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Constant Anisotropic in Material model

kpk

Hi,

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

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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

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.