ME2355 HEAT TRANSFER BY FREE CONVECTION - Computer Programming

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# heat transfer by free convection

Date:
aim:
To find the heat transfer coefficient under natural convection environment.

description of apparatus:
Convection is a mode of heat transfer where by a moving fluid transfers heat from a surface.  When the fluid movement is caused by density differences in the fluid due to temperature variations, it is called FREE or NATURAL CONVECTION.
This apparatus provides students with a sound introduction to the features of free convection heat transfer from a heated vertical rod.  A vertical duct is fitted with a heated vertical placed cylinder.  Around this cylinder air gets heated and becomes less dense, causing it to rise.  This in turn gives rise to a continuous flow of air upwards in the duct.  The instrumentation provided gives the heat input and the temperature at different points on the heated cylinder.
Specification:
Length of cylinder = 50 cm

PROCEDURE:
1.      Switch on the unit and adjust the regulator to provide suitable power input.
2.      Allow some time for the unit to reach steady state condition.
3.      Note the temperature of inlet air, outlet air and temperatures along the heater rod.
4.      Note ammeter and voltmeter readings.
5.      For different power inputs the experiments may be repeated.
The readings are tabulated as below: -

FORMULA USED:
The power input to heater = V X A = hAΔt
Where A = Area of heat transfer = χdl
D = Dia. Of heater rod = 40mm
L = Length of heater rod = 500mm
Δt= Avg. temp. Of heater rod – Avg. temp. of air.
H = Overall heat transfer co-efficient.

# THEORETICAL METHOD

Using free convection correlations for vertical cylinders.
Nu = hl / K = 0.53(GrPr)1/4 for GrPr < 105
Nu = hl / K = 0.56(GrPr)1/4 for 105 < GrPr < 108
Nu = hl / K = 0.13(GrPr)1/3 for 108 < GrPr < 1012
Characteristic length is the height of the cylinder (l)
K = Thermal conductivity of air
P = Prandtl number of air
Gr = ßgl3 Δt / υ2
ß = 1 / Mean temp. of air + 273 K
The properties of air at mean temperature = (T1+T2+T3+…+T8 )/ 8
Hence h can be evaluated.

NATURAL CONVECTION:
V         A         T10c     T20c     T30c     T40c     T50c     T60c
85        0.38     30        55        60        65        63        38
ß = 1/51.8 + 273 = 3 X 10-3
Gr = ßgl3 Δt / υ2                       Δt = [(T2 + T3 + T4 + T5) / 4 ]– [(T1+F6)/2]
= 3 X 10-3 X 9.81 X (0.5)3 X 26.75 / (17.96 X 10-6)2
= 3.05 X 108
where l = length of heater
υ = Kinematic viscosity of air at mean temp.
Pr = from data book for air mean temp.
= 0.698
Hence GrPr = 2.13 X 108
Hence using free convection correlations
Nu = hl / K = 0.13 (GrPr)1/3 where K is the Thermal conductivity of air at mean temp.
= 72.82
Overall heat transfer co-efficient h = 72.82 X 28.26 X 10-3 / 0.5 = 4.11 w/m2-0c

Result:
The heat transfer coefficient is found to be -------------- W/m2K