Overview
The following function of space describes the temperature field in ℃:
T(x, y) = 0.5x + 2y + 5
A fluid particle travels through space with a velocity vector given by: V = − sin(t) î + cos(t) ĵ a) Using the material derivative, derive an expression describing the temperature experienced by the fluid particle, as it travels, starting from the origin (xo, yo) = (1, 0).
b) What is the temperature difference between t1 = 0 and t2 = 2π s experienced by the fluid particle. How do you explain this outcome? Would you expect a different outcome if T(x, y, t)?
FYI: I attached an example problem from class that is different but the same concept!