Calculation of Cooling Time for an AISI 304 Steel Heating Rod

Sayantan GhoshAvinesh Ojha

IntroductionDescription of Project: This experiment is concerned with the

cooling of an AISI 304 steel heating rod. We want to see how much time the rod takes to cool from an initial temperature to final temperature in the laboratory and compare it to the analytical results. The experiment mainly focuses on heat transfer between the heated cylinder and the environment in an external cross flow of air. This is an important problem in the real world because steel rods need to be moved from one place to another in factories. The final deformation processes are carried out at specific temperatures. Knowing the time taken to reach these temperatures is extremely important for the industry.

MaterialsCylindrical heating rod.Fan.Thermocouple.Velocity anemometer.Wattmeter.

Experimental SetupA heating rod was taken and heated by

passing electricity through it.The rod was heated until a maximum

temperature of 442˚ C.The fan was operated and the rod was

allowed to cool to a steady temperature of 162 ˚C.

The velocity of the fan was noted to be 2830 ft/min.

Experimental Setup

Fig: Experimental setup Fig: Recording air velocity

•Convection.•Radiation.

AssumptionsAtmospheric pressure was assumed because all the values

given in the book are at atmospheric pressure.Velocity of the fan at the center is the average velocity of

air.Temperature of the wall, ceiling and floor was assumed to

be the same as the temperature of the air inside.

Convection Effects

Dimension of RodDiameter of rod = .0126 m

Velocity of Air Calculation

Velocity of air from the fan was calculated by using a velocity anemometer.

Velocity of air (V) = 2830 ft/s = 14.38 m/s

Density: CalculationPressure (P)= 0.85 atmT-surr (Temperature of air and walls)= 22 deg C= 295 KT-initial of rod= 442 ˚C T-final of rod= 160 ˚CT-avg (For calculation of Reynold’s number)

= (160+22)/2= 91 ˚C = 364 Kk of air@ 364 K= 0.0315 W/m.K

Reynolds Numberʋ (kinematic viscosity) of air @ 364 K= 23*10-6 m2/sRe= (V*D)/ ʋRe= (14.38 *.0126)/(23*10-6)= 7878

Nusselts Number CalculationFrom Table 7.2 in the book, for Re= 7878Pr= 0.694C= 0.193m= 0.618Nu= C * Rem * Pr 1/3

= 0.193*(7878)0.618 * (0.694)1/3 = 43.7

Convection-coefficient Calculation

h = (Nu*k)/D= (43.7*.0315)/.0126= 109 W/m2.K

Radiation Effects

Constants

ε= 0.88σ (Boltzmann’s constant)= 5.67*10-8 J/K

hr calculation

hr = σ * ε* (Ts+Tsurr)* (Ts2 + Tsurr2)

= 5.67*10-8 * 0.88 * ( 574+295) * ( 5742+2952)

= 18 W/m2.K

Combined Effect

hT = h+hr

= 109+18

= 127 W/m2.K

hT is the combined “h” for convection and radiation.

Calculation of Biot Number

T-avg (steel)= (442+162)/2 = 302 ˚C= 575 Kk of AISI 304 steel = 18 W/m2*KBiot Number for Cylinder = (h*(r/2)*k)

= (127*.0063)/(2*18)

=.0211< 0.1

Hence, Lumped Capacitance method can be used.

Calculation of time

Density(ρ) AISI 304 Steel = 7900 kg/m3

Cp AISI 304 Steel = 477 J/kg.KTime (t)= (ρ * Cp * r * (Tsurr- Tinitial of rod))/(hT * 2 * (Tsurr-T

final of rod))

= (7700*477* 0.0063 *420)/(127.3*2*138.2)

= 283 seconds

Experimental time Vs Calculated timeExperimental Time required for the process was recorded

to be 224 seconds.%Error = (Time Calculated - Time Experimental)*100/

Time Calculated

= (283-224)/283

= 20.84%

ConclusionThere is an error of 20.84% which is considerable. The possible reasons for this are given below:1.All the values were taken at atmospheric pressure but the atmospheric pressure of Provo is about 85% of that at sea level.2.There are different velocities of the fan at different cross section and the assumption that the velocity is average at the center may not be correct entirely.3.There might be error in the temperature sensor.4.There might be some error in the radiation calculation due to the assumption that the wall temperature is the same as room temperature.

RecommendationsPerform the experiments at standard conditions.Use devices that can measure the temperature of the walls

and the heated rod correctly.Take velocity measurements of air at different points and

use the mean of these velocities for Reynolds number calculations.

AppendicesFormulas.........................1Parameters………………….2References…………………..3

FormulasBiot Number for Cylinder = (h*(r/2)*k)Time (t)= (ρ * Cp * r * (Tsurr- Tinitial of rod))/(hT *2*(Tsurr-Tfinal of rod))

Re= (V*D)/ ʋNu= C * Rem * Pr 1/3

Propertiesk of air@ 364 K= 0.0315 W/m.KDensity(ρ) AISI 304 Steel = 7900 kg/m3

Cp AISI 304 Steel = 477 J/kg.K

ReferencesIncorpora, F.P., Dewitt D.P., et al.,

Fundamentals of Heat and Mass Transfer. New Jersey: Wiley, 2007. Print.