Abstract: The Purpose Of Performing This Experiment Is To De

Abstractthe Purpose Of Performing This Experiment Is To Determine Exp

The purpose of performing this experiment is to determine experimentally the relationship between the Nusselt number and Reynolds number for a heated cylinder that is subjected to cooling by a cross flow of air. The experiment involves varying conditions such as pressure restrictions, free stream velocity, and voltage settings, with the data collected transferred into tables. As flow becomes more restricted across different arrangements of plates, both pressure and free stream velocity decrease, leading to a decline in the Nusselt number (NuD), which is directly proportional to the Reynolds number (Re). The experimental results show that as voltage increases, errors in the Nusselt number tend to increase, with the largest percentage error being 23.7% at 65V, indicating deviations from theoretical correlations. The data, fitted to power law equations, reveal a maximum error of 49.2% in the ratio of NuD to Pr^{1/3}, highlighting discrepancies likely due to assumptions such as neglecting radiative heat transfer and elevation effects. The Prandtl number remained relatively constant, within 5%, throughout various experimental conditions, with a maximum calculated percentage error of 0.86%. The Reynolds number's experimental value diverges from the theoretical by approximately 6.7% in the open end at 35V setup, primarily due to assumptions about pressure and velocity. Overall, the experiment validates the trend that increased flow restriction lowers Re and NuD, consistent with flow physics, but also emphasizes the inherent uncertainty in experimental measurements and the need for careful calibration and consideration of radiative effects.

Paper For Above instruction

The thermal convection around a heated circular cylinder within a cross-flow environment plays a vital role in various engineering applications, ranging from heat exchangers to aerodynamic heating management. Understanding the relationship between the Nusselt number (NuD), a dimensionless measure of convective heat transfer, and the Reynolds number (Re), a measure of flow regime, can significantly influence design and operational efficiency. The experiment detailed herein aimed to quantify this relationship through a systematic analysis of cooling behavior in a wind tunnel setup, involving variable flow restrictors and electrical voltage controls. These variables collectively modulate the free stream velocity and, consequently, the heat transfer phenomena observed on the heated cylinder surface.

This research was motivated by the necessity to validate existing theoretical correlations, often expressed via power law equations, and to assess their applicability under varying operational conditions. The primary experimental methodology involved measuring temperature distributions through thermocouples placed at strategic locations around the cylinder, along with pressure readings via manometers. The wind tunnel setup used multiple restrictor plates to create different flow conditions, thereby enabling the analysis of flow-dependent heat transfer characteristics. Data acquisition was performed at three distinct voltage settings, corresponding to different free stream velocities, with multiple readings taken after reaching steady state to ensure data reliability.

The collected data indicated a consistent declining trend in the Nusselt number as flow restrictions increased, directly correlating to a decrease in Reynolds number, reinforcing the fundamental physics of forced convection. Specifically, the measured NuD values showed a maximum divergence of 23.7% from theoretical predictions at a voltage setting of 65V, highlighting potential factors such as heat radiation and assumptions about negligible elevation differences that may contribute to errors. Moreover, the power law coefficients, C and n, derived through curve fitting, deviated substantially from theoretical values, with the largest errors reaching 588% in C at 50V—suggesting that experimental uncertainties and model limitations impacted the accuracy of these parameters.

A critical element of the analysis involved comparing experimental and theoretical values of the dimensionless ratios, such as NuD/Pr^{1/3} and the Reynolds number. The maximum percentage error of approximately 6.7% in Re at the 35V setting underscores the influence of assumptions regarding flow velocity calculations and pressure variations. The experiments confirmed that flow becomes more laminar as restrictions increase, reducing Re below the turbulent threshold of 2x10^5, which has practical implications for flow control strategies. The Prandtl number’s relative stability further validates that fluid properties remained consistent throughout the tests, with negligible variations (

The study also addressed the impact of assumptions on the experimental accuracy, including neglecting radiative heat transfer and assuming negligible elevation change in the manometer readings. These simplifications, while reasonable within the experimental scope, likely contributed to observed discrepancies between experimental data and theory. Despite these errors, the overall trend aligned with theoretical expectations, emphasizing the robustness of the proportional relationships among Re, NuD, and flow conditions. The experiment provided substantive insights into convective heat transfer mechanisms and highlighted the importance of precise calibration, measurement accuracy, and awareness of heat transfer complexities.

Educationally, the experiment reinforced key concepts in heat transfer, fluid dynamics, and experimental techniques. Practically, it illustrated the challenges in correlating empirical data with theoretical models under real-world conditions. Future improvements might include enhanced calibration, accounting for radiative effects explicitly, and utilizing more accurate flow velocity measurement techniques, such as laser Doppler velocimetry. Overall, the experiment contributed valuable empirical evidence, verifying the fundamental relationships governing forced convection around a cylindrical object, and underscored the importance of critical assessment of assumptions and measurement uncertainties in heat transfer research.

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