PDE Toolbox point source
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From: Meagan on 11 Mar 2010 13:08 Hi all, I am trying to model a problem in the PDE toolbox and I am not sure if I have the correct boundary conditions or PDE's defined. My problem is basically a small rectangular plate with a point source in the center. How am I supposed to model the point source? Do I model it as a PDE with the same physical properties as the plate and instead of q=0 make it q=source watts or do I make the plate have a hole in it and model the hole as a heat flux? I am not sure that either way is correct so any help would be greatly appreciated. Thanks in advance, Meagan
From: Torsten Hennig on 11 Mar 2010 16:40 > Hi all, > > I am trying to model a problem in the PDE toolbox and > I am not sure if I have the correct boundary > conditions or PDE's defined. > > My problem is basically a small rectangular plate > with a point source in the center. How am I supposed > to model the point source? Do I model it as a PDE > with the same physical properties as the plate and > instead of q=0 make it q=source watts or do I make > the plate have a hole in it and model the hole as a > heat flux? I am not sure that either way is correct > so any help would be greatly appreciated. > > Thanks in advance, > Meagan If the point source is to be supplied in grid point x_i, add a source term in the discretized PDE at x_i of magnitude q [W/m^3]. Usually your point source Q will have unit [W] ; so you will have to divide it by the volume of influence in x_i (in one dimension, one usually takes ((x_i-x_(i-1))/2 + (x_(i+1)-x(i))/2)*area in the other two coordinate directions. Best wishes Torsten.
From: Meagan on 16 Mar 2010 12:58 Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1026946862.367245.1268379662534.JavaMail.root(a)gallium.mathforum.org>... > > Hi all, > > > > I am trying to model a problem in the PDE toolbox and > > I am not sure if I have the correct boundary > > conditions or PDE's defined. > > > > My problem is basically a small rectangular plate > > with a point source in the center. How am I supposed > > to model the point source? Do I model it as a PDE > > with the same physical properties as the plate and > > instead of q=0 make it q=source watts or do I make > > the plate have a hole in it and model the hole as a > > heat flux? I am not sure that either way is correct > > so any help would be greatly appreciated. > > > > Thanks in advance, > > Meagan > > If the point source is to be supplied in grid point > x_i, add a source term in the discretized PDE at x_i > of magnitude q [W/m^3]. Usually your point source Q > will have unit [W] ; so you will have to divide it > by the volume of influence in x_i (in one dimension, > one usually takes > ((x_i-x_(i-1))/2 + (x_(i+1)-x(i))/2)*area in the other > two coordinate directions. > > Best wishes > Torsten. Torsten, Thank you for such a fast reply. I am still a little confused though. I am using the PDE toolbox from MATLAB. I have created a geometry of a square plate with a circle in the middle of it. The toolbox gives you the option to define the PDE for each section. For the circle (point source) I have defined a parabolic heat transfer PDE with equation: rho*C*T'-div(k*grad(T))=Q+h*(Text-T) where T=temperature where the user fills in values for rho (density), C (heat capacity), k (coeff of heat conduction), Q (heat source), h (convective heat transfer coeff), and Text (external temperature) My values are rho=7854, C=434, k=60.5, Q=10000, h=7.9, and Text=0 for the circle point source. I use the same values for the square except Q=0 because there is no heat generation. When I plug these values in and solve, I get the temperature at the center of the 10000W point source is about 0.0141K which can not be correct. Am I using the correct equations to model my problem? Should I try making a square plate with a hole in it and then converting the point source into a heat flux boundary condition? It may be hard to visualize what I am asking without access to the toolbox but any suggestions on how to get a better answer would be greatly appreciated. Thanks, Meagan
From: Torsten Hennig on 16 Mar 2010 23:29 > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote > in message > <1026946862.367245.1268379662534.JavaMail.root(a)gallium > .mathforum.org>... > > > Hi all, > > > > > > I am trying to model a problem in the PDE toolbox > and > > > I am not sure if I have the correct boundary > > > conditions or PDE's defined. > > > > > > My problem is basically a small rectangular plate > > > with a point source in the center. How am I > supposed > > > to model the point source? Do I model it as a PDE > > > with the same physical properties as the plate > and > > > instead of q=0 make it q=source watts or do I > make > > > the plate have a hole in it and model the hole as > a > > > heat flux? I am not sure that either way is > correct > > > so any help would be greatly appreciated. > > > > > > Thanks in advance, > > > Meagan > > > > If the point source is to be supplied in grid point > > x_i, add a source term in the discretized PDE at > x_i > > of magnitude q [W/m^3]. Usually your point source Q > > will have unit [W] ; so you will have to divide it > > by the volume of influence in x_i (in one > dimension, > > one usually takes > > ((x_i-x_(i-1))/2 + (x_(i+1)-x(i))/2)*area in the > other > > two coordinate directions. > > > > Best wishes > > Torsten. > > Torsten, > > Thank you for such a fast reply. I am still a little > confused though. I am using the PDE toolbox from > MATLAB. > > I have created a geometry of a square plate with a > circle in the middle of it. The toolbox gives you the > option to define the PDE for each section. For the > circle (point source) I have defined a parabolic heat > transfer PDE with equation: > > rho*C*T'-div(k*grad(T))=Q+h*(Text-T) where > T=temperature > > where the user fills in values for rho (density), C > (heat capacity), k (coeff of heat conduction), Q > (heat source), h (convective heat transfer coeff), > and Text (external temperature) > > My values are rho=7854, C=434, k=60.5, Q=10000, > h=7.9, and Text=0 for the circle point source. I use > the same values for the square except Q=0 because > there is no heat generation. When I plug these values > in and solve, I get the temperature at the center of > the 10000W point source is about 0.0141K which can > not be correct. > > Am I using the correct equations to model my problem? > Should I try making a square plate with a hole in it > and then converting the point source into a heat flux > boundary condition? It may be hard to visualize what > I am asking without access to the toolbox but any > suggestions on how to get a better answer would be > greatly appreciated. > > Thanks, > Meagan You have to divide Q = 10000 [W] by (area of the circle* thickness of the plate) to be consistent with the units. If you prescribe T_ext = 0 K, a temperature of 0.0141 K is not that unrealistic without the above mentionned modification. Best wishes Torsten.
From: Meagan on 23 Mar 2010 09:44
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1491592455.394287.1268810973396.JavaMail.root(a)gallium.mathforum.org>... > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote > > in message > > <1026946862.367245.1268379662534.JavaMail.root(a)gallium > > .mathforum.org>... > > > > Hi all, > > > > > > > > I am trying to model a problem in the PDE toolbox > > and > > > > I am not sure if I have the correct boundary > > > > conditions or PDE's defined. > > > > > > > > My problem is basically a small rectangular plate > > > > with a point source in the center. How am I > > supposed > > > > to model the point source? Do I model it as a PDE > > > > with the same physical properties as the plate > > and > > > > instead of q=0 make it q=source watts or do I > > make > > > > the plate have a hole in it and model the hole as > > a > > > > heat flux? I am not sure that either way is > > correct > > > > so any help would be greatly appreciated. > > > > > > > > Thanks in advance, > > > > Meagan > > > > > > If the point source is to be supplied in grid point > > > x_i, add a source term in the discretized PDE at > > x_i > > > of magnitude q [W/m^3]. Usually your point source Q > > > will have unit [W] ; so you will have to divide it > > > by the volume of influence in x_i (in one > > dimension, > > > one usually takes > > > ((x_i-x_(i-1))/2 + (x_(i+1)-x(i))/2)*area in the > > other > > > two coordinate directions. > > > > > > Best wishes > > > Torsten. > > > > Torsten, > > > > Thank you for such a fast reply. I am still a little > > confused though. I am using the PDE toolbox from > > MATLAB. > > > > I have created a geometry of a square plate with a > > circle in the middle of it. The toolbox gives you the > > option to define the PDE for each section. For the > > circle (point source) I have defined a parabolic heat > > transfer PDE with equation: > > > > rho*C*T'-div(k*grad(T))=Q+h*(Text-T) where > > T=temperature > > > > where the user fills in values for rho (density), C > > (heat capacity), k (coeff of heat conduction), Q > > (heat source), h (convective heat transfer coeff), > > and Text (external temperature) > > > > My values are rho=7854, C=434, k=60.5, Q=10000, > > h=7.9, and Text=0 for the circle point source. I use > > the same values for the square except Q=0 because > > there is no heat generation. When I plug these values > > in and solve, I get the temperature at the center of > > the 10000W point source is about 0.0141K which can > > not be correct. > > > > Am I using the correct equations to model my problem? > > Should I try making a square plate with a hole in it > > and then converting the point source into a heat flux > > boundary condition? It may be hard to visualize what > > I am asking without access to the toolbox but any > > suggestions on how to get a better answer would be > > greatly appreciated. > > > > Thanks, > > Meagan > > You have to divide Q = 10000 [W] by (area of the circle* > thickness of the plate) to be consistent with the units. > If you prescribe T_ext = 0 K, a temperature of > 0.0141 K is not that unrealistic without the above > mentionned modification. > > Best wishes > Torsten. Torsten, That modicfication made my answer a lot more reasonable. Thank you. My last question is this: the units for all of the terms are in W/m^3 except for the last term of h(Text-T) which has units of W/m^2. Do I need to divide by the plate thickness for this term as well to get the correct units? Thank you so much for your help, Meagan |