GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\overrightarrow{\mathit{V}}=\left(2\mathit{x}\right)\hat{\mathit{i}}+\left(\mathit{y}+3\mathit{t}\right)\hat{\mathit{j}},$ and the temperature field in the fluid is T = 2x² + xy + 4t, where x and y are the spatial coordinates, and t is the time. The time rate of change of temperature recorded by the probe at (x = 1, y = 1, t = 1) is _______.