This chapter introduces convective heat transfer as energy transport driven by fluid motion. It explains convection from a microscopic viewpoint, formulates energy conservation in moving fluids, and distinguishes forced, natural, and mixed convection. Boundary layer concepts, laminar–turbulent behavior, and regime classification are presented with emphasis on physical interpretation and numerical modeling implications.

Why Convection Is Fundamentally Different from Conduction

Conduction:

Exists even if the fluid is at rest
Requires temperature gradients

Convection:

Exists only if the fluid moves
Transfers energy even if temperature is spatially uniform
Couples momentum, mass, and energy transport

This coupling makes convection:

Nonlinear
Often unsteady
Potentially turbulent and chaotic

In engineering practice, convection is almost always the dominant heat transfer mode whenever fluids are involved.

Microscopic Origin of Convection

At the molecular level:

All fluids consist of randomly moving molecules
Heat conduction comes from random molecular motion

Key conceptual step:

Molecular velocity is split into:
- A mean (macroscopic) velocity
- A random (drift) velocity

Physical interpretation:

Drift velocity → conduction
Mean velocity → convection

Important consequence:

Conduction and convection share the same physical origin
There is no such thing as “pure” convection; conduction is always present

Energy Storage in Moving Fluids

4.1 Specific Total Energy

In a moving fluid, energy includes:

Internal (microscopic) energy
Kinetic energy due to bulk motion

Specific total energy represents:

All energy stored per unit mass that is transported with the flow

This quantity is central for writing conservation laws in convection problems.

4.2 Enthalpy and Total Enthalpy

Enthalpy extends internal energy by accounting for:

Pressure work needed to “make room” for the fluid

Total enthalpy further includes:

Kinetic energy
(Optionally) potential energy due to gravity

Why enthalpy matters:

It is the natural variable in flowing systems
It simplifies the energy equation
It directly relates to what machines can extract as useful work

Convective Heat Flux: Physical Meaning

Convective heat flux is:

Energy transported across a surface due to fluid motion

Key characteristics:

Proportional to fluid velocity normal to the surface
Proportional to the energy stored per unit volume

Fundamental difference from conduction:

Convection does not require temperature gradients
Uniform-temperature flow can still transport heat

Liquids generally convect more heat than gases because:

Higher density
Higher heat capacity

Energy Conservation in a Moving Fluid

6.1 Control Volume Perspective

Energy conservation balances:

Time rate of change of energy inside the fluid
Convective transport across boundaries
Conductive heat transfer
Work done by pressure, viscous stresses, and body forces
Internal heat sources

Unlike solids:

Fluids can exchange energy by doing work
Pressure and viscous stresses matter

6.2 Local (Differential) Perspective

At each point in space:

Energy changes due to:
- Advection by velocity
- Diffusion by conduction
- Mechanical work
- Volumetric heat sources

This equation is:

Strongly coupled with momentum equations
Central to CFD solvers

Boundary Conditions and Interfaces

At solid–fluid interfaces:

Temperature is continuous
Heat flux is continuous

Physically:

Energy leaving the solid must enter the fluid

In CFD:

This coupling is the basis of conjugate heat transfer
Mesh quality near walls becomes critical

Order-of-Magnitude Analysis and Regimes

Because the full equations are complex:

Scale analysis is used to identify dominant mechanisms

Key outcomes:

Identification of boundary layers
Separation of forced, natural, and mixed convection
Simplified models for engineering use

Forced Convection

9.1 Physical Definition

Forced convection occurs when:

Flow is imposed externally (pump, fan, pressure gradient)
Heat transfer does not create the flow

Examples:

Pipe flows
External flows over plates
Heat exchangers

9.2 Boundary Layers

Near walls:

Velocity goes to zero
Temperature adjusts from wall value to bulk value

Two coupled boundary layers exist:

Momentum boundary layer
Thermal boundary layer

Their relative thickness depends on:

Fluid properties
Flow regime

9.3 Laminar vs Turbulent Forced Convection

Laminar flow:

Heat transfer dominated by molecular diffusion
Predictable, smooth profiles

Turbulent flow:

Strong mixing enhances heat transfer
Heat transfer coefficients increase significantly
Near-wall resolution becomes critical in CFD

9.4 Turbulent Boundary Layer Structure

Turbulent boundary layers contain:

Viscous sublayer
Buffer layer
Logarithmic region
Outer layer

Thermal boundary layers mirror this structure but depend strongly on:

Prandtl number

Modeling implication:

Wall functions vs wall-resolved approaches must be chosen carefully

Natural Convection

10.1 Physical Mechanism

Natural convection arises when:

Temperature differences create density differences
Gravity converts density differences into motion

The flow exists because of heat transfer itself

10.2 Buoyancy and the Boussinesq Approximation

For small temperature differences:

Density variations can be neglected everywhere
Except in the gravity term

This approximation:

Simplifies equations
Retains correct buoyancy physics
Is widely used in CFD

10.3 Regimes and Transition

Natural convection behavior depends on:

Relative strength of buoyancy vs diffusion

Key idea:

Below a critical threshold → pure conduction
Above it → convective motion develops

Transition from laminar to turbulent occurs gradually and over wide ranges

10.4 Numerical Implications

Natural convection simulations:

Require gravity and energy equations
Strongly couple momentum and energy
Are sensitive to mesh resolution near walls

Best practice:

Resolve both velocity and thermal sublayers (y⁺ ≈ 1)

Mixed Convection

Mixed convection occurs when:

Forced flow and buoyancy are comparable

Typical examples:

Heated pipes with moderate flow rates
Electronic cooling
Atmospheric and environmental flows

Engineering challenge:

Flow direction can change
Heat transfer may be enhanced or suppressed

Study Priorities

If time is limited, the most important concepts to look into:

Microscopic interpretation of convection
Difference between convective and conductive heat flux
Energy conservation in moving fluids
Boundary layer concepts
Forced vs natural convection mechanisms
CFD implications near walls

Key Takeaways

Convection is energy transport due to fluid motion.
It is inherently coupled to momentum and mass transfer.
Boundary layers control convective heat transfer.
Turbulence greatly enhances heat transfer.
Natural convection is driven by buoyancy, not external forcing.
Correct regime identification is essential for modeling.

Heat transfer Chapter 3: Convective heat transfer