# Robin BC for T

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 September 28, 2011, 07:57 Robin BC for T #1 New Member   Join Date: Oct 2010 Posts: 13 Rep Power: 6 Dear all, one equation in my case is Code: ```solve ( fvm::ddt(T) + fvm::div(phi,T) - fvm::laplacian(lambda,T) );``` with lambda being a function of space and time. In the BC I would like to specify a heat flux q_dot = alpha(T_inf - T_bc). T_inf ...const. Far field temperature alpha ...const. Heat transfer coefficient T_bc ...Temperature at boundary Energy conservation yields q_dot = -lambda (del T)/(del n) = alpha(T_inf - T_bc) which is my BC. * Does such a BC exist? * How should I proceed if I want to implement it? * I know that it is similar to the BC "mixed" but I think mixed cannot account for non-constant lambda. Are there other BCs that might be useful templates? Thank you for any comments! Cheers

 September 29, 2011, 04:19 #2 Member   cosimo bianchini Join Date: Mar 2009 Location: Florence, Tuscany, Italy Posts: 88 Rep Power: 8 I wrote such a BC few time ago (you find the code here) and it actually is a mixed boundary condition. The idea is simple, just rewriting the equation you wrote (I also add a general thermal power to handle radiation Q) you end up with: h/(h+k*deltaCoeff) * T_w + k*deltaCoeff/(h+k*deltaCoeff) * gradT_w = h/(h+k*deltaCoeff) * T_ref + Q*deltaCoeff/(h+k*deltaCoeff) satisfying both the physical constraint and the form of the mixed boundary condition i.e. VF * T_w + (1-VF) * gradT_w =VF*T_ref + (1-VF) * gradT_ref. So it just set: VF = h/(h+k*deltaCoeff) T_ref = T_ref gradT_ref = Q*deltaCoeff*VF/(1-VF)/h in order to make it work you just have to define in your solver a volScalarField kond to store values for the thermal conductivity (optionally you can define it inside the BC if you like). It was compiled on 1.6.x but I guess you will not have troubles importing it in 1.6-ext or 1.7. Not sure about 2.0, drop me an email if you need a help. Hope you find this useful. __________________ Cosimo Bianchini Energy Engineering Department "S. Stecco" University of Florence Via di S.Marta, 3 50139 Florence - ITALY Tel: +39 055 4796575 Fax: +39 055 4796342 Mob: +39 320 9460153 e-mail: cosimo.bianchini@htc.de.unifi.it URL: www.htc.de.unifi.it

 October 10, 2011, 08:47 #3 New Member   Join Date: Oct 2010 Posts: 13 Rep Power: 6 Hi Cosimo, thanks so much for writing down your thoughts! You helped me a lot! Regards, Moritz

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