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

QuantityMeaningUnits
TemperatureIndirect measure of thermal energy storedK or °C
Heat EnergyThermal energy transferred over timeJ
Heat Transfer RateTransfer of thermal energy per unit timeJ/s or W
Heat FluxTransfer of energy per unit time and surface areaW/m²

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{(T1 - T2)}{\Delta x}
      • Where: k is thermal conductivity, A is area,
        T1 and T2 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{conduct} = k imes A imes \frac{(T1 - 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(T1 - T2)}{\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(Ts - T∞)
    • Where h is heat transfer coefficient, Ts is surface temperature, T∞ 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{total} = R{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.