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Apr24-11, 11:37 AM
P: 1,402
You could express it with the dyadic product as

[tex]\nabla \cdot \text{diag}(\textbf{k} \otimes \nabla T) = \nabla \cdot \text{diag}([k] [\nabla T]^T),[/tex]

taking "diag" to mean "form a vector whose components are the diagonal entries of this matrix". Here [k] is a 3x1 matrix (a column vector), and the transpose of [del T] a 1x3 matrix (row vector), so that their product is a 3x3 matrix.

Or simply use the summation sign:

[tex]\sum_{i=1}^{n} \partial_i (k_i \partial_i T) = \sum_{i=1}^{n} \frac{\partial }{\partial x_i}\left ( k_i \frac{\partial T}{\partial x_i} \right ).[/tex]