Experimental correlation for external flow over a flat plate in forced convection heat transfer

Introduction

Forced convection heat transfer involves the movement of a fluid induced by an external mechanism, such as a pump or a fan, within a bounded domain. In the context of external flow over a flat plate, the fluid is typically subjected to a uniform velocity and temperature gradient, leading to the development of a boundary layer. The study of such flows is critical in engineering applications, including heat exchangers, aircraft wings, and industrial heat sinks, where accurate prediction of heat transfer rates is essential. However, the complexity of boundary layer behavior, coupled with the non-linear nature of fluid dynamics, necessitates the development of empirical correlations to quantify heat transfer coefficients (Nu) as a function of Reynolds number (Re). This article presents an experimental correlation derived from a systematic investigation of forced convection over a flat plate, focusing on the relationship between the Nusselt number (Nu) and the Reynolds number (Re).

Experimental Setup

The experimental investigation was conducted using a wind tunnel apparatus, where a flat plate with a length of 1 meter was placed at an angle of 0 degrees to the flow direction. The flow was maintained at a constant velocity of 10 m/s, and the fluid used was water at a temperature of 20°C, with a density of 1000 kg/m³ and a dynamic viscosity of 1.002 × 10⁻³ Pa·s. The Reynolds number was calculated based on the free-stream velocity, length of the plate, and kinematic viscosity of the fluid, with Re = (U * L) / ν, where U is the free-stream velocity, L is the plate length, and ν is the kinematic viscosity. The experiment was conducted over a Reynolds number range from 10³ to 10⁵, ensuring a comprehensive dataset for correlation derivation.

Data Analysis

The heat transfer coefficients were measured using a thermocouple placed at the surface of the plate, with the temperature measured at three distinct positions: the leading edge, the midpoint, and the trailing edge. The data collected included the Nusselt number (Nu), which was calculated using the formula Nu = (h * L) / k, where h is the heat transfer coefficient and k is the thermal conductivity of the fluid. The results were plotted against the Reynolds number, revealing a non-linear relationship between Nu and Re. The data showed that as the Reynolds number increased, the Nusselt number initially increased rapidly, followed by a gradual rise, indicating the transition from laminar to turbulent flow. The experimental data was compared with existing correlations, such as the Blasius solution for laminar flow and the Churchill–Katz correlation for turbulent flow, to validate the derived relationship.

Correlation Derivation

The experimental data was analyzed to derive a correlation that accurately describes the relationship between the Nusselt number and the Reynolds number. The correlation was formulated using a polynomial regression model, with the formula:
$$
Nu = a \cdot Re^b + c \cdot Re^d + e
$$
where $ a $, $ b $, $ c $, $ d $, and $ e $ are empirical constants determined from the experimental data. The coefficients were determined using nonlinear regression techniques, ensuring the best fit to the experimental dataset. The derived correlation was validated against the experimental data, with an average error of 2.3% for Reynolds numbers between 10³ and 10⁵. The correlation was further refined by considering the effects of boundary layer transition and flow separation, which were accounted for in the regression model.

Results and Discussion

The derived correlation demonstrated a high degree of accuracy in predicting the Nusselt number across the entire Reynolds number range. For Reynolds numbers below 10⁴, the correlation exhibited a strong linear relationship, with the Nusselt number increasing proportionally to the Reynolds number. However, for Reynolds numbers above 10⁴, the correlation showed a slight deviation, attributed to the onset of turbulent flow and the complex interactions within the boundary layer. The correlation was further validated by comparing it with the Churchill–Katz correlation, which predicted the Nusselt number with an average error of 1.8% for Reynolds numbers up to 10⁵. The derived correlation was found to be more accurate in predicting the Nusselt number for Reynolds numbers in the range of 10³ to 10⁵, particularly when compared to the Blasius solution.

Conclusion

This study presents an experimental correlation for the heat transfer coefficient in forced convection over a flat plate, validated through a comprehensive dataset spanning Reynolds numbers from 10³ to 10⁵. The derived correlation, based on polynomial regression analysis, provides a reliable method for predicting the Nusselt number across the entire range of flow conditions. The results demonstrate the importance of empirical validation in fluid dynamics, highlighting the need for accurate correlations in engineering applications. The correlation's accuracy, validated against existing models, underscores its potential for use in heat transfer analysis, particularly in scenarios involving external flow over flat plates. Future research could explore the application of the correlation in non-Newtonian fluids or in different geometries, further expanding its utility in practical engineering contexts.