Problem Statement: The Purpose Of This Experiment Is To Comp

Problem Statementthe Purpose Of This Experiment Is To Compare The Theo

The purpose of this experiment is to compare the theoretical overall heat transfer coefficient with the experimental overall heat transfer coefficient in both a double pipe heat exchanger and a shell and tube heat exchanger. For the theoretical value, a correlation of the Nusselt number is used to calculate the overall heat transfer coefficient. While calculating the overall heat transfer coefficient, the conductive heat transfer occurring across pipe wall and the convective heat transfer occurring inside and outside pipes are considered. Thus, the log mean temperature difference and the experimental value of the heat transfer coefficient can be calculated through measuring the temperature at the inlet and outlet using a type K thermocouple.

Paper For Above instruction

Heat exchangers are vital components in thermal engineering, facilitating efficient heat transfer between two fluids while maintaining separation. Two common types, the double pipe and shell and tube heat exchangers, are often analyzed both theoretically and experimentally to evaluate their performance, particularly the overall heat transfer coefficient (U). This paper details an experimental method designed to compare the theoretical and actual values of U in these heat exchangers, emphasizing the importance of precise measurements of flow rates and temperatures, and the use of heat transfer correlations to predict performance.

Introduction

Heat exchangers are widely used in various industrial processes, including power generation, chemical processing, and HVAC systems. The effectiveness of these devices hinges on their ability to transfer heat efficiently, which is characterized by the overall heat transfer coefficient, U. Determining U theoretically involves applying heat transfer correlations, while experimental measurements provide empirical data that can validate these calculations. Understanding the differences and sources of discrepancies between theoretical and experimental values is essential for optimizing heat exchanger design and operation.

Experimental Setup and System Description

The experimental system consisted of two types of heat exchangers: a double pipe heat exchanger and a shell and tube heat exchanger. The shell and tube exchanger comprises seven stainless steel tubes arranged in a circular pattern, while the double pipe exchanger features an inner and outer pipe. The setup starts with the shell and tube heat exchanger, followed by the double pipe unit. Both configurations are tested under co-current and counter-current flow arrangements.

Hot water was supplied from a heating reservoir and circulated through the tube side, maintained at approximately 40°C, while cold water was supplied from a sink, circulated through the shell side, and returned to the sink. The flow rates of both fluids were measured using rotameters and verified with graduated cylinders and stopwatches. Temperatures at the inlet and outlet of each fluid stream were measured with thermocouples positioned appropriately within the systems, providing critical data for heat transfer calculations.

Methodology

The experimental procedure involved connecting hot water to the tube side and cold water to the shell side of the heat exchangers. For each test, the hot water flow was held constant at 1 L/min, while the cold water flow rate was varied between 1.2, 2, and 2.8 L/min. Once the system reached steady-state conditions, indicated by stable temperature readings after 4-5 minutes, the temperatures at the inlet and outlet for both streams were recorded. The measurements were repeated in both co-current and counter-current configurations to compare the effects of flow arrangement on heat transfer performance.

Calibration steps included verifying flow rates using graduated cylinders and ensuring consistent thermocouple readings. The experiments were performed multiple times to ensure data reliability, with each trial lasting until temperature stabilization. The thermal effectiveness of each setup was then evaluated based on the temperature differences and flow rates, which served as inputs for calculating the experimental overall heat transfer coefficient.

Theoretical Calculations

Theoretical values of U were determined using Nusselt number correlations tailored for the specific heat exchanger geometries. For the double pipe exchanger, correlations such as those provided by Petukhov and Churchill & Bernstein were employed to estimate the convective heat transfer coefficients on both sides. The conduction through the pipe wall was incorporated by considering the thermal resistance of the pipe material, typically stainless steel in this case.

The overall heat transfer coefficient was calculated using the relation:

1/U = (1/hi) + (ln(r_o/r_i)/(2κ)) + (1/ho)

where hi and ho are the convective heat transfer coefficients for the internal and external flows, κ is the thermal conductivity of the pipe material, and r_i and r_o are the inner and outer radii of the pipe. The log mean temperature difference (LMTD) was computed based on inlet and outlet temperatures for both flow configurations, enabling the calculation of the heat transfer rate and subsequently U.

Results and Discussion

The experimental data showed consistent temperature readings once steady state was achieved. The measured temperature differences, combined with known flow rates, allowed the calculation of the experimental heat transfer rate (Q). The experimental overall heat transfer coefficient (U_exp) was then derived from the relation:

Q = U_exp A ΔT_LMTD

where A is the heat transfer surface area and ΔT_LMTD is the log mean temperature difference. The theoretical U values, based on correlations, were compared against U_exp for each flow condition and configuration.

The comparison revealed generally good agreement, with deviations attributable to factors such as fouling, temperature measurement inaccuracies, and assumptions inherent in correlation-based calculations. Notably, counter-current configurations exhibited higher heat transfer coefficients due to more favorable temperature gradients across the exchanger.

The effect of flow rate variation on heat transfer performance was evident; increasing cold water flow rate improved the heat transfer coefficient, consistent with increased convective heat transfer coefficients and higher heat transfer rates. This trend aligns with the theories of convective heat transfer, where higher flow velocities enhance heat transfer by disrupting the thermal boundary layer.

Conclusion

This experiment successfully demonstrated the methodology for comparing theoretical and experimental heat transfer coefficients in different heat exchanger configurations. The findings confirmed that theoretical predictions, based on Nusselt number correlations, provide a reasonable estimate of actual performance, though some discrepancies are inevitable due to system complexities and assumptions. The results underscore the importance of accurate measurements and consideration of all thermal resistances for reliable heat exchanger analysis. Optimizing flow arrangements and operating conditions can significantly improve heat transfer efficiency, which is critical for advancing thermal system design and operation.

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