a) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\nabla T\)
b) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\nabla .T\)
c) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\vec{V}.\nabla T\)
d) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\nabla \times T\)

Answer: c
Explanation:
\(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y}+w \frac{\partial T}{\partial z}\)
\(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+(u\vec{i}+v\vec{j}+w\vec{k}).(\frac{\partial T}{\partial x} \vec{i}+\frac{\partial T}{\partial y}\vec{j}+\frac{\partial T}{\partial z}\vec{k})\)
\(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\vec{V}.\nabla T.\)