Heat transfer Chapter 1: Introduction
These notes introduce heat transfer as the study of energy exchange rates driven by temperature differences. They clarify the distinction between energy and temperature, explain how energy is stored at the microscopic level, introduce the concept of local thermodynamic equilibrium, and provide a first overview of the fundamental heat transfer mechanisms: conduction, convection, radiation, and phase change. The emphasis is on physical meaning and modeling intuition rather than equations
Context & Motivation
Heat transfer complements thermodynamics.
Thermodynamics tells us how much energy is required to move between equilibrium states.
Heat transfer tells us how fast that energy is exchanged.
Engineering systems rarely operate at equilibrium:
Engines cool down.
Walls lose heat.
Fluids warm up as they flow.
Phase changes occur over finite time.
Understanding rates of energy exchange is therefore essential for:
Thermal design
Safety analysis
Efficiency optimization
Multiphysics CFD simulations
Energy vs. Temperature
3.1 What Energy Really Means
Energy is a conserved property of matter and fields. It can:
Be stored
Be transferred
Change form
but cannot be created or destroyed.
In heat transfer, we mainly care about how energy is stored inside matter and how it moves between regions.
3.2 Microscopic Energy Storage Mechanisms
Energy is stored in matter through discrete microscopic modes:
In gases
Translational motion (molecule moving)
Rotational motion (molecule spinning)
Vibrational motion (atoms oscillating)
Electronic excitation (electrons at higher energy states)
Each mode becomes active only when sufficient energy is available.
At low temperatures, only translation is active; at higher temperatures, more modes contribute.
This explains why thermal properties depend on temperature.
In liquids
Same molecular modes as gases
Plus intermolecular potential energy
Energy added to a liquid can be used to:
Increase molecular agitation (temperature rise)
Break intermolecular bonds (phase change)
In solids
Atoms vibrate around fixed lattice positions
Collective vibrations (phonons) dominate
Temperature in solids primarily measures vibrational energy, not motion through space.
3.3 Energy in Vacuum
Energy can also exist without matter:
Electromagnetic radiation
Vacuum energy (quantum effects)
Radiation is especially important for high-temperature heat transfer and does not require a material medium.
What Temperature Actually Measures
Temperature is not a measure of total energy.
Instead:
It measures the energy stored in the most fundamental active mode:
Translational kinetic energy (gases/liquids)
Vibrational kinetic energy (solids)
Other energy storage modes may exist but are not directly reflected by temperature unless equilibrium is achieved.
Local Thermodynamic Equilibrium (LTE)
In real materials, energy constantly redistributes between storage modes through collisions and interactions.
Key insight:
This redistribution happens very fast (microseconds or less)
Much faster than typical engineering time scales
Therefore, in most heat transfer problems:
Each small region can be assumed to be in local thermodynamic equilibrium
Classical thermodynamic relations remain valid locally
Exceptions:
Rarefied gases
Shock waves
Very fast transients
High-altitude or vacuum environments
Conservation of Energy (Conceptual View)
All heat transfer problems are governed by energy conservation.
Physically, this means:
Energy inside a region can change
Energy can move by different mechanisms
Energy can be generated or absorbed (chemical reactions, phase change)
In CFD, this is captured by the energy equation, which accounts for:
Convection
Conduction
Radiation
Viscous dissipation
Species diffusion
Phase change sources
Fundamental Heat Transfer Mechanisms
7.1 Conduction
Occurs within solids and fluids at rest
Driven by temperature gradients
Microscopic origin:
Molecular collisions (fluids)
Lattice vibrations and electron motion (solids)
Conduction dominates when:
Velocities are small
Solids are involved
Thin layers resist heat flow
7.2 Convection
Heat transfer due to fluid motion
Energy is transported with the flow
Types:
Forced convection: flow driven externally
Natural convection: buoyancy-driven
Boiling convection: phase change at surfaces
Convection tightly couples:
Momentum equations
Energy equation
This is why heat transfer problems often require solving flow and energy simultaneously.
7.3 Radiation
Energy transfer by electromagnetic waves
Requires no medium
Strongly temperature-dependent
Radiation becomes important when:
Temperatures are high
Large surfaces are involved
Conduction and convection are weak
Radiation modeling is computationally expensive and must be chosen carefully based on optical thickness.
7.4 Phase Change Heat Transfer
Energy absorbed or released during state change
Temperature may remain nearly constant during the process
Examples:
Evaporation
Condensation
Boiling
Melting / solidification
Phase change often dominates heat transfer rates due to latent heat and requires specialized multiphase models
Engineering and CFD Perspective
From a modeling standpoint:
Heat transfer problems require:
Energy equation activation
Correct material properties
Appropriate boundary conditions
Multiple mechanisms often act simultaneously
Convergence must be assessed via heat balances, not just residuals
Radiation and phase change significantly increase model complexity and numerical stiffness.
Study Priorities
If time is limited, the most important concepts to look into:
Difference between heat transfer and thermodynamics
Meaning of temperature vs energy
Local thermodynamic equilibrium
Physical meaning of conduction, convection, radiation
Why phase change dominates heat transfer
Key Takeaways
Heat transfer studies rates of energy exchange.
Energy is stored in discrete microscopic modes.
Temperature measures only part of total energy.
Local thermodynamic equilibrium enables classical modeling.
Conduction, convection, radiation, and phase change are fundamentally different mechanisms.
Most real problems involve multiple mechanisms simultaneously.