Lecture on Heat Transfer: Convection

Introduction

• Overview of three modes of heat transfer:
  • Conduction: Described by Fourier's law
  • Convection: Focus of today’s lecture, described by Newton's law of cooling
  • Radiation: Typically surface to surface, described by the Stefan-Boltzmann law

Heat Transfer Basics

• Driving Force: Temperature difference (ΔT)
• Convection:
  • Heat transfer from a surface to a moving fluid
  • Involves bulk and random motion of fluid
  • Different from conduction, which occurs in solids with bound molecules

Convection Explained

• Heat travels from hot to cold due to ΔT
• Example:
  • Heated plate with cooler air above
  • Air flow carries heat away
  • Heat flux can be expressed as Q convection

Newton's Law of Cooling

• Equation: Q = hA(T_s - T_∞)
  • h: Convective heat transfer coefficient
  • T_s: Surface temperature
  • T_∞: Bulk fluid temperature
  • A: Surface area
• Units: Watts per meter squared per Kelvin
• Heat Rate Version: Total heat rate calculated by multiplying by surface area

Example Problems

1. Problem 1:
   • Roof at 35°C, ambient temperature 20°C
   • Surface area 50 m², h = 10 W/m²K
   • Calculate heat loss: 7,500 Watts
2. Problem 2:
   • Roof at 20°C, ambient temperature 30°C
   • Similar parameters
   • Result: Heat gain of 5,000 Watts

Concepts and Applications

• Temperature Profiles
  • Velocity and temperature profiles form near surfaces (boundary layer)
  • Practical problems often ignore boundary layer details
• Convection Types
  • Forced Convection: Requires external force (e.g., fan)
  • Natural/Free Convection: Driven by buoyancy
  • Boiling/Condensation: Induce fluid motion

Important Notes

• Use correct form of Newton's law based on heat direction
• Energy Balance:
  • Out-term: Q = hA(T_s - T_∞)
  • In-term: Q = hA(T_∞ - T_s)
• Complexity: Convection can be complicated, requires careful treatment

Conclusion

• Understanding convection is crucial for solving complex heat transfer problems
• Convection is used in combination with conduction at boundaries in many applications

These notes capture the main ideas and processes discussed in the lecture, focusing on convection and how it fits into the overall topic of heat transfer. They should serve as a useful reference for understanding the concepts and solving related problems.