14:650:432:02

Lab # 5: Convection Heat Transfer

Max Tenorio

Purpose• Convection Heat Transfer occurs almost

everywhere• Examine characteristics of heat transfer to

turbulent air flow through a uniformly heated pipe

• Measure temperature distribution for two air flow rates and two power settings to calculate the heat transfer coefficient, Reynolds, Stanton, and Prandtl numbers and friction factor.

Setup

Specifications

Total 5.75 feet longInsulation thickness: 0.813”13 total thermocouples (1 broken)Connected to labview

Raw DataUnits        

Run - 1 2 3 4

Current A 2.5 4 2.5 4

Voltage V 140 210 135 210

Pa fan inH2O 13.2 13.2 3.9 4

Pb plate inH2O 3.5 3.5 1 0.9

Pc test sec inH2O 2.7 3.1 1 1.1

T1 C 49.284 71.7899 61.2062 98

T2 C 51.681 77.642 65.6576 108.864

T3 C 53.486 81.9689 68.7393 116.241

T4 C 54.358 83.922 70.1089 119.572

T5 C 55.261 86.2335 71.821 123.37

T6 C 56.692 90.0934 74.3735 129.035

T7 C 66.038 88.3502 71.821 123.121

T8 C 72.319 130.436 81.9377 143.198

T9 C 24.662 29.7354 29.4553 33.5331

T10 C 74.02456 135.1535 87.80725 160.2529

T11 C 26.8405 33.2529 33.4397 39.3852

T12 C 74.716 137.066 90.1868 167.167

T13 C 25.035 30.2335 29.7354 35.0895

Ttest section C 37 48.5 38 39

Tamb C 20 20 20 20

Pbarom atm 1 1 1 1

Mass Flow Rate

Mass Flow Rate (kg/s) Volume Flow Rate (L/s)Run 1 0.038239322 46.17119692Run 2 0.038239322 46.17119692Run 3 0.020908521 25.24551677Run 4 0.021617485 26.10153888

Heat FluxMethod 1

q" in q"loss avg q" heat flux

Run W/m^2 W/m^2 W/m^2

1 1949.11 460.94 1488.18

2 4677.87 986.90 3690.97

3 1879.50 533.59 1345.91

4 4677.87 1156.50 3521.37

Thermal Profile

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

Thermal Profile 1

PipeInner InsulationOuter Insulation

Position (in)

Temperature (°C)

0 10 20 30 40 50 60 70 800

20

40

60

80

100

120

140

160

Thermal Profile 2

PipeInner InsulationOuter Insulation

Position (in)

Temperature (°C)

0 10 20 30 40 50 60 70 800

102030405060708090

100

Thermal Profile 3

PipeInner InsulationOuter Insulation

Position (in)

Temperature (°C)

0 10 20 30 40 50 60 70 800

20406080

100120140160180

Thermal Profile 4

PipeInner InsulationOuter Insulation

Position (in)

Temperature (°C)

Heat FluxMethod 2

Requires Thermal Profiles

dTs(x)/dx q" (b) q" in (b) q"(d)

assuming b is

correct

Run °K/m W/m^2 W/m^2 W/m^2 % error

1 5.2741 1488.175 1949.11 1992.005 33.85554

2 12.672 3690.965 4677.87 4786.16 29.67233

3 9.1567 1345.912 1879.5 1891.012 40.50035

4 21.183 3521.365 4677.87 4522.979 28.44389

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.450

60

70

80

90

100

110

120

130

f(x) = 21.1825880255534 x + 94.3726383647799

f(x) = 9.15673748328628 x + 59.2626808176101

f(x) = 12.6715198336057 x + 68.8739742138365

f(x) = 5.27410488783243 x + 48.0553616352201

Pipe Thermal Profile Run 1

Linear (Run 1)

Run 2

Linear (Run 2)

Run 3

Linear (Run 3)

Run 4

Linear (Run 4)

Position (m)

Temperature (°C)

Discussion b: The heat flux values in b and d are different because b uses raw experimental values to perform the heat balance and assumes that for q”out, the maximum heat loss is uniform for the entire circumference for the pipe, when in reality the heat loss is most likely not uniform through a cross section. Additionally, d assumes laminar flow and relies on a constant specific heat capacity for air and a constant flow rate.

Although the percent error is somewhat high, it is worth noting that the heat flux from d is close to the q”in from b. The difference is most likely equipment error and incorrect values

Bulk Air TemperatureThe Bulk Air temperature is the average temperature of air in a section of pipe.

xcm

qDTxT

p

i

1)(

Tx Tx Tx Tx

x (m) 1 2 3 4

0.3175 38.25 51.60 40.07 44.24

0.714375 39.81 55.48 42.66 50.78

1.0287 41.05 58.55 44.70 55.97

1.196975 41.72 60.20 45.80 58.74

1.36525 42.38 61.84 46.90 61.52

1.533525 43.04 63.49 47.99 64.29

1.7018 43.71 65.13 49.09 67.07

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

20

40

60

80

100

120

140

Wall vs Bulk Temperatures

Run 1 WallRun 1 BulkRun 2 WallRun 2 bulkRun 3 WallRun 3 BulkRun 4 WallRun 4 Bulk

Position (m)

Temperature (°C)

Heat Transfer Coefficient

)()( xTxT

qh

s

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

Difference Between Wall and Bulk Temperatures

1234

Position (m)ΔT (°C)

1 2 3 4

h3 119.6978 157.625 55.99791 58.42102

h4 117.7191 155.5743 55.36919 57.88724

h5 115.5261 151.3197 54.002 56.93004

havg 117.648 154.84 55.123 57.7461

Discussion a: The wall temperature is easily measured using the thermocouples and the bulk temperature is the average temperature of air in that cross section. They vary; the wall temperature will be higher because it is closer to the heating element and the temperatures are higher in general because energy is being transferred to the air as it travels. The beginning and end points are skewed because of end effects. The slopes of both are constant in the middle section because the rate at which temperature changes is the same for both the wall and air inside the tube.

Reynolds Number

Ratio of inertial forces (Vρ) to viscous forces (μ / L)

Reynolds Number

Run 1 114957.3

Run 2 114957.3

Run 3 62856.41

Run 4 64987.74

Nusselt NumberRatio of convective to conductive heat transfer

across the boundary

Correlation Regular

Run 1 229.13 153.48

Run 2 229.13 202.00

Run 3 141.36 71.91

Run 4 145.18 75.33

Friction factor

Correlation Regular

Run 1 0.017161 0.004274

Run 2 0.017161 0.002137

Run 3 0.019957 0

Run 4 0.019792 -0.00334

Stanton Number

Ratio of heat transferred into a fluid to the thermal capacity of fluid

Correlation Regular

Run 1 0.002702 0.002103

Run 2 0.002702 0.002768

Run 3 0.003142 0.001802

Run 4 0.003116 0.001826

Calculated Values

Re

q“ (w/m^2K

) Nu, exp. Nu, corr. f, exp. f, corr St, exp. St, corr.

Run 1 114957.3 1488.175 153.48 229.13 0.004274 0.017161 0.002103 0.002702

Run 2 114957.3 3690.965 202.00 229.13 0.002137 0.017161 0.002768 0.002702

Run 3 62856.41 1345.912 71.91 141.36 0 0.019957 0.001802 0.003142

Run 4 64987.74 3521.365 75.33 145.18 -0.00334 0.019792 0.001826 0.003116

Discussion c: For the Nusselt Number and friction factor, the experimental values are much lower than the correlation values. These most likely result from equipment error, since the friction factors for runs 3 and 4 drop to zero and even go negative, meaning the pressure at the exit is higher than the entrance pressure. As far as the Stanton number goes, the values for the high speed regions (runs 1 and 2) are close, but the values for low speed are off, meaning that less energy was transferred into the air than anticipated.

Sample CalculationsRun 1

Pa Fan Pb Plate Δh (m) A (m^2)g (m/s^2)

Air Density (kg/m^3)

Water Density (kg/m^3)

Flow Coefficient

Mass Flow Rate (kg/s)

1 0.33528 0.08890.2463

80.0008354 9.8 1.207427199 998.2071 0.6 0.038239322

T8 T10 T12 T9 T11 T13 ΔT1 ΔT2 ΔT3 R q" loss 1 q" loss 2 q" loss 3q"loss avg

C C C C C C C C Cm^2K/W W/m^2 W/m^2 W/m^2 W/m^2

172.31

974.0245576

9 74.716 24.662 26.8405 25.035 47.65747.1840

6 49.6810.10451

3 455.989451.463

8475.354

9460.93

6

Mass Flow Rate pi cp Di dTs(x)/dx q"kg/s J/kgK m °K/m W/m^2

10.03823

93.14159

3 10120.03261

4 5.27411992.00

5

x (m) Ts TxTs(x) - T(x)

h (W/M^2K)

0.3175 49.284 38.251 11.033 134.8840.714375 51.68139.8147411.86626125.4123

1.0287 53.48641.0532312.43277119.69781.196975 54.35841.7162512.64175117.7191

1.36525 55.26142.3792812.88172115.52611.533525 56.69243.0423113.64969109.0263

1.7018 66.03843.7053422.3326666.63671

Sample CalculationsRe 1Re=QD/VA Q 0.046171197

D 0.0326136ν 1.57E-05A 0.000835386Re 114957.27

Prν/α α 2.22E-05

Pr 7.08E-01

NuNu=0.023*Re^0.8*Pr^1/3 Nu 229.1302522Nu=hD/k

h 117.6476779D 0.0326136k 0.025Nu 153.4765723

Friction factorf 0.01716141

p1 871.8115p2 672.5403air density 1.207427199mass flow rate 0.038239322L 1.7526

Equation f 0.004273717

Stanton NumberCorrelation St 0.002701544St=h/ρcpV St 0.002103386