A20-m long cylindrical titanium rod with diameter 3.0 cm initially at 600 k is immersed in large bath of engine oil at 320 k. the oil has a convective heat transfer coefficient of 24.0 w/m²-k; other properties can be found in table a.5. the properties of titanium can be found in table a.1 you may ignore heat transfer by radiation, and heat transfer from the flat ends of the cylinder. a. can lumped capacitance by used to solve for t(t)? b. determine the t(r) temperature profile for the rod after 20 seconds being immersed in the oil, and 5.0 minutes after immersion (sketch this on a t(r) vs. r plot; be as accurate as possible). c. how long will it take for the rod to cool to 400 k? d. if the oil were mixed so that it had turbulent flow and hoil = 1480 w/m2-k, show qualitatively on a plot how the temperature profiles t(r) would look. discuss any differences with your answer in b. note: you should use properties of the rod at 600 k. since density is only listed at 300 k, use that.