Lab Report: Forced Convection Heat Transfer

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Abstract:

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 non-dimensional 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.

Nomenclature:

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/m²·K
6	P	Pressure	Pa
7	T	Temperature	°C
8	g	Gravity acceleration	m/s²
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/m³

Introduction:

The convection heat transfer mode encompasses two mechanisms.

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In addition to energy transfer through random molecular motion (diffusion), energy is also transferred via the bulk, or macroscopic, motion of the fluid.

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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.

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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.

Objectives:

Measurement of forced convection heat transfer coefficient and Nusselt number inside a constant cross-section pipe.
Prediction of convection heat transfer inside a round pipe using non-dimensional parameters.

Theory:

When examining the heat transfer coefficient and deriving its mathematical expression, it is essential to consider the boundary layer, which adheres to the no-slip 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).

Methodology:

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.

Experimental Setup:

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:

Copper Pipe: A copper pipe with a constant cross-section was employed as the primary heat exchange surface. This pipe served as the medium for transferring heat from the electrical heater to the surrounding air.
Electrical Heater: An electrical heater was used to generate heat within the copper pipe. It was located within the pipe, heating the copper surface to a specified temperature.
Fan: A fan was strategically positioned to generate forced convection by blowing air over the heated copper surface. The airflow created by the fan was instrumental in enhancing heat transfer.
Orifice and Manometer: An orifice and a manometer were integrated into the setup to measure pressure drops across the system. These measurements provided valuable data for calculating flow rates and fluid properties.
Temperature Sensors (Thermocouples): A network of thermocouples was distributed along the length of the copper pipe. These sensors monitored and recorded temperature values at various points within the system, enabling the analysis of temperature gradients and heat transfer.
Voltage Control: The electrical heater was equipped with a voltage control system that allowed precise adjustments to the heating element's power input. This control mechanism was essential for regulating the heat generated within the copper pipe.
Digital Temperature Indicator: A digital temperature indicator was used to display real-time temperature readings from the thermocouples, ensuring accurate data collection.
Lab Room Environment: The entire experimental setup was conducted within a controlled laboratory environment. The ambient temperature and pressure in the lab room were measured and accounted for in the analysis.

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.

Procedure:

Start by setting up the apparatus at a specified flow rate (angle of closure) and an initial voltage of 50 V. Prior to commencing the experiment, record the ambient temperature and pressure in the laboratory. Allow the system to stabilize for approximately 15 minutes to ensure steady readings.
Record the pressure readings displayed on both the manometer and orifice meter gauges.
Measure the temperatures at various points indicated on the panel screen. Take the inlet temperature reading twice: once from a manometer and another from the main digital panel, both of which are connected to different thermocouples.
After recording the measurements at the initial flow rate and voltage, increase the voltage to 100 and wait for another 15 minutes to attain new steady-state readings.
Repeat the procedures conducted in the previous step but with the new values selected for the flow rate and voltage.
Wait for 2 minutes and capture readings under the same voltage and flow rate conditions as in one of the two preceding rounds to verify steady-state conditions and account for potential errors.

Results:

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
Laboratory Conditions	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.

Calculated Averages:

**Average Temperatures**
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

Thermophysical Properties of Air:

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.

Table 2: Calculations of the Experiment
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
Stanton Number (St)	Nu Prediction Error	%	54.34	36.62	24.58	15.67	10.28

Calculations:

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.

Sample of Calculations:

Table 3: Calculations of the Experiment
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).

Discussion:

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.

References:

Frank P. Incropera. Principles of Heat and Mass Transfer, "Convection", Global edition.
Mechanical Lab 1 Notebook. "Forced Convection Experiment" - 2020.

Lab Report: Forced Convection Heat Transfer. (2024, Jan 18). Retrieved from https://studymoose.com/document/lab-report-forced-convection-heat-transfer