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Heat Transfer: Free convection with bioheat transfer
Posted Jan 15, 2012, 3:42 p.m. EST Fluid & Heat, Heat Transfer & Phase Change Version 4.2, Version 4.2a 4 Replies
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Hi all,
I would like to model two coupled heat transfer problems. My model is a sphere within a sphere; thus I have two domains, an inner sphere surrounded by a spherical shell. The inner sphere is a liquid which will be a heat source. The shell is biological tissue.
My goal is to model the inner sphere as an internal source that heats up (assigned as a heat source W/m^3). Since the material of the inner sphere is water, I would like to model the free convection (due to gravity) as it is heating up. Finally, I would like the physics of the shell to be the bioheat equation. Of course the temperature of this region changes because it is in direct contact with the inner sphere, whose temperature increases with time.
This problem is similar to the cold water glass example in the model examples (www.comsol.com/showroom/animations/195/). The main difference is that I now have two physics problems. The modules I think I need are Heat Transfer (ht) and Non-Isothermal Flow (nitf). However, once I set this up with the appropriate boundary conditions, the simulation runs without reaching a solution. I am running both physics models simultaneously, I don't think it is appropriate to decouple them.
Does anyone have any suggestions?
I would like to model two coupled heat transfer problems. My model is a sphere within a sphere; thus I have two domains, an inner sphere surrounded by a spherical shell. The inner sphere is a liquid which will be a heat source. The shell is biological tissue.
My goal is to model the inner sphere as an internal source that heats up (assigned as a heat source W/m^3). Since the material of the inner sphere is water, I would like to model the free convection (due to gravity) as it is heating up. Finally, I would like the physics of the shell to be the bioheat equation. Of course the temperature of this region changes because it is in direct contact with the inner sphere, whose temperature increases with time.
This problem is similar to the cold water glass example in the model examples (www.comsol.com/showroom/animations/195/). The main difference is that I now have two physics problems. The modules I think I need are Heat Transfer (ht) and Non-Isothermal Flow (nitf). However, once I set this up with the appropriate boundary conditions, the simulation runs without reaching a solution. I am running both physics models simultaneously, I don't think it is appropriate to decouple them.
Does anyone have any suggestions?
4 Replies Last Post May 31, 2012, 6:03 a.m. EDT
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Posted:
1 decade ago
Consider running the heat transfer analysis only, then using the resulting temperature as the initial condition for the coupled analysis. That may help with convergence. Also check the Rayleigh and Grashofs numbers to see the significance of natural convection and whether it is laminar or turbulent.
Nagi Elabbasi
Veryst Engineering
Nagi Elabbasi
Veryst Engineering
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Posted:
1 decade ago
Thanks Nagi for your response. Based on your advice I tried to break up the problem into running the heat transfer analysis only and then using it as an initial condition for the non-isothermal flow solver. While playing around with this concept, I think my problem is with how I setup the non-isothermal flow solver. For some reason my non-isothermal flow solver simulation does not converge.
I just setup a simplified model in which I had a sphere that had properties of water. I applied a constant heat source to this domain. The boundary conditions were no slip and thermal insulation on the outer boundaries. I applied an initial pressure of nitf.rho*g_const*(50e-3[m]-z), where 50e-3 is the radius of the sphere. I also added a volume force of -g_const*nitf.rho. My basis for these settings was from the cold water glass example from the COMSOL library. The simulation appears to not converge because after 24 hours of running it, no progress was being made. I was hoping to see the free convection inside the sphere as the water was being heated up.
Any suggestions?
I just setup a simplified model in which I had a sphere that had properties of water. I applied a constant heat source to this domain. The boundary conditions were no slip and thermal insulation on the outer boundaries. I applied an initial pressure of nitf.rho*g_const*(50e-3[m]-z), where 50e-3 is the radius of the sphere. I also added a volume force of -g_const*nitf.rho. My basis for these settings was from the cold water glass example from the COMSOL library. The simulation appears to not converge because after 24 hours of running it, no progress was being made. I was hoping to see the free convection inside the sphere as the water was being heated up.
Any suggestions?
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Posted:
1 decade ago
Convergence can be difficult in these free convection problems. I have some suggestions. Make sure that you are solving a transient analysis with a small initial time increment, and use a fine mesh that can capture the fluid boundary layer.
Nagi Elabbasi
Veryst Engineering
Nagi Elabbasi
Veryst Engineering
Please login with a confirmed email address before reporting spam
Posted:
1 decade ago
Hi all
i must say this is like the 5th thread i see dealing with natural convection and problems with the analysis.
this is also not the first time i have seen reference to "natural convection must be solved under transient solver".
well, the solution to the whole natural convection problem is complex but possible in both STATIONARY and TRANSIENT (i personally prefer for engineering application to use the stationary solution unless i am interested in the "Ramp-up" process) if only you define the physics properly , see below:
the system:
1. you need to create a large enough volume of fluid around the object to make sure that you don't get artifacts in the computation field due to the boundaries (usually 2-5 times the nominal dimension of the object in length in all directions)
2. define the fluid field: under 'absolute pressure' choose "pressure(nitf/fluid1)" , and as reference pressure enter the ambient pressure.
Mesh:
1. choose a "fine" mesh for most cases where the geometry is more elaborate then cubic presentations (you need a fine enough mesh to capture the fine temperature gradients in the near wall region, as well as the sharp directional acceleration gradients of the velocity field from the entrainment into the plum)
Boundary conditions:
1. the face where the plum (the heat plum raising from the object) is to be defined as "outflow" (under heat transfer BC) AND "outlet" (under laminar BC - set P0=P, ambient)
2. the faces where the fluid enters the system (to satisfy the entrainment of the plum) is to be defined as "open boundary" (with "no viscus stress" condition and T0=T, ambient)
3. Volume force, is to be defined as "-g_const*(nitf.rho-rho_ref)"
4. heat source, what ever is relevant to you system.
summation of BC:
1. volume force
2. open boundary
3. outflow
4. outlet
5. heat source
Solver:
1. choose the stationary solver and change
under study>solver configurations>solver1>fully coupled 1 , change the 'damping and termination' definition to being "automatic highly non-linear"
regarding convergence in Stationary studies:
as we all know and like you can find in many places in the literature, indeed natural convection has a transient element to it, as the plum and flow field fluctuates along the heated surface, HOWEVER, there is still the possibility to achieve a Stationary study that complies with the system.
the thing is, should you run a stationary solver, you will see that after some iterations as the convergence 'green bar' goes all the way to 90% it will then drop sharply to approximately 50%... this phenomena will fluctuate back and forth ENDLESSLY!
what you need to understand it that this is happening because the solver set on one solution then loss stability as it "moves" to another.
What you need to do: let the solution fluctuates aback and forth 1-2 times, once you see the pattern - stop the solver, and there you have it!!! - your solution (you will see that should you stop the solver at a different fluctuation the flow filed will look slightly different 'Plum-wise' but the temperature will be identical)
i have attached a working example, that has been lab tested to make sure the solver results are accurate.
Best regards to all
M.sc Yoav matia.
i must say this is like the 5th thread i see dealing with natural convection and problems with the analysis.
this is also not the first time i have seen reference to "natural convection must be solved under transient solver".
well, the solution to the whole natural convection problem is complex but possible in both STATIONARY and TRANSIENT (i personally prefer for engineering application to use the stationary solution unless i am interested in the "Ramp-up" process) if only you define the physics properly , see below:
the system:
1. you need to create a large enough volume of fluid around the object to make sure that you don't get artifacts in the computation field due to the boundaries (usually 2-5 times the nominal dimension of the object in length in all directions)
2. define the fluid field: under 'absolute pressure' choose "pressure(nitf/fluid1)" , and as reference pressure enter the ambient pressure.
Mesh:
1. choose a "fine" mesh for most cases where the geometry is more elaborate then cubic presentations (you need a fine enough mesh to capture the fine temperature gradients in the near wall region, as well as the sharp directional acceleration gradients of the velocity field from the entrainment into the plum)
Boundary conditions:
1. the face where the plum (the heat plum raising from the object) is to be defined as "outflow" (under heat transfer BC) AND "outlet" (under laminar BC - set P0=P, ambient)
2. the faces where the fluid enters the system (to satisfy the entrainment of the plum) is to be defined as "open boundary" (with "no viscus stress" condition and T0=T, ambient)
3. Volume force, is to be defined as "-g_const*(nitf.rho-rho_ref)"
4. heat source, what ever is relevant to you system.
summation of BC:
1. volume force
2. open boundary
3. outflow
4. outlet
5. heat source
Solver:
1. choose the stationary solver and change
under study>solver configurations>solver1>fully coupled 1 , change the 'damping and termination' definition to being "automatic highly non-linear"
regarding convergence in Stationary studies:
as we all know and like you can find in many places in the literature, indeed natural convection has a transient element to it, as the plum and flow field fluctuates along the heated surface, HOWEVER, there is still the possibility to achieve a Stationary study that complies with the system.
the thing is, should you run a stationary solver, you will see that after some iterations as the convergence 'green bar' goes all the way to 90% it will then drop sharply to approximately 50%... this phenomena will fluctuate back and forth ENDLESSLY!
what you need to understand it that this is happening because the solver set on one solution then loss stability as it "moves" to another.
What you need to do: let the solution fluctuates aback and forth 1-2 times, once you see the pattern - stop the solver, and there you have it!!! - your solution (you will see that should you stop the solver at a different fluctuation the flow filed will look slightly different 'Plum-wise' but the temperature will be identical)
i have attached a working example, that has been lab tested to make sure the solver results are accurate.
Best regards to all
M.sc Yoav matia.