Constant Anisotropic in Material model

kpk

Hi,

Can anybody tell me details about how to use Constant Anisotropic 3x3 array for Conductivity in Acusolve

acupro

Best place to look is in the AcuSolve Command Reference Manual - included in the 'Help' system of the distribution.  It will be in 'Material Model Commands' > CONDUCTIVITY_MODEL.  From this: "The elements of the anisotropic conductivity tensor are always specified in the order k11, k22, k33, k12, k23, k31."  Thus, for a material aligned with the X/Y/Z coordinate system, the first entry k11 is the X-direction conductivity, the second k22 is the Y-direction, and the third k33 is the Z-direction.  If the body is not aligned, you will need to perform the appropriate tensor transform.

kpk

Thanks for the reply, i am clear with k11,k22,k33 , but not clear with k12,k23,k31 if possible can you share any examples

acupro

kpk said:

Thanks for the reply, i am clear with k11,k22,k33 , but not clear with k12,k23,k31 if possible can you share any examples

Those off-diagonal terms are for anisotropic materials.  The general heat transfer equation is:

q=-k*Grad(T) with k>0

To expand the thermal conductivity tensor:

q_x = k_11(dT/dx) + k_12(dT/dy) + k_13(dT/dz)

q_y = k_21(dT/dx) + k_22(dT/dy) + k_23(dT/dz)

q_z = k_31(dT/dx) + k_32(dT/dy) + k_33(dT/dz)

(There may be some sign differences in there...)  Also, the conductivity tensor is symmetric so e.g. k_21=k_12.  This follows general thermal conductivity theory, which one can research.

Those off-diagonal terms are for heat transfer due to temperature changes in more than one direction.  For example, if there is heat transfer in the x-direction with a temperature change in the y-direction, k_12 would be non-zero.