Dear friends,

I want to apply heat flux inthermal simulation using LBM…

I’ve used this formulae:

T(i,1)= (q"/k)*2/3*deltax+4/3*T(i,2)-1/3*T(i,3)

in which i is the directions and T(i,1) is the directional temperatue on wall, T(i,2)&T(i,3) are the directional temperatures on one node and two nodes above the that respectively. I distribute the heat flux along the directions based on their weights:

for example:

T(0,1)= (4/9*q"/k) 2/3deltax+4/3*T(0,2)-1/3

*T(0,3)*

T(1,1)= (1/9q"/k)

T(1,1)= (1/9

*2/3*deltax+4/3

*T(1,2)-1/3*T(1,3)

T(2,1)= (1/9

*q"/k)*T(2,2)-1/3

*2/3*deltax+4/3*T(2,3)*

T(4,1)= (1/9q"/k)

T(4,1)= (1/9

*2/3*deltax+4/3

*T(4,2)-1/3*T(4,3)

T(5,1)= (1/36

*q"/k)*T(5,2)-1/3

*2/3*deltax+4/3*T(5,3)*

T(7,1)= (1/36q"/k)

T(7,1)= (1/36

*2/3*deltax+4/3

*T(7,2)-1/3*T(7,3)

However, when I want to calculate the local Nusselt number which calculates through the following formulae:

Nu=(T-Tref)/(q"*l/k)

the Nu number is obtained high number which does not corroborate the classical CFD…

is this algorithm correct!!!

I’d really appreciate if you can give me a good refrence or article pertaining to modeling heat flux using LBM…

Or

help me…

Many thanks in advance…

cheers