Question

Which of these terms represent the convective derivative of temperature (T)?

(a) \(\vec{V}.\nabla T\)

(b) \(\frac{DT}{Dt}\)

(c) ∇T

(d) \(\frac{\partial T}{\partial t}\)

The question was asked during an online exam.

I'm obligated to ask this question of Governing Equations in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Right option is (a) \(\vec{V}.\nabla T\)

Easiest explanation: \(\vec{V}.\nabla T\) (dot product of velocity vector gradient of T) is the convective derivative which is the time rate of change due to the movement of the fluid element.