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The heat transfer coefficient plays a crucial role in distinguishing between forced convection and free convection. External forces significantly influence its value, while free convection is characterized by the absence of external forces. This experiment focuses on forced convection to calculate the heat transfer coefficient, as it determines the fluid's ability to transfer heat efficiently. Additionally, we calculate two important nondimensional numbers closely associated with the heat transfer coefficient: the Nusselt number and the Stanton number.
Our findings indicate that the temperature difference between the fluid and the surface has a substantial impact on the accuracy of the heat transfer coefficient value.
No.  Symbol  Physical Meaning  Unit 

1  Re  Reynolds number   
2  Nu  Nusselt number   
3  Pr  Prandtl number   
4  St  Stanton number   
5  h  Heat transfer coefficient  W/m^{2}·K 
6  P  Pressure  Pa 
7  T  Temperature  °C 
8  g  Gravity acceleration  m/s^{2} 
9  V  Velocity  m/s 
10  ṁ  Mass flow rate  Kg/s 
11  CP  Specific heat  J/K 
12  k  Thermal conductivity  W/m·K 
13  ⍴  Density  kg/m^{3} 
The convection heat transfer mode encompasses two mechanisms.
In addition to energy transfer through random molecular motion (diffusion), energy is also transferred via the bulk, or macroscopic, motion of the fluid.
Convection heat transfer can be categorized based on the nature of the flow: forced convection occurs when the flow is induced by external means, such as a fan, pump, or atmospheric winds. Conversely, free (or natural) convection arises from buoyancy forces driven by density variations resulting from temperature fluctuations in the fluid.
Convection is closely associated with the heat transfer coefficient (h), which represents the proportionality constant between the heat flux and the thermodynamic driving force for heat flow.
Forced convection typically exhibits a relatively high heat transfer coefficient, while free convection is characterized by a lower coefficient. This discrepancy is attributed to the significant inertia forces acting on the boundary layer in forced convection due to external forces, whereas free convection relies on buoyancy forces, resulting in smaller effects on the heat transfer coefficient.
In this experiment, our focus is on forced convection, where the heat transfer coefficient assumes paramount importance due to its strong correlation with external forces.
When examining the heat transfer coefficient and deriving its mathematical expression, it is essential to consider the boundary layer, which adheres to the noslip condition. In this layer, direct contact occurs between the working fluid and the surface being either cooled or heated. The heat transfer coefficient within the boundary layer can be defined as:
h = k_{f} (∂T/∂y)_{ y=0} / (T_{s}  T_{∞})
Hence, the conditions within the thermal boundary layer, particularly the wall temperature gradient (∂T/∂y)_{ y=0}, govern the rate of heat transfer across the boundary layer. Since (T_{s}  T_{∞}) remains constant, independent of x (distance along the surface), while δ_{t} increases with x, temperature gradients within the boundary layer must decrease with increasing x. Consequently, the magnitude of (∂T/∂y)_{ y=0} decreases with increasing x, resulting in a decrease in both q_{s'} and h with increasing x.
Another significant parameter to be measured and discussed is the Nusselt number (Nu). The Nusselt number is closely related to the heat transfer coefficient and represents the ratio between the heat transfer rate for pure convection and the heat transfer rate for pure conduction. It is also a function of the Reynolds number (Re) and the Prandtl number (Pr).
The experimental setup is described below, and the notations used in Figure 2 are explained.
Component  Description 
Orifice and Manometer  Measurement components for pressure drop determination. 
Voltage Switch  Control switch for the experiment. 
Local Temperature Indicator  Device indicating the local temperature within the system. 
Digital Screen  Display screen providing experimental readings. 
The experimental setup for this study involved a controlled system designed to investigate forced convection heat transfer between air and a heated copper surface. The setup comprised several key components:
The setup was carefully calibrated, and data were collected at various flow rates and voltage settings to investigate the heat transfer coefficient, Nusselt number, and other relevant parameters. The controlled conditions and systematic data collection process allowed for a comprehensive analysis of forced convection heat transfer in the experimental system.
The experimental readings obtained during the study are presented in Table 1 below:
Category  Parameter  Unit  Test 1  Test 2  Test 3  Test 4  Test 5 

Laboratory Conditions  Atmospheric Pressure  Pa  101320  101320  101320  101320  101320 
Ambient Temperature  °C  20  20  20  20  20  
Flow Conditions  Test Number (X)  1  2  3  4  5  
Orifice Pressure Drop  mm H2O  47  47  45  44  45  
Inlet Temperature (Test Section)  °C  30  30  32  31.8  30  
Heater Voltage  Volt  50  70  100  150  200  
Heater Current  Ampere  1.00  1.35  1.95  2.95  3.90  
Thermocouples  Outer Surface of Copper Tube (T1)  °C  36.8  38  43.5  51.6  60.6 
Outer Surface of Copper Tube (T2)  °C  38.3  41.1  50.1  66.5  86.1  
Outer Surface of Copper Tube (T3)  °C  38.7  41.7  52.1  70.8  93.4  
Outer Surface of Copper Tube (T4)  °C  39.2  42.6  53.6  74.6  100.4  
Outer Surface of Copper Tube (T5)  °C  39.4  42.7  54.4  76.5  103.5  
Outer Surface of Copper Tube (T6)  °C  39.1  41.4  51.9  70.7  93.5  
Outer Surface of Copper Tube (T7)  °C  38.5  41.2  51.3  70  92.1  
Inner Surface Insulation (T8)  °C  33  32.6  34.5  33.9  32.4  
Inner Surface Insulation (T10)  °C  41.3  48.7  67.8  107.1  154.5  
Inner Surface Insulation (T12)  °C  41.9  52.6  77.4  129.6  187.9  
Outer Surface Insulation (T9)  °C  25.5  25.3  26  25.6  25.5  
Outer Surface Insulation (T11)  °C  29.3  32.6  40  55.3  75.5  
Outer Surface Insulation (T13)  °C  29.5  33  42  60.4  79.2  
Tranverse Centrline (T14)  °C  35.7  36.3  40.9  45.1  49.8  
Averages  Outer Surface of Copper  °C  38.57  41.24  50.99  68.67  89.94 
Inner Surface Insulation  °C  38.73  44.63  59.90  90.20  124.93  
Outer Surface Insulation  °C  28.10  30.30  36.00  47.10  60.07  
Average Fluid Temperature  °C  32.85  33.15  36.45  38.45  39.90 
Table 1 presents the collected data, including ambient temperature, atmospheric pressure, orifice pressure drop, inlet temperature, heater voltage, heater current, and temperatures from 14 thermocouples. Averages for each section have been calculated to determine the respective temperature values for subsequent calculations.
Location  Average Temperature (°C) 

Outer surface of copper  38.57 
Inner surface insulation  38.73 
Outer surface insulation  28.10 
Average fluid temperature  32.85 
Prior to performing calculations, it is essential to refer to the thermophysical properties of gases at atmospheric pressure, as documented in the appendices of the Fundamentals of Heat and Mass Transfer textbook. These properties include air viscosity, thermal conductivity, specific heat, and Prandtl number.
Category  Parameter  Unit  Test 1  Test 2  Test 3  Test 4  Test 5 

From Tables  Air Density  kg/m³  1.2049  1.2049  1.2049  1.2049  1.2049 
Air Viscosity  Pa·s  0.00001811  0.00001811  0.00001811  0.00001811  0.00001811  
Air Thermal Conductivity  W/m·K  0.02574  0.02574  0.02574  0.02574  0.02574  
Specific Heat  kJ/kg·K  1.005  1.005  1.005  1.005  1.005  
Flow Conditions  Test Number  1  2  3  4  5  
Heated Pipe Length  m  1.685  1.685  1.685  1.685  1.685  
Pipe Diameter (Dp)  m  0.076  0.076  0.076  0.076  0.076  
Pipe Cross Sectional Area (A1)  m²  0.004538  0.004538  0.004538  0.004538  0.004538  
Orifice Diameter (Do)  m  0.04  0.04  0.04  0.04  0.04  
Orifice Cross Sectional Area (A2)  m²  0.001257  0.001257  0.001257  0.001257  0.001257  
Pipe Surface Area  m²  3.0191  3.0191  3.0191  3.0191  3.0191  
Orifice Meter Coefficient of Discharge (Dc)  0.613  0.613  0.613  0.613  0.613  
Operating Conditions  Air Averaged Velocity in Heated Pipe  m/s  27.717  27.717  27.121  26.818  27.121 
Air Mass Flowrate  kg/s  0.0267  0.0267  0.0261  0.0259  0.0261  
Average Pipe Surface Temperature  °C  38.571  41.243  50.986  68.671  89.943  
Average Fluid Bulk Temperature  °C  32.850  33.150  36.450  38.450  39.900  
Experimental  Heat Generated by Electrical Heater  W  50.0  94.5  195.0  442.5  780.0 
Heat Lost Through Lagging  W  5.985  8.067  13.452  24.259  36.510  
Net Heat Transfer  W  44.015  86.433  181.548  418.241  743.490  
Heat Actually Gained by Air  W  153.047  169.157  233.829  345.525  520.203  
Thermal Losses Percentage  %  11.970  8.537  6.898  5.482  4.681  
Heat Flux  W/m²  259.837  510.244  1071.746  2469.035  4389.099  
h (Heat Transfer Coefficient)  W/m²·K  45.415  63.049  73.732  81.698  87.707  
Nu  56.460  78.382  91.664  101.567  109.037  
Analytical  Reynold's Number (Re)  54686.22  54686.22  53510.04  52912.14  53510.04  
Prandtl Number (Pr)  0.709  0.709  0.709  0.709  0.709  
Nu  123.664  123.664  121.532  120.444  121.532  
Stanton Number (St)  0.00146  0.00202  0.00242  0.00271  0.00287  
Nu Prediction Error  %  54.34  36.62  24.58  15.67  10.28 
After obtaining the necessary operational data, such as average velocity and mass flow rate for the air, we proceeded with the experimental calculations. These calculations allowed us to determine the heat transfer, heat flux, experimental heat transfer coefficient (h_{exp}), Nusselt number (Nu), and Stanton number (St).
Subsequently, we performed analytical calculations, commencing with the determination of the Reynolds number (Re) and Prandtl number (Pr), which were obtained from reference tables. With these values, we calculated the analytical Nusselt number (Nu) and analytical heat transfer coefficient (h_{theo}).
The prediction error of the Nusselt number was then calculated using the experimental and analytical Nu values.
No.  Symbol  Equation and Sample Calculation  Comments 

1  Air density (𝜌)  𝜌 = 𝑃 / (𝑅 × 𝑇) = 101320 / ((20 + 273) × 287) = 1.2049 kg/m³  From ideal gas equation 
2  Air average velocity (V̅)  V̅ = [𝜌𝑎𝑖𝑟𝐴²𝐷𝐶 / √(2Δ𝑃𝜌𝑎𝑖𝑟 (1  (𝐴₂/𝐴₁)²))] × [𝜌𝑎𝑖𝑟𝐴]ℎ𝑒𝑎𝑡𝑒𝑑 𝑝𝑖𝑝𝑒 = 27.717 m/s 

3  Air mass flow rate (ṁ)  ṁ = V̅ × [𝜌𝑎𝑖𝑟𝐴]ℎ𝑒𝑎𝑡𝑒𝑑 𝑝𝑖𝑝𝑒 = 0.0267 kg/s  
4  Heat generated by electrical heater (𝑞𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙)  𝑞𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 = 𝑉 × 𝐼 = 50 × 1 = 50 W  
5  Heat lost through lagging (𝑞𝑙𝑜𝑠𝑡)  𝑞𝑙𝑜𝑠𝑡 = 2𝜋 × 𝑘 × 𝐿 × Δ𝑇 × ln(𝑟𝑜𝑟𝑖) = 5.985 W  
6  Experimental heat transfer coefficient (ℎ𝑒𝑥𝑝)  ℎ𝑒𝑥𝑝 = 𝑞𝑓𝑙𝑢𝑥 / Δ𝑇𝑓𝑙𝑢𝑥 = 45.415 W/m²·K  
7  Reynold's number (𝑅𝑒)  𝑅𝑒 = 𝜌V̅D / 𝜇 = 54686.22  
8  Nusselt number (𝑁𝑢)  𝑁𝑢 = 0.023 𝑅𝑒⁰·⁸ 𝑃𝑟⁰·⁴ = 123.664  
9  Theoretical heat transfer coefficient (ℎ𝑡ℎ𝑒𝑜)  ℎ𝑡ℎ𝑒𝑜 = 𝑁𝑢 × 𝑘 / 𝐷 = 101.405 W/m²·K  
10  Stanton number (𝑆𝑡)  𝑆𝑡 = 𝑁𝑢 / (𝑅𝑒 × 𝑃𝑟) = 0.00319  
11  Nu prediction error (𝐸𝑟𝑟𝑜𝑟 %)  𝐸𝑟𝑟𝑜𝑟 % = (ℎ𝑡ℎ𝑒𝑜  ℎ𝑒𝑥𝑝) / ℎ𝑡ℎ𝑒𝑜 × 100 = 54.34% 
Table 3 provides a sample of calculations performed during the experiment. Key parameters, such as air density (𝜌), air average velocity (V̅), air mass flow rate (ṁ), heat generated by the electrical heater (q_{electrical}), heat lost through lagging (q_{lost}), experimental heat transfer coefficient (h_{exp}), Reynolds number (Re), Nusselt number (Nu), theoretical heat transfer coefficient (h_{theo}), Stanton number (St), and Nu prediction error, are presented along with sample equations and comments.
The calculations are based on fundamental properties such as room temperature (T = 20°C), air density (𝜌 = 1.2049 kg/m³), and the specific heat of air (C_{P} = 1.005 kJ/kg·K).
In this experiment, we determined the heat transfer coefficient under forced convection conditions by utilizing a fan to cool a copper surface heated by an electrical heater.
We initiated the experiment by collecting readings from thermocouples positioned throughout the experimental setup and subsequently calculated the average temperature for each section, as illustrated in Table 1.
The fundamental data required for our calculations were obtained from the thermophysical properties of gases at atmospheric pressure, accessible in the appendices of the Fundamentals of Heat and Mass Transfer textbook. These properties assisted us in calculating air velocity and mass flow rate, crucial in determining the heat transfer coefficient.
Table 2 summarizes our findings, showcasing the basic data, average velocity, and mass flow rate calculations for the air. Subsequently, we computed the heat transfer to the air, which allowed us to determine the experimental heat transfer coefficient. It is noteworthy that the heat transfer coefficient exhibited a minimum value in the first test and a maximum value in the last test, primarily influenced by the higher temperatures observed in the latter test compared to the earlier ones.
Following the completion of the experimental data analysis, we embarked on the analytical phase, commencing with the determination of the Nusselt number to subsequently find the heat transfer coefficient.
We examined the error between the experimental and analytical Nusselt numbers and observed a progressive decrease from its maximum value in the first test to its minimum value in the last test, attributed to temperature variations. The higher temperatures in the last test resulted in more accurate measurements, as the temperature disparity between the air and copper surfaces increased.
Our conclusion is that higher temperature differences between the copper and the air lead to more precise and accurate heat transfer coefficient values. These findings highlight the significance of temperature variation in forced convection heat transfer experiments.
Lab Report: Forced Convection Heat Transfer. (2024, Jan 18). Retrieved from https://studymoose.com/document/labreportforcedconvectionheattransfer
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