Lecture Notes: Chapter 1 - Introduction to Heat Transfer

What is Heat Transfer?

• Exchange of thermal energy due to a temperature difference.
• Examples:
  • Oven heating a turkey (coils glow red due to heat transfer).
  • Toaster (wires are hot, bread is cool - heat transfer occurs).
  • Microwave (energy transfer without glowing red, involves microwave energy).
• Focus of the class is on thermal energy, not microwave energy.

First Law of Thermodynamics for a Closed System

• Equation: ( Q = \Delta U + W )
  • ( Q ): Heat transfer.
  • ( \Delta U ): Change in internal energy (can be found with pressure and temperature data).
  • ( W ): Work done during the process.
• In thermal courses, heat transfer ( Q ) often provided but not calculated.

Modes of Heat Transfer

1. Conduction
2. Convection
3. Radiation

Conduction

• Transfer of energy from more to less energetic particles.
• Example: Heating one side of a steel plate.
• Governed by Fourier's Law:
  • ( q''_x = -k \frac{T_2 - T_1}{L} )
  • ( q'' ): Heat flux (watts per square meter)
  • ( q ): Heat rate (watts)
  • ( k ): Thermal conductivity of the material.
• Important equation for conduction:
  • ( q_x = kA \frac{\Delta T}{L} )
  • Area ( A ) affects energy transfer direction.
• Derived from experimental observations by Fourier._

Convection

• Requires fluid flow over a surface.
• Relation to fluid mechanics (boundary layer concepts).
• Newton’s Law of Cooling:
  • ( Q = hA(T_s - T_\infty) )
  • ( h ): Convection heat transfer coefficient (depends on fluid properties, geometry, flow regime).
• ( h ) values vary significantly between gases and liquids.
• Enhancing convection:
  • Use of fins (e.g., in radiators) to increase surface area._

Radiation

• Can occur in a vacuum, important for space applications.
• Stefan-Boltzmann Law for ideal emitters (blackbody):
  • ( q'' = \sigma T_s^4 )
  • ( \sigma ): Stefan-Boltzmann constant.
• Non-blackbody emissivity ( \varepsilon ):
  • ( q'' = \varepsilon \sigma T_s^4 )
  • ( \varepsilon ) values can be found in textbooks.
• Heat transfer between a small object and large enclosure:
  • Equation provided for specialized cases (e.g., dime in a basketball).

Summary

• Chapter 1 introduces the basics of conduction, convection, and radiation heat transfer.
• Each mode has its governing laws and equations, applicable under specific conditions.
• Future chapters delve deeper into each mode with detailed calculations and scenarios.