Wall heat transfer boundary condition

francesco_capuano · October 15, 2015, 06:29

Hi,
I would like to model a radiative and convective heat transfer through a wall.
In practice, I would need an equilibrium boundary condition of the type

$\dot{q_w} = -\lambda \left(\dfrac{\partial T}{\partial n}\right)_w = \sigma\epsilon \left(T_w^4-T_e^4\right) + h\left(T_w-T_e \right)$ ,

where

is the wall temperature and

is the environment temperature outside the domain. The wall temperature would then be calculated from (a discretized version of) the above equation to yield the heat flux exchanged at the wall.

Is there any available boundary condition to model such problem?
Or, did anyone encounter the same issue (and maybe developed a customized b.c.)?

Many thanks in advance.

akidess · October 18, 2015, 11:52

A mixed boundary condition (i.e. groovyBC) should do the trick. I'm sure you can find a copy&paste solution here on the forum.

Simeone_Parolisi · October 19, 2015, 06:11

We successfully modeled it with this implementation in file 'T' in directory '0'

boundaryField
{
fixedWalls
{
type groovyBC;
refValue uniform 288;
refGradient uniform 0;
valueFraction uniform 1;
value uniform 288;
valueExpression "0";
gradientExpression "h*(T-Tinf)+(sigma)*E*(T*T*T*T-Tinf*Tinf*Tinf*Tinf)";
fractionExpression "0";
evaluateDuringConstruction 0;
variables
4
(
"h=50;"
"sigma=5.6e-8;"
"E=0.8;"
"Tinf=288;"
)
;

After, we was forced to change the string thermoType>energy from 'sensibleEnthalpy' to 'sensibleInternalEnergy' in file 'thermophysicalProperties' in directory 'constant' for other reasons and we obtained a floating point exception error.
What is the problem? Is there an alternative method to implement heat transfer written above?

October 15, 2015, 06:29	Wall heat transfer boundary condition	#1
francesco_capuano Member Francesco Capuano Join Date: May 2010 Posts: 81 Rep Power: 15	Hi, I would like to model a radiative and convective heat transfer through a wall. In practice, I would need an equilibrium boundary condition of the type $\dot{q_w} = -\lambda \left(\dfrac{\partial T}{\partial n}\right)_w = \sigma\epsilon \left(T_w^4-T_e^4\right) + h\left(T_w-T_e \right)$ , where is the wall temperature and is the environment temperature outside the domain. The wall temperature would then be calculated from (a discretized version of) the above equation to yield the heat flux exchanged at the wall. Is there any available boundary condition to model such problem? Or, did anyone encounter the same issue (and maybe developed a customized b.c.)? Many thanks in advance.

October 18, 2015, 11:52		#2
akidess Senior Member Anton Kidess Join Date: May 2009 Location: Germany Posts: 1,377 Rep Power: 29	A mixed boundary condition (i.e. groovyBC) should do the trick. I'm sure you can find a copy&paste solution here on the forum. __________________ On twitter @akidTwit Spend as much time formulating your questions as you expect people to spend on their answer.

October 19, 2015, 06:11	GroovyBC	#3
Simeone_Parolisi New Member Napoli Join Date: Oct 2015 Posts: 2 Rep Power: 0	We successfully modeled it with this implementation in file 'T' in directory '0' boundaryField { fixedWalls { type groovyBC; refValue uniform 288; refGradient uniform 0; valueFraction uniform 1; value uniform 288; valueExpression "0"; gradientExpression "h(T-Tinf)+(sigma)E(TTTT-TinfTinfTinf*Tinf)"; fractionExpression "0"; evaluateDuringConstruction 0; variables 4 ( "h=50;" "sigma=5.6e-8;" "E=0.8;" "Tinf=288;" ) ; After, we was forced to change the string thermoType>energy from 'sensibleEnthalpy' to 'sensibleInternalEnergy' in file 'thermophysicalProperties' in directory 'constant' for other reasons and we obtained a floating point exception error. What is the problem? Is there an alternative method to implement heat transfer written above?

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