Lecture on Convection in Heat Transfer

Introduction to Convection

• Convection: Heat transfer from a surface to a fluid.
• Importance: Characteristics of the fluid impact how well thermal energy is transferred.

Boundary Layers

• Boundary Layer Concept: Critical in understanding fluid flow and heat transfer.
• Example: Laying down in strong winds reduces wind impact due to lower wind speed near the ground.
• Windmills: Tall to access higher wind velocities for energy extraction.

Fluid Mechanics in Convection

• Fluid Flow Impact: Fluid mechanics knowledge is crucial to understanding convection.
• Leading Edge and Velocity Profile:
  • Uniform velocity profile becomes influenced by viscous effects at the leading edge.
  • Velocity decreases closer to the surface due to viscous forces.
  • Velocity Boundary Layer: Develops as viscous forces propagate up the fluid layers.

Velocity Boundary Layer

• Definition: The point where velocity in the x-direction is 99% of the free stream velocity.
• Plotting: Shows increasing thickness of the boundary layer as viscous forces extend.

Thermal Boundary Layer

• Scenario: Heated plate with cooler incoming fluid.
• Heat Transfer: From hot plate to cooler fluid as fluid flows over the plate.
• Temperature Profile Development:
  • Starts flat at bulk fluid temperature.
  • Develops as the fluid absorbs heat from the plate.
• Thermal Boundary Layer Thickness:
  • Point where temperature reaches 99% of the bulk fluid temperature.
  • Indicates penetration of thermal effects into the fluid.

Convection and Heat Transfer

• Convection Equation: Q = H ( \Delta T )
  • H: Heat transfer coefficient.
  • Delta T: Temperature difference from the surface to the bulk fluid.
• Conduction in Fluids:
  • Occurs when fluid is stationary.
  • Characterized by temperature gradient at the boundary layer.
• Convective Heat Transfer Coefficient:
  • Relates to fluid thermal conductivity and flow characteristics.

Advection and Turbulence

• Advection: Heat transfer by fluid flow.
  • Equation: Q = m ( \dot{C_p \Delta T} )
  • Fluid motion contributes to heat transfer efficiency.
• Turbulent Flow:
  • Eddies and mixing increase heat transfer.
  • Combines conduction and fluid motion for effective heat transfer.

Summary

• Convection is a complex process combining conduction and advection.
• Understanding boundary layers is key to analyzing convective heat transfer.
• Future lectures will explore methods to handle convection complexities.