Temperature Gradient - Mathematical Description

Mathematical Description

Assuming that the temperature T is an intensive quantity, i.e., a single-valued, continuous and differentiable function of three-dimensional space (often called a scalar field), i.e., that

where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as

\nabla T = \begin{pmatrix} {\frac{\partial T}{\partial x}}, {\frac{\partial T}{\partial y}}, {\frac{\partial T}{\partial z}} \end{pmatrix}

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