Answer Happy

Question 3: THERMOFLUIDS - HEAT TRANSFER An array of rods is immersed in a flowing fluid as shown in Fig. Q3. The rods all have one of their individual ends fused at a base that is maintained at a temperature of To=115°C. The state of the fluid is also given. Consider that the length Los of each of these rods are sufficiently long to be considered "infinitely long”. Take K= 400 W/mK and D=15 mm. = 2 ho = 140W/mK T. = 300K 11,00 K D L2,00 K2 To = 115°C = D2 L3,00 K3 D3 Fig. Q3: An array of “infinitely long” thin rods in a fluid Q3(a) A thin rod with a fixed thermal (Dirichlet) boundary condition on one end is surrounded by a stream of fluid. By justification or from first principles, how would you carry out analytical calculations to determine the temperature profile and heat transfer if the rod is infinitely long? Hint: Use schematics and state any assumptions in your explanations. You do not have to derive but understand the steps.
Fig. 03: An array of "infinitely long thin rods in a fluid Q3(a) A thin rod with a fixed thermal (Dirichlet) boundary condition on one end is surrounded by a stream of fluid. By justification or from first principles, how would you carry out analytical calculations to determine the temperature profile and heat transfer if the rod is infinitely long? Hint: Use schematics and state any assumptions in your explanations. You do not have to derive but understand the steps. Q3(b) Using Mathematical calculations and commentaries, justify if the following are true or false: (i) If K1 = 2K2 = 5K3=K & D = D2=D3 =D then is 11,00 > L2,00 L3,00? (ii) If K1 = 2K2= 5K3=K & Di = 4D2= 5D3=D then is L1,00 < L2,60 < L3,00? (iii) For any one of the rods, if Ty is fixed then is 3 xq;(h) = 9:(3 h)? i.e. increasing the flow rate of the surrounding fluid in a way to triple the heat transfer coefficient will remove thrice as much heat as the current condition. (iv) The temperature profile at a position x from the base of the rod can be read as T(x). For rod 1, 2, and 3, these would be Ty(x), T2(x) and Tz(x) respectively. Then: Is Tz(x = 0.5L1,00) = T2(x = 0.25L1,00)? (i.e. is the temperature profile at 25% and 50% of the infinite length the same?) Is T1(x = 0.121,00) = T2(x = 0.5L2,00)? Is Tz(x = 0.25L3,00) = Tz(x = 0.411,00)? = Page 3 of 6