Notes on Steady State Heat Transfer and Heat Exchangers

Overview of Presentation

• This lecture addresses the following topics:
  • Lecture 5: Steady State Heat Transfer
  • Lecture 6: Heat Exchangers
• Aim of seminar:
  • Review of Block 1 and 2
  • Reinforce learning so far
  • Opportunity for students to ask questions

Heat Transfer Mechanisms

• Mechanisms of Heat Transfer:
  • Conduction: Heat transfer through solid materials
  • Convection: Heat transfer through fluids (liquids or gases)
  • Radiation: Transfer of heat through electromagnetic waves
• Thermal Resistance: Resisting heat flow through materials
• Critical Radius of Insulation: Insight into optimal insulation thickness

Quantity Definitions

Overview of Heat Transfer

• Definition: Heat transfer is energy movement between systems (or to surroundings) due to a temperature difference, flowing from high to low temperatures.
• Modes of Heat Transfer:
  • Conduction: Direct contact transfer
  • Convection: Fluid motion transfer
  • Radiation: Transfer without direct contact (e.g., heat from the sun)

Thermal Management Examples

• Understanding Causes of Problems:
  • Identify type of heat transfer involved to formulate effective solutions.
• Example Problems and Solutions:
  • Radiation causing excessive heat from exhaust causing damage -> Solution: Insulate exhaust or add radiation shields.
  • Hot air convection causing issues in engine bay -> Solution: Increase airflow or use air deflectors.

Conduction

• Process: Energy transfers from energetic particles to less energetic ones.
• Fourier’s Law:
  • Rate of heat conduction: $Q = kA \frac{(T<em>1 - T</em>2)}{\Delta x}$
    • Where: $k$ is thermal conductivity, $A$ is area,
      $T<em>1$ and $T</em>2$ are temperatures on respective sides,
      $\Delta x$ is thickness of material.

Thermal Conductivity

• Definition: Ability of a material to conduct heat.
• Units: $(W/m°C \, or \, W/mK)$
• High Thermal Conductivity: Good conductor; conversely, low value indicates poor conduction (insulator).
• Conduction Equation:
  $H<em>{conduct} = k imes A imes \frac{(T</em>1 - T_2)}{\Delta x}$

Worked Example of Heat Loss Through a Wall

• Parameters:
  • Thickness (0.15 m), thermal conductivity ($k$) (1.7 W/mK), inner (1400 K), outer (1150 K) temperatures.
• Heat Loss Calculation: $Q = \frac{kA(T<em>1 - T</em>2)}{\Delta x}$
  • Rate of heat loss is 1700 W, and heat flux can be derived by dividing heat loss by area.

Convection

• Definition: Energy transfer between solid and moving fluid.
• Newton’s Law of Cooling: $Q = hA(T<em>s - T</em>∞)$
  • Where $h$ is heat transfer coefficient, $T<em>s$ is surface temperature, $T</em>∞$ is ambient temperature.
• Heat Transfer Coefficient Ranges:
  • Free Convection: $h = 5 - 10 \, W/m²K$
  • Forced Convection: h > 10 \, W/m²K

Worked Example of Convection

• Parameters:
  • Square plate (width 5 cm), plate temperature (85 °C), air temperature (15 °C), $h$ (200 W/m²K).
• Calculation: Use above convection equation to find heat rejection.

Radiation

• Definition: Energy emitted by matter in electromagnetic form.
• Stefan-Boltzmann Law describes heat radiation from black body: $Q = \epsilon \sigma A (T^4)$
  • Where $\sigma = 5.67 \times 10^{-8} W/m²K^4$ and $\epsilon$ is emissivity.
• Effective Surfaces:
  • Black body (emissivity = 1) Vs. Grey body (emissivity < 1).

Critical Radius of Insulation

• Understanding Critical Thickness:
  • Flat Plate: More insulation reduces heat transfer.
  • Cylinders/Spheres: Adding insulation can decrease convective resistance due to increased surface area, thus increasing heat transfer under certain conditions.

Thermal Resistance Analogy

• Electrical vs. Thermal Resistance Comparison:
  • Electrical Circuit Components:
  • Voltage = Temperature difference
  • Current = Heat Flow
• Thermal Resistance Calculation:
  $R<em>{total} = R</em>{conv} + R_{cond}$

Key Learning Points

• The variation of temperature and heat flow increases when thermal resistance reduces and/or temperature differences increase.
• Heat flow effectiveness is intricately related to materials' properties like thermal conductivity $(k)$ and heat transfer coefficient $(h)$.

Final Questions and Examples

• Apply knowledge through real-world heat transfer scenarios involving conduction, convection, and radiation common in engineering applications.
• Complete suggested exercises to reinforce the understanding of heat transfer concepts and calculations.