaps next step to take into account the blood flow, or total volume passing through, as the blood temperature might not manage to take/give all the heat, unaffected, if you have a sever feber, but I would propose not to use non-linear terms to start with.

by the way you know about this book: www.comsol.com/academic/books/imtp/
you should have a look, it's excellent for your type of activities (I just got it a week ago)

Good luck
Ivar

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