3.2 Forced Convection: External Flow
4 min read•august 13, 2024
Forced convection in is all about how fluids move over surfaces like flat plates, cylinders, and spheres. It's crucial for understanding heat transfer in everyday situations, from cooling computer chips to designing efficient car radiators.
This topic dives into velocity and thermal boundary layers, flow regimes, and heat transfer coefficients. We'll explore empirical correlations, dimensionless numbers, and how surface roughness affects heat transfer. It's the nuts and bolts of predicting and calculating heat transfer in real-world scenarios.
External Flow Characteristics
Velocity and Thermal Boundary Layers
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- External flow characterized by development of velocity and thermal boundary layers when fluid flows over surface
- Velocity boundary layer is region near surface where fluid velocity varies from zero at surface to free-stream velocity at edge of boundary layer
- Thermal boundary layer is region near surface where fluid temperature varies from surface temperature to free-stream temperature at edge of boundary layer
- Thickness of velocity and thermal boundary layers increases with distance from leading edge of surface
Flow Regimes and Heat Transfer
- Local heat transfer coefficient depends on thickness of thermal boundary layer, with thinner boundary layers resulting in higher heat transfer coefficients
- Flow over flat plate can be laminar, turbulent, or combination of both, depending on and distance from leading edge (critical Reynolds number determines transition)
- Flow over cylinders and spheres characterized by formation of wake region behind object, which affects heat transfer characteristics
- , representing ratio of convective to conductive heat transfer, is function of Reynolds number and for external flows
Heat Transfer Coefficients for External Flow
Empirical Correlations
- Empirical correlations used to estimate average heat transfer coefficient for external flows over various geometries
- Dittus-Boelter correlation commonly used for turbulent flow over flat plates, while Sieder-Tate correlation used for laminar flow
- Churchill-Bernstein correlation used for estimating average Nusselt number for flow over cylinder, which can be used to calculate heat transfer coefficient
- Whitaker correlation used for estimating average Nusselt number for flow over sphere, which can be used to calculate heat transfer coefficient
Dimensionless Numbers and Fluid Properties
- Correlations typically involve dimensionless numbers such as Reynolds number, Prandtl number, and , which characterize flow and fluid properties
- Reynolds number represents ratio of inertial forces to viscous forces (determines flow regime)
- Prandtl number represents ratio of momentum diffusivity to thermal diffusivity (characterizes fluid's ability to convect heat relative to its ability to conduct heat)
- Grashof number represents ratio of buoyancy forces to viscous forces (important in natural convection)
- Fluid properties used in correlations should be evaluated at film temperature, which is average of surface temperature and free-stream temperature
Calculating Heat Transfer Rate
- Heat transfer coefficient obtained from correlations can be used to calculate convective heat transfer rate using Newton's law of cooling
- Newton's law of cooling: , where is heat transfer rate, is heat transfer coefficient, is surface area, is surface temperature, and is free-stream temperature
Surface Roughness Impact on Convective Heat Transfer
Roughness Effects on Boundary Layer and Turbulence
- Surface roughness can have significant impact on convective heat transfer in external flows, especially in turbulent flow conditions
- Roughness elements on surface can disrupt velocity boundary layer and promote turbulence, which enhances heat transfer
- Equivalent sand-grain roughness is measure of size of roughness elements on surface, used to characterize effect of roughness on heat transfer
- Relative roughness, ratio of equivalent sand-grain roughness to characteristic length of surface, is key parameter in determining effect of roughness on heat transfer
Roughness Effects in Different Flow Regimes
- For turbulent flow, Nusselt number and heat transfer coefficient increase with increasing relative roughness, up to certain limit
- In laminar flow, surface roughness can cause premature transition to turbulence, leading to increase in heat transfer
- Empirical correlations, such as Dipprey-Sabersky correlation, used to estimate effect of surface roughness on Nusselt number and heat transfer coefficient in turbulent flow
Convective Heat Transfer Problem Solving
Problem-Solving Steps
- Identify appropriate geometry, flow conditions, and fluid properties
- Determine flow regime (laminar or turbulent) based on Reynolds number and critical Reynolds number for given geometry
- Select appropriate empirical correlation based on geometry and flow conditions (Dittus-Boelter for turbulent flow over flat plate, Churchill-Bernstein for flow over cylinder)
- Evaluate fluid properties (density, viscosity, thermal conductivity, Prandtl number) at film temperature
- Calculate average heat transfer coefficient using selected correlation and fluid properties
- Use Newton's law of cooling to calculate convective heat transfer rate, given heat transfer coefficient, surface area, and temperature difference between surface and fluid
Accounting for Surface Roughness
- For problems involving surface roughness, calculate relative roughness
- Apply appropriate correction factor or correlation (Dipprey-Sabersky correlation) to smooth-surface Nusselt number or heat transfer coefficient
- Iterate solution process if necessary, as film temperature and fluid properties can change based on calculated heat transfer rate
Key Terms to Review (18)
Bernoulli's Principle: Bernoulli's Principle states that in a flowing fluid, an increase in the fluid's velocity occurs simultaneously with a decrease in pressure or potential energy. This principle helps explain the behavior of fluid dynamics, particularly in forced convection scenarios where external forces cause fluid movement, influencing temperature distribution and heat transfer rates.
Continuity equation: The continuity equation is a mathematical statement that expresses the principle of mass conservation within a fluid flow system. It ensures that mass cannot be created or destroyed in a control volume, meaning the mass entering a system must equal the mass exiting it. This principle applies to various flow situations, including external forced convection, internal forced convection, and diffusion processes, highlighting the interconnectedness of mass transfer in different contexts.
Convective Heat Transfer Coefficient: The convective heat transfer coefficient is a measure of the heat transfer between a solid surface and a fluid flowing over it. This coefficient depends on the nature of the flow, the properties of the fluid, and the characteristics of the surface, making it crucial for understanding how heat is transferred in various situations involving convection.
Cooling Systems: Cooling systems are mechanisms designed to remove excess heat from a designated area, ensuring that temperatures remain within acceptable limits for operational efficiency and safety. These systems are crucial in various applications, including industrial processes, electronics cooling, and HVAC systems, as they facilitate heat transfer through forced convection, either externally or internally. Understanding the principles of forced convection in cooling systems is essential to optimize their performance and ensure effective heat management.
Cross Flow: Cross flow refers to a fluid flow pattern where the primary flow direction is perpendicular to another flow direction, commonly seen in heat exchangers and external convection scenarios. This flow configuration can significantly influence heat transfer rates and performance, especially in forced convection situations, where external forces like fans or pumps drive the fluid motion.
External Flow: External flow refers to the movement of fluid over a surface or object that is not enclosed, allowing heat and mass transfer between the fluid and the surface. This type of flow is crucial for understanding how fluids interact with solid boundaries, affecting heat transfer rates and overall thermal performance. Analyzing external flow helps engineers design efficient systems in applications like cooling fins, heat exchangers, and aerodynamic bodies.
Film Coefficient: The film coefficient is a measure of the heat transfer rate between a solid surface and a fluid flowing over it, indicating how effectively heat is transferred through the layer of fluid adjacent to the surface. It reflects the convective heat transfer characteristics of the fluid and is influenced by factors such as fluid velocity, viscosity, and temperature. The film coefficient plays a crucial role in determining the overall heat transfer in processes involving both forced convection and phase changes, like boiling and condensation.
Grashof Number: The Grashof number is a dimensionless quantity used in fluid mechanics to characterize the ratio of buoyant forces to viscous forces within a fluid. It plays a crucial role in understanding natural convection phenomena, indicating whether buoyancy-driven flow is significant compared to viscous effects. This number helps determine flow regimes and influences heat transfer rates in various fluid situations, especially where temperature differences lead to density variations.
Heat Exchangers: Heat exchangers are devices designed to efficiently transfer heat from one medium to another, often between liquids or gases, without mixing them. They play a crucial role in various applications, such as in heating, cooling, and energy recovery systems, facilitating the transfer of thermal energy through conduction and convection.
Internal Flow: Internal flow refers to the movement of fluid within a confined space, such as pipes, ducts, or channels, where the flow is governed by both viscous and inertial forces. Understanding internal flow is crucial for analyzing heat and mass transfer in systems where fluids move through boundaries, impacting the efficiency of energy systems and equipment designs.
Laminar boundary layer: A laminar boundary layer is a thin region adjacent to a solid surface where fluid flow is smooth and orderly, characterized by parallel layers of fluid that slide past each other without mixing. In this layer, the velocity of the fluid changes from zero at the solid surface (due to the no-slip condition) to nearly the free stream velocity outside the boundary layer. This concept is crucial in understanding heat and mass transfer in various flow scenarios.
Nusselt Number: The Nusselt number is a dimensionless quantity used in heat transfer that represents the ratio of convective to conductive heat transfer across a boundary. It helps to characterize the efficiency of convective heat transfer in fluid flows, making it essential for understanding processes involving both heat and mass transfer.
Parallel Flow: Parallel flow is a configuration in heat exchangers where the hot and cold fluids move in the same direction, entering at the same end and exiting at the opposite end. This arrangement affects the temperature change of both fluids and influences the efficiency of heat transfer. Understanding parallel flow is crucial for optimizing heat exchanger performance and analyzing forced convection scenarios, as it directly relates to how heat is distributed and exchanged between fluids.
Prandtl Number: The Prandtl number is a dimensionless number that measures the relative thickness of the momentum boundary layer to the thermal boundary layer in a fluid. It helps characterize the heat transfer and fluid flow properties in convection processes, highlighting the relationship between momentum diffusivity (viscosity) and thermal diffusivity (heat conduction). Understanding the Prandtl number is crucial for analyzing various heat transfer scenarios, especially in both forced and natural convection.
Reynolds Number: Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations by comparing inertial forces to viscous forces. It is a critical factor in determining whether the flow is laminar or turbulent, influencing heat and mass transfer rates in various contexts.
Rough Surfaces: Rough surfaces refer to surfaces that have a significant amount of texture or irregularities, impacting the interaction between a fluid and the surface it flows over. These surfaces can influence the behavior of fluid flow, affecting characteristics such as drag, turbulence, and heat transfer rates. The roughness of a surface plays a critical role in determining how efficiently heat and mass transfer occurs during forced convection processes.
Smooth Surfaces: Smooth surfaces are defined as surfaces that have minimal roughness, allowing for a more streamlined interaction with fluid flow. This characteristic is crucial in the context of forced convection, as it affects how fluid moves over a surface and influences heat transfer efficiency. A smoother surface typically results in lower friction drag and improved thermal performance compared to rough surfaces.
Turbulent boundary layer: A turbulent boundary layer is a layer of fluid in which the flow is chaotic and characterized by velocity fluctuations, typically occurring near a solid surface. In this layer, the effects of viscosity are significant, and the flow transitions from a smooth, laminar state to a more complex turbulent state, impacting heat and mass transfer rates as well as the overall drag on surfaces. Understanding this concept is crucial for analyzing convection phenomena and designing systems involving fluid flow over surfaces.