PROBLEM 7: 4-58 A long iron rod (p = 7870 kg/m³, cp = 447 J/kg-K, k= 80.2 W/m-K, and a = 23.1 x 10-6 m²/s) with diameter of 25 mm is initially heated to a uniform temperature of 700°C. The iron rod is then quenched in a large water bath that is maintained at constant temperature of 50°C and convec- tion heat transfer coefficient of 128 W/m².K. Determine the time required for the iron rod surface temperature to cool to 200°C. Solve this problem using analytical one-term approxi- mation method (not the Heisler charts). Water, 50°C h = 128 W/m².K Iron rod What is the Biot Number Bi? Is the lumped body analysis valid?

P34.9 Two parallel metal plates separated by 1 cm are held at 300, and 298 K, respectively. The space between the plates is filled with N2 (or = 0.430 nm² and Cv, m = 5/2 R). Cv.m Determine the heat flux between the two plates in units of W cm².

A long 3-mm diameter rod of steel (ρ = 7840 kg/m3, c = 460 J/kgK, k = 43 W/mK)has a uniform initial temperature of 650C. The rod is then suddenly immersed in alarge container of 25C water. The hot rod causes the water immediately surroundingthe rod to boil, giving rise to a heat transfer coefficient of 5600 W/m2K. The boilingstops when the rod reaches a temperature of 100C, at which time the heat transfercoefficient becomes 750 W/m2K. Find the time period during which boiling occursand the total time required for the rod to reach a temperature of 40C. Use acharacteristic length for this problem.

A 50-mm thick plate of carbon steel (AISI 1010) is annealed with a reheat stage taking the steel from its initial uniform temperature of 200 C to a minimum final temperature of 550 C. HEating is effected in a gas-fired furnace where products of combustion at Tamb = 800 C maintain a convection coefficient of h = 100 W/m^2K on both sides of the plate. How long should the plate be left in the furnace? Substantiate with relevant analysis and calculations.