3.4 Correlations for convective heat transfer
4 min read•july 31, 2024
Convective heat transfer correlations are essential tools for estimating heat transfer coefficients in various flow scenarios. They use dimensionless numbers like Nusselt, Reynolds, and Prandtl to relate fluid properties and flow characteristics to heat transfer rates.
These correlations cover internal, external, and flows. While they simplify complex heat transfer processes, it's crucial to understand their limitations and applicability ranges to ensure accurate results in engineering calculations and thermal system designs.
Convective Heat Transfer Correlations
Empirical Relationships and Dimensionless Numbers
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- Convective heat transfer correlations estimate the convective heat transfer coefficient based on fluid properties, flow characteristics, and geometry
- Correlations are expressed in terms of dimensionless numbers
- Nusselt number (Nu) represents the ratio of convective to conductive heat transfer
- (Re) represents the ratio of inertial forces to viscous forces
- (Pr) represents the ratio of momentum diffusivity to thermal diffusivity
- (Gr) represents the ratio of buoyancy forces to viscous forces
Flow Configurations and Corresponding Correlations
- (pipe and duct flow)
- widely used for in pipes and ducts
- more accurate for a wider range of Reynolds and Prandtl numbers in turbulent pipe flow
- (flow over plates, cylinders, and spheres)
- for flow over a cylinder
- for flow over a sphere
- Natural convection (fluid motion driven by buoyancy forces)
- for vertical plates
- for horizontal plates
Limitations of Correlations
Ranges of Applicability
- Convective heat transfer correlations are empirical and have specific ranges of applicability based on experimental conditions
- Correlations are valid for a certain range of Reynolds numbers, Prandtl numbers, and geometrical parameters (aspect ratios, diameter-to-length ratios)
- Accuracy may decrease when applied to conditions outside their intended range (very high or very low Reynolds numbers, fluids with unusual properties)
- Some correlations are limited to specific fluid types (gases, liquids, or supercritical fluids) or flow regimes (laminar, turbulent, or transitional)
Additional Factors Affecting Accuracy
- Presence of , non-uniform heat flux, or variable fluid properties may affect the accuracy of correlations
- Essential to consult the original source of the correlation and verify its applicability to the specific problem
- Computational fluid dynamics (CFD) simulations or experimental data may be necessary for complex flow conditions or geometries
Estimating Heat Transfer Coefficients
Internal Flow Correlations
- Dittus-Boelter equation:
- Widely used for turbulent flow in smooth circular pipes with fully developed velocity and temperature profiles
- Gnielinski equation:
- More accurate than Dittus-Boelter for a wider range of Reynolds and Prandtl numbers in turbulent pipe flow
- :
- For in circular pipes with constant wall temperature, accounts for variation of fluid properties with temperature
External Flow Correlations
- Žukauskas correlation:
- Used for cross-flow over a cylinder, where C, m, and n are constants depending on the Reynolds number range
- Churchill-Bernstein correlation:
- Applicable for flow over a sphere
Natural Convection Correlations
- Churchill-Chu correlation:
- Used for vertical plates
- Morgan correlation:
- Used for horizontal plates, where C and n depend on the Rayleigh number range
Fluid Properties and Accuracy
Influence of Fluid Properties
- Fluid properties (, , density, specific heat capacity) significantly influence the convective heat transfer coefficient and the accuracy of correlations
- Prandtl number is a key parameter in determining the relative thickness of the velocity and thermal boundary layers
- High Prandtl number fluids (oils) have a thinner thermal boundary layer, resulting in higher convective heat transfer coefficients
- Low Prandtl number fluids (liquid metals) have a thicker thermal boundary layer, resulting in lower convective heat transfer coefficients
- Reynolds number determines the flow regime (laminar, transitional, or turbulent) and affects the convective heat transfer coefficient
- Higher Reynolds numbers generally lead to higher convective heat transfer coefficients due to increased turbulence and mixing
Factors Affecting Correlation Accuracy
- Variation of fluid properties with temperature, especially in cases with large temperature differences between the fluid and the surface, can affect the accuracy of correlations
- Presence of non-uniform heat flux, surface roughness, or complex geometries can impact the accuracy of correlations by altering flow and heat transfer characteristics
- In some cases, computational fluid dynamics (CFD) simulations or experimental data may be necessary to obtain more accurate convective heat transfer coefficients for complex flow conditions or geometries
Key Terms to Review (26)
Aerodynamics: Aerodynamics is the branch of physics that deals with the study of the behavior of air as it interacts with solid objects, particularly in motion. This field is crucial for understanding how objects, like vehicles or aircraft, move through air, and how forces like drag and lift influence their performance. It's closely tied to concepts like fluid dynamics and plays a significant role in heat transfer processes as well as momentum and thermal boundary layers.
Churchill-Bernstein Correlation: The Churchill-Bernstein correlation is a widely used empirical relationship for estimating heat transfer coefficients during forced convection in smooth tubes. This correlation connects the Nusselt number to the Reynolds number and Prandtl number, providing a reliable method for predicting convective heat transfer performance in various fluid flow situations.
Churchill-Chu Correlation: The Churchill-Chu correlation is an empirical correlation used to predict the Nusselt number, which describes convective heat transfer in a flow over a flat plate. This correlation is particularly significant for laminar and turbulent flow regimes, as it accounts for the effects of Reynolds number and Prandtl number, providing a way to estimate heat transfer coefficients in various fluid flow scenarios.
Circular tube: A circular tube is a hollow cylindrical structure that is commonly used to facilitate the flow of fluids, such as liquids or gases, through its interior. The geometry of a circular tube significantly affects the heat and mass transfer characteristics, making it crucial in various engineering applications, including heat exchangers and pipe flow systems.
Dittus-Boelter Equation: The Dittus-Boelter Equation is a widely used empirical correlation that predicts the heat transfer coefficient for turbulent flow in circular tubes. This equation is significant in understanding convective heat transfer, specifically in cases where a fluid flows over a heated surface, making it essential for various engineering applications like heat exchangers and cooling systems. It provides a relationship between the Nusselt number, Reynolds number, and Prandtl number, facilitating the calculation of heat transfer rates in practical scenarios.
External flow: External flow refers to the flow of fluid over a solid surface, where the fluid is not confined within any boundaries like pipes or ducts. This type of flow is critical in understanding heat transfer processes because it involves the interaction between a moving fluid and a stationary object, which can significantly influence the rate of convective heat transfer from the object to the fluid or vice versa. Analyzing external flow helps in deriving correlations for convective heat transfer coefficients, which are essential for predicting how efficiently heat can be transferred in various applications.
Flat Plate: A flat plate refers to a surface that is uniformly flat and typically used in heat and mass transfer applications, where it can be subjected to fluid flow on one or both sides. In the context of convective heat transfer and mass transfer, flat plates serve as a simple model for analyzing the behavior of fluid flow and the resulting heat or mass exchange, allowing for correlations and equations to be developed for different geometries and conditions.
Forced Convection: Forced convection refers to the process of heat transfer in a fluid, where the fluid motion is generated by an external force, such as a fan or pump. This mechanism enhances heat transfer rates significantly compared to natural convection, where fluid movement occurs due to buoyancy differences. Understanding forced convection is crucial for optimizing thermal systems, analyzing heat transfer coefficients, and applying empirical correlations to predict performance in various applications.
Gnielinski Equation: The Gnielinski equation is a widely used empirical correlation that calculates the heat transfer coefficient for turbulent flow in circular tubes. It combines the effects of both convection and conduction, taking into account the Reynolds number and Prandtl number, which are essential for predicting heat transfer performance in fluid systems. This equation is particularly useful in applications involving heat exchangers, where accurate predictions of heat transfer rates are crucial for system design and efficiency.
Grashof Number: The Grashof Number is a dimensionless quantity that measures the relative significance of buoyancy forces to viscous forces in a fluid. It plays a crucial role in determining the flow regime in natural convection scenarios, helping to predict how heat transfer will occur in a fluid due to density differences caused by temperature variations.
Heat Exchangers: Heat exchangers are devices designed to efficiently transfer heat from one fluid to another without mixing them. They play a critical role in many applications, including heating and cooling systems, where managing temperature and energy transfer is essential for optimal performance.
Internal flow: Internal flow refers to the movement of fluids within a confined space, such as pipes, ducts, or channels, where the flow is influenced by factors like pressure gradients, viscosity, and temperature changes. Understanding internal flow is crucial for analyzing convective heat transfer, as it plays a key role in determining how effectively heat is transferred between a fluid and its surroundings.
Laminar Flow: Laminar flow is a fluid flow regime characterized by smooth, orderly layers of fluid that move in parallel, with minimal disruption between the layers. This type of flow often occurs at low velocities and in small conduits, resulting in predictable behavior and lower resistance compared to turbulent flow.
Morgan correlation: Morgan correlation is a mathematical relationship used in heat transfer calculations to estimate the convective heat transfer coefficient based on various flow characteristics. This correlation is particularly relevant for situations involving forced convection and can be derived from experimental data, allowing for a more accurate assessment of heat transfer performance in different systems. It connects fluid dynamics with thermal characteristics, playing a vital role in engineering applications where efficient heat transfer is crucial.
Natural Convection: Natural convection is a heat transfer process driven by the buoyancy forces that occur due to temperature differences within a fluid. As a fluid heats up, it becomes less dense and rises, while cooler, denser fluid sinks, creating a circulation pattern that facilitates heat transfer. This process is significant in various applications where heat exchange occurs without the need for external mechanical forces.
Nusselt Number Correlation: A Nusselt number correlation is a mathematical expression that relates the Nusselt number, which quantifies convective heat transfer, to various influencing parameters such as Reynolds number and Prandtl number. These correlations are essential for predicting heat transfer rates in fluid flow situations and are derived from experimental data or theoretical analyses, making them critical for engineers and scientists when designing thermal systems.
Prandtl Number: The Prandtl Number is a dimensionless number that characterizes the relative thickness of the momentum and thermal boundary layers in fluid flow. It provides insight into the relative rates of momentum diffusion (viscosity) and thermal diffusion (thermal conductivity), playing a vital role in understanding convection, heat transfer, and fluid dynamics.
Reynolds Number: The Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is calculated using the ratio of inertial forces to viscous forces and is crucial for determining whether a flow will be laminar or turbulent, which affects momentum, energy, and mass transfer in various processes.
Sieder-Tate Correlation: The Sieder-Tate correlation is a widely used empirical relationship for estimating heat transfer coefficients in turbulent flow conditions, particularly in forced convection scenarios. It connects the Nusselt number, Reynolds number, and Prandtl number to predict the effectiveness of heat transfer in various systems, such as pipes and ducts.
Surface Roughness: Surface roughness refers to the texture of a surface characterized by its microscopic variations in height and depth. These variations can significantly influence heat and mass transfer processes, affecting phenomena like convective heat transfer, radiation properties, and thermal interactions between surfaces. Understanding surface roughness is essential for predicting how effectively surfaces will exchange energy and how they will perform in different thermal environments.
Temperature Gradient: A temperature gradient is the rate of change of temperature in a specific direction, typically measured in degrees per unit distance. This concept is crucial in understanding how heat transfers through different materials, affecting the efficiency of processes like convective heat transfer, mass transfer, and coupled heat and mass transfer.
Thermal conductivity: Thermal conductivity is a material property that quantifies how well a substance can conduct heat. This property plays a crucial role in various heat transfer processes, influencing the rate at which heat moves through different materials and affecting energy efficiency in systems involving thermal management.
Transitional flow: Transitional flow refers to the flow regime that exists between laminar flow and turbulent flow, characterized by unpredictable and fluctuating flow patterns. In this state, the behavior of fluid flow can switch between orderly layers and chaotic movements, making it a complex area of study in heat transfer and fluid dynamics. Understanding transitional flow is crucial for analyzing convective heat transfer and recognizing its influence on dimensionless numbers that define the flow characteristics.
Turbulent flow: Turbulent flow is a type of fluid motion characterized by chaotic changes in pressure and flow velocity. Unlike laminar flow, where fluid particles move in smooth, parallel layers, turbulent flow involves irregular movements and eddies, significantly impacting momentum, energy, and mass transfer within the fluid.
Viscosity: Viscosity is a measure of a fluid's resistance to flow and deformation, which is influenced by its internal friction. It plays a crucial role in understanding how fluids behave under various conditions, affecting transport properties and flow characteristics in many processes such as heat transfer, mass transfer, and diffusion.
žukauskas correlation: The žukauskas correlation is a mathematical relationship used to predict heat transfer coefficients in forced convection, particularly in turbulent flow over flat plates and in ducts. This correlation is valuable for engineers and researchers as it provides a reliable means to estimate the heat transfer performance in various flow scenarios, which is crucial for efficient thermal management in engineering applications.