Intorduction of Thermal Resistance

Heat Transfer Fundamentals

Heat Transfer Modes

• Heat transfer occurs through three primary modes:
  • Conduction: Transfer of heat through materials due to temperature difference without movement.
  • Convection: Transfer of heat through fluid movement; requires close contact between the fluid and solid surface.
  • Radiation: Transfer of heat through electromagnetic waves; does not require a medium.
• Definitions of Resistance:
  • Each mode of heat transfer has an associated resistance that can be analyzed.

Key Equations and Concepts

• General Convection Equation:

  • The heat transfer through convection can be expressed as:
    $Q = h imes A imes (T_{s} - T_{ ext{surrounding}})$
  • Where:
  • $Q$ = Heat transfer
  • $h$ = Heat transfer coefficient
  • $A$ = Area
  • $T_{s}$ = Surface temperature
  • $T_{ ext{surrounding}}$ = Surrounding temperature

• Stefan-Boltzmann Law for Radiation:

  • The radiation heat transfer is given as:
    $Q = ext{Stefan-Boltzmann constant} imes A imes (T_{s}^4 - T_{ ext{surroundings}}^4)$
  • Importance of Temperature Difference:
  • This equation highlights that the radiation varies with the fourth power of temperature.

Thermal Resistance Expressions for Conduction, Convection, and Radiation

• The resistances can be derived for conduction, convection, and radiation, denoted as:

  • For Conduction:
  • $R_{ ext{cond}} = \frac{L}{kA}$
  • Where $L$ = Thickness of material, $k$ = Thermal conductivity
  • For Convection:
  • $R_{ ext{conv}} = \frac{1}{hA}$
  • For Radiation:
  • The resistance for radiation involves deriving the expression:
  • $R_{ ext{rad}} = ext{combined factors}$

• Composite Systems:

  • In composite materials, the total resistance is the sum of individual resistances.
  • For a heat transfer system including convection and conduction,
  • The overall heat transfer can be expressed as:
    $Q = \frac{T_{ ext{hot}} - T_{ ext{cold}}}{R_{ ext{total}}}$
  • Where $R_{ ext{total}} = R_{ ext{conv1}} + R_{ ext{cond1}} + R_{ ext{cond2}} + R_{ ext{cond3}} + R_{ ext{conv2}}$

Practical Applications and Examples

• Example with Ducts/Walls:

  • Understanding heat transfer in windows with different configurations to minimize heat loss.
  • For instance, evaluating single versus double pane windows (thicknesses and materials).
  • Inner temperature: 25°C and outer temperature: -10°C.
  • Calculate temperature difference: $ext{Delta }T = 25 - (-10) = 35°C$

• Resistance Calculations:

  • Calculate resistances for each configuration:
  • Resistance for single-pane glass:
    $R_{ ext{single}} = \frac{L_{ ext{single}}}{k A}$
  • For double-pane glass use:
    $R_{ ext{double}} = \frac{L_{ ext{double}}}{kA}+\frac{4 imes ext{air thickness}}{k_{ ext{air}}A}$

• Thermal Conductivity Considerations:

  • Use of materials like copper for cooking (high conductivity) vs. aluminum for thermal barrier (low conductivity).

Subjective Reflection and Conclusion

• The importance of considering thermal resistance and designing effective thermal barriers to minimize heat loss.

• Homework Assignments:

  • Complete given exercises on heat transfer, with follow-up discussions scheduled individually.

• Assessment Guidance:

  • Completion and understanding of practical applications can aid in future exams and group projects.
  • Encourage participation in discussions and evaluations, reflecting truths and improving knowledge.