6.3 Convection

Convection is a crucial heat transfer mechanism in chemical engineering. It involves the movement of fluids to transfer heat, occurring naturally due to temperature differences or forced by external means. Understanding convection is key to designing efficient heat exchangers and cooling systems.

Newton's Law of Cooling quantifies convective heat transfer rates, while dimensionless numbers help predict heat transfer coefficients. Fluid properties, flow characteristics, and surface geometry all play vital roles in determining convection effectiveness. This knowledge is essential for optimizing heat transfer processes in various applications.

Natural vs Forced Convection

Mechanisms Driving Fluid Motion

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• Natural convection occurs when fluid motion is driven by buoyancy forces arising from density differences due to temperature gradients in the fluid
• Forced convection occurs when an external means, such as a pump or fan, is used to drive fluid motion over a surface
• The primary difference between natural and forced convection is the mechanism driving the fluid motion: buoyancy forces in natural convection and external forces in forced convection

Heat Transfer Rates and Examples

• Natural convection is typically slower and results in lower heat transfer rates compared to forced convection
• Examples of natural convection include:
  • Heat transfer from a hot object to surrounding air
  • Fluid motion in a pot of water heated from below
  • Air circulation in a room with a radiator
• Forced convection examples include:
  • Heat transfer in heat exchangers with pumps or fans
  • Cooling systems for electronic devices with fans
  • Fluid flow over a car radiator driven by a fan

Newton's Law of Cooling

Convective Heat Transfer Rate Equation

• Newton's law of cooling states that the rate of convective heat transfer is proportional to the temperature difference between the surface and the fluid
• The convective heat transfer rate ($Q$) is calculated using the equation: $Q = hA(T_s - T_f)$
  • $h$ is the convective heat transfer coefficient
  • $A$ is the surface area
  • $T_s$ is the surface temperature
  • $T_f$ is the fluid temperature
• The temperature difference ($T_s - T_f$) is the driving force for convective heat transfer, with heat flowing from the higher temperature to the lower temperature

Assumptions and Factors Affecting Convective Heat Transfer

• The convective heat transfer coefficient ($h$) depends on fluid properties, flow characteristics, and surface geometry
• Newton's law of cooling assumes that the fluid properties and heat transfer coefficient remain constant during the heat transfer process
• Factors influencing the convective heat transfer coefficient include:
  • Fluid velocity: higher velocities generally increase $h$
  • Fluid properties: thermal conductivity, viscosity, and specific heat capacity affect $h$
  • Surface geometry: shape and roughness of the surface can impact $h$
  • Flow regime: laminar or turbulent flow can result in different values of $h$

Convective Heat Transfer Coefficients

Dimensionless Numbers and Empirical Correlations

• Convective heat transfer coefficients can be determined using empirical correlations based on dimensionless numbers, such as Nusselt number ($Nu$), Reynolds number ($Re$), and Prandtl number ($Pr$)
• The Nusselt number represents the ratio of convective to conductive heat transfer and is defined as $Nu = hL/k$
  • $h$ is the convective heat transfer coefficient
  • $L$ is a characteristic length
  • $k$ is the thermal conductivity of the fluid
• The Reynolds number represents the ratio of inertial forces to viscous forces and is defined as $Re = \rho VL/\mu$
  • $\rho$ is the fluid density
  • $V$ is the fluid velocity
  • $L$ is a characteristic length
  • $\mu$ is the fluid dynamic viscosity
• The Prandtl number represents the ratio of momentum diffusivity to thermal diffusivity and is defined as $Pr = \mu C_p/k$
  • $\mu$ is the fluid dynamic viscosity
  • $C_p$ is the fluid specific heat capacity
  • $k$ is the thermal conductivity of the fluid

Flow Configurations and Correlations

• Different empirical correlations are used for various flow configurations, such as:
  • Flow over a flat plate
  • Flow through a pipe
  • Flow across a bank of tubes
• The Dittus-Boelter correlation is commonly used for turbulent flow in pipes: $Nu = 0.023 \times Re^{0.8} \times Pr^n$
  • $n = 0.4$ for heating
  • $n = 0.3$ for cooling
• Other correlations exist for different flow configurations and conditions, such as:
  • Laminar flow in pipes (Sieder-Tate correlation)
  • Flow over a flat plate (Pohlhausen correlation for laminar flow, Colburn correlation for turbulent flow)
  • Flow across a bank of tubes (Zukauskas correlation)

Fluid Properties & Convection

Impact of Fluid Properties on Heat Transfer

• Fluid properties, such as density, viscosity, thermal conductivity, and specific heat capacity, influence convective heat transfer
• Higher thermal conductivity and specific heat capacity of the fluid enhance convective heat transfer
  • Thermal conductivity determines the rate of heat conduction through the fluid
  • Specific heat capacity affects the amount of energy required to change the fluid temperature
• Higher viscosity can reduce heat transfer by dampening fluid motion and increasing the thickness of the boundary layer
• Density variations due to temperature gradients drive natural convection currents

Flow Characteristics and Heat Transfer

• Flow characteristics, such as velocity, turbulence, and boundary layer development, also affect convective heat transfer
• Increasing fluid velocity generally enhances convective heat transfer by:
  • Promoting mixing and reducing the thermal boundary layer thickness
  • Increasing the Reynolds number, which leads to higher convective heat transfer coefficients
• Turbulent flow typically results in higher convective heat transfer rates compared to laminar flow due to:
  • Increased mixing and disruption of the thermal boundary layer
  • Enhanced transport of heat and momentum across the boundary layer
• The development of velocity and thermal boundary layers along a surface affects local heat transfer coefficients
  • Higher values occur near the leading edge where the boundary layers are thinner
  • As the boundary layers grow along the surface, the local heat transfer coefficients decrease
• Surface roughness can enhance convective heat transfer by promoting turbulence and disrupting the boundary layer, but it also increases pressure drop