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
| Quantity | Meaning | Units |
|---|
| Temperature | Indirect measure of thermal energy stored | K or °C |
| Heat Energy | Thermal energy transferred over time | J |
| Heat Transfer Rate | Transfer of thermal energy per unit time | J/s or W |
| Heat Flux | Transfer of energy per unit time and surface area | W/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.