Lab # 5: Convection Heat Transfer Max Tenorio 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 long Insulation thickness: 0.813” 13 total thermocouples (1 broken) Connected to labview

Raw Data Units Run - 1 2 3 4 Current A 2.5 Voltage V 140 210 135   Run - 1 2 3 4 Current A 2.5 Voltage V 140 210 135 Pa fan inH2O 13.2 3.9 Pb plate 3.5 0.9 Pc test sec 2.7 3.1 1.1 T1 C 49.284 71.7899 61.2062 98 T2 51.681 77.642 65.6576 108.864 T3 53.486 81.9689 68.7393 116.241 T4 54.358 83.922 70.1089 119.572 T5 55.261 86.2335 71.821 123.37 T6 56.692 90.0934 74.3735 129.035 T7 66.038 88.3502 123.121 T8 72.319 130.436 81.9377 143.198 T9 24.662 29.7354 29.4553 33.5331 T10 74.02456 135.1535 87.80725 160.2529 T11 26.8405 33.2529 33.4397 39.3852 T12 74.716 137.066 90.1868 167.167 T13 25.035 30.2335 35.0895 Ttest section 37 48.5 38 39 Tamb 20 Pbarom atm

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

Heat Flux Method 1 q" in q"loss avg q" heat flux Run 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 1156.50 3521.37

Thermal Profile

Heat Flux Method 2 Requires Thermal Profiles 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. dTs(x)/dx q" (b) q" in (b) q"(d) assuming b is correct Run °K/m 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 4522.979 28.44389 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 Temperature The Bulk Air temperature is the average temperature of air in a section of pipe. 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

Heat Transfer Coefficient 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 Run 3 62856.41 Run 4 64987.74

Nusselt Number Ratio of convective to conductive heat transfer across the boundary Correlation Regular Run 1 229.13 153.48 Run 2 202.00 Run 3 141.36 71.91 Run 4 145.18 75.33

Friction factor Correlation Regular Run 1 0.017161 0.004274 Run 2 0.002137 Run 3 0.019957 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 0.002768 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 3690.965 202.00 0.002137 0.002768 Run 3 62856.41 1345.912 71.91 141.36 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 Calculations Run 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 0.0889 0.24638 0.0008354 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 3 q"loss avg C m^2K/W W/m^2 1 72.319 74.02455769 74.716 24.662 26.8405 25.035 47.657 47.18406 49.681 0.104513 455.989 451.4638 475.3549 460.936 Mass Flow Rate pi cp Di dTs(x)/dx q" kg/s J/kgK m °K/m W/m^2 1 0.038239 3.141593 1012 0.032614 5.2741 1992.005 x (m) Ts Tx Ts(x) - T(x) h (W/M^2K) 0.3175 49.284 38.251 11.033 134.884 0.714375 51.681 39.81474 11.86626 125.4123 1.0287 53.486 41.05323 12.43277 119.6978 1.196975 54.358 41.71625 12.64175 117.7191 1.36525 55.261 42.37928 12.88172 115.5261 1.533525 56.692 43.04231 13.64969 109.0263 1.7018 66.038 43.70534 22.33266 66.63671

Sample Calculations Re 1 Re=QD/VA Q 0.046171197 D 0.0326136 ν 1.57E-05 0.000835386 114957.27 Pr ν/α α 2.22E-05 7.08E-01 Nu Nu=0.023*Re^0.8*Pr^1/3 229.1302522 Nu=hD/k h 117.6476779 k 0.025 153.4765723 Friction factor f 0.01716141 p1 871.8115 p2 672.5403 air density 1.207427199 mass flow rate 0.038239322 L 1.7526 Equation 0.004273717 Stanton Number Correlation St 0.002701544 St=h/ρcpV 0.002103386