Question

1. Quenching is a widely used method to increase yield strength and hardness of various materials. During this process, beside water and oil, air is also a widely used cooling fluid. With a knowledge of 4.5 °C/s average cooling rate's generating optimal results, determine the required roller diameter for this cooling rate of ductile iron from 825 °C to 300 °C while falling in 20 °C air with a speed of 1 m/s. Notes: - Use one of the suitable empirical correlations for convection coefficient around the cylindrical roller in crossflow. -Show validity of your assumptions and empirical correlations. -Refer the source of each property data that you use.

Answer 1

As per given data : dT 4.5 °C/s dy To Cinitial temperatured = 825ć Tf (final temperature) = 300°c Aio temperature = 20°C v= Air speed Assumption : : Assuming the air How out side the cylindrical roler is turbulant in nature Hence, the Empirical correlation for convection Coefficient around the cylindrical roller is 0.8 n 0.023 (Re) (Py) where n=0.3 for 08 cooling Nu 0.3 hd к CO-023(eved (eved] Leonardo from the property table of Air J/kg k Air at zoc K= 0.02514 W/mk (p= 1.007 KJ 11825x10-5 Pr = 0.7309 Pair = 1.204 al = kg/m3

hrd 0.8 0.3 0.0231.204 Xixd 1.825 X10-5 *(0.7309) 0002514 0.8 hd = 3,77 Xd -0.2 h. 3-77x d - balance equation for lumped By using energy parameter me di h ASA * (To-T6) x (To-Tf) - de where, iron Im = 니 A SA= -0.2 6446 Жак = m = lion Piron = 7874 kg/m3 Piront - I d²XL Volume of cylindrical roller = Surface area S.A (surface area =d of cylindrical roller of roller) de diameter of roller Put all value in equation ③ C = specific heat of Piront a la xd TV 3.77x0x7d4 iron = 0.46 KJ X(To-TF length of cylindre will cance from both side 7874x54x0.46xlox 4.5 = 3:17x4°258AX (825-309) 3.777 525 X4 -4 = 4085 Xlo joo2 7874x 0:46X103x4-5 d = 4.85 x154 = 1.73X10m Are 4 व - 1:2 dia, of cyl
Properties of air taken from the below table

Properties of air at 1 atm pressure Temp T. °C Thermal Density Specific Heat Conductivity Air of Air Air p. kg/m2 CpJ/kg-K kW/m-K Thermal Dynamic Kinematic Prandti Diffusivity Air Viscosity Air Viscosity Air Number Air kg/m-s v. m/s Pr a m²/s - 150 2.866 983 0.01171 4.158 x 10-6 8.636x 10-5 3.013 x 10-6 0.7246 100 2.038 966 0.01582 8.036x 10-6 1.189 x 10-5 5.837 x 10-6 0.7263 50 1.582 999 0.01979 1.252 x 10-5 1.474 x 10-5 9.319 x 10-6 0.7440 - 40 1.514 1002 0.02057 1.356 x 10-5 1.527 x 10-5 1.008 x 10-5 0.7436 30 1.451 1004 0.02134 1.465 x 10-5 1.579 x 10-5 1.087 x 10-5 0.7425 - 20 1.394 1005 0.02211 1.578 x 10-5 1.630 x 10-5 1.169 x 10-5 0.7408 - 10 1.341 1006 0.02288 1.696 x 10-5 1.680 x 10-5 1.252 x 10-5 0.7387 0 1.292 1006 0.02364 1.818 x 10-5 1.729 x 10-5 1.338 x 10-5 0.7362 5 1.269 1006 0.02401 1.880 x 10-5 1.754 x 10-5 1.382 x 10-5 0.7350 10 1.246 1006 0.02439 1.944 x 10-5 1.778 x 10-5 1.426 x 10-5 0.7336 15 1.225 1007 0.02476 2.009 x 10-5 1.802 x 10-5 1.470 x 10-5 0.7323 20 1.204 1007 0.02514 2.074 x 10-5 1.825 x 10-5 1.516 x 10-5 0.7309 25 1.184 1007 0.02551 2.141 x 10-5 1.849 x 10-5 1.562 x 10-5 0.7296 30 1.164 1007 0.02588 2.208 x 10-5 1.872 x 10-5 1.608 x 10-5 0.7282

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