## Heat Conduction

#### Fourier’s Law

The rate of heat transfer by conduction is expressed as:

where:

= rate of heat transfer (W) = thermal conductivity of the material (W/m·K) = area of the cross-section (m²) = temperature gradient (K/m)

#### Transient Conduction Equation

For a transient state, the one-dimensional heat conduction equation can be used:

where:

= temperature (K) = time (s) = density (kg/m³) = specific heat capacity (J/kg·K)

## Heat Convection

#### Newton’s Cooling Law

The rate of heat transfer by convection is expressed as:

where:

= rate of heat transfer (W) = convective heat transfer coefficient (W/m²·K) = surface area (m²) = surface temperature (K) = temperature of the fluid far from the surface (K)

## Heat Radiation

#### Stefan-Boltzmann Law

The rate of heat transfer by radiation is expressed as:

where:

= rate of heat transfer (W) = emissivity of the surface (dimensionless) = Stefan-Boltzmann constant ( ) = surface area (m²) = surface temperature (K) = surrounding temperature (K)

## Heat Transfer in Composite Systems

#### Thermal Resistance

The total thermal resistance

where each

with:

= thickness of the layer (m) = thermal conductivity of the layer (W/m·K)

#### Heat Transfer in Parallel

The rate of heat transfer in a parallel system can be calculated as:

where each

## Heat Transfer by Evaporation and Condensation

#### Latent Heat

The heat transferred during evaporation or condensation is calculated as:

where:

= heat transferred (J) = mass of the fluid (kg) = latent heat of evaporation or condensation (J/kg)

## Heat Transfer Efficiency

#### Efficiency of a Heat Exchanger

Efficiency can be defined as:

where:

= actual rate of heat transfer (W) = maximum rate of heat transfer (W)

## Dimensionless Numbers

#### Nusselt Number (Nu)

The Nusselt number is a dimensionless number that characterizes heat transfer by convection compared to conduction. It is defined as:

where:

= convective heat transfer coefficient (W/m²·K) = characteristic length (m), which can be the diameter of a pipe, the height of a plate, etc. = thermal conductivity of the fluid (W/m·K)

**Interpretation:**

- A high Nusselt number indicates that convection is significant compared to conduction. This is often the case in turbulent flows or in systems where high temperatures are applied.
- A low Nusselt number suggests that conduction is the predominant mode of heat transfer, as in laminar flow situations.

#### Reynolds Number (Re)

The Reynolds number is a dimensionless number that describes the relationship between inertial forces and viscous forces in a moving fluid. It is defined as:

where:

= density of the fluid (kg/m³) = velocity of the fluid (m/s) = characteristic length (m) = dynamic viscosity of the fluid (Pa·s)

**Interpretation:**

: laminar flow. : turbulent flow. : transitional regime.

#### Prandtl Number (Pr)

The Prandtl number is a dimensionless number that relates momentum diffusion (viscosity) to heat diffusion. It is defined as:

where:

= dynamic viscosity (Pa·s) = specific heat capacity (J/kg·K) = thermal conductivity (W/m·K)

**Interpretation:**

- A
indicates that heat diffusion is faster than momentum diffusion (light fluid). - A
suggests that momentum diffusion is faster than heat diffusion (heavy fluid).

#### Schmidt Number (Sc)

The Schmidt number is a dimensionless number that relates mass diffusion to momentum diffusion in a fluid. It is defined as:

where:

= mass diffusion coefficient (m²/s)

**Interpretation:**

- A
indicates that mass diffusion is faster than momentum diffusion. - A
indicates that momentum diffusion is faster than mass diffusion.

#### Grashof Number (Gr)

The Grashof number is a dimensionless number that measures the importance of buoyancy forces in a fluid due to temperature differences. It is defined as:

where:

= acceleration due to gravity (m/s²) = thermal expansion coefficient (1/K) = surface temperature (K) = surrounding temperature (K) = characteristic length (m) = kinematic viscosity (m²/s)

**Interpretation:**

- A high
indicates that buoyancy forces dominate the flow, as in natural convection. - A low
suggests that the flow is dominated by viscosity.

## Physical Constants

Table with some of the main physical constants and properties that are useful in the analysis of heat transfer and fluid mechanics.

Constant/Property | Symbol | Value | Units | Description |
---|---|---|---|---|

Stefan-Boltzmann Constant | W/m²·K⁴ | Constant that relates thermal radiation to temperature. | ||

Thermal Conductivity of Air | W/m·K | Thermal conductivity of air at 25 °C. | ||

Thermal Conductivity of Water | W/m·K | Thermal conductivity of water at 25 °C. | ||

Specific Heat Capacity of Water | J/kg·K | Specific heat capacity of water. | ||

Density of Water | kg/m³ | Density of water at 4 °C. | ||

Dynamic Viscosity of Water | Pa·s | Dynamic viscosity of water at 25 °C. | ||

Dynamic Viscosity of Air | Pa·s | Dynamic viscosity of air at 25 °C. | ||

Density of Air | kg/m³ | Density of air at 25 °C and 1 atm. | ||

Gravity | m/s² | Acceleration due to gravity on Earth. | ||

Latent Heat of Vaporization of Water | J/kg | Heat required to vaporize 1 kg of water at 100 °C. | ||

Emissivity of Steel | dimensionless | Emissivity of the steel surface. | ||

Emissivity of Water | dimensionless | Emissivity of the water surface. |

### Notes on Constants:

- The provided values are approximate and may vary with temperature and pressure. It is important to consult specific tables or technical literature for more precise values under particular conditions.
- Properties such as density and viscosity of air and water change with temperature, so be sure to consider the specific conditions of the problem you are analyzing.

## Properties of Substances

Table with some important properties of the main materials and substances commonly used in heat transfer analysis.

Material/Substance | Thermal Conductivity | Specific Heat Capacity | Density | Viscosity | Emissivity | Description |
---|---|---|---|---|---|---|

Water | Liquid commonly used in heating and cooling systems. | |||||

Air | Gas used as a heat transfer medium in convection systems. | |||||

Copper | Metal with high thermal conductivity, used in electrical and thermal applications. | |||||

Aluminum | Lightweight metal efficient in heat transfer, used in heat exchangers. | |||||

Steel | Material used in structures and thermal equipment components. | |||||

Glass | Material used in windows and containers, with low thermal conductivity. | |||||

Polypropylene (PP) | Plastic used in low-temperature applications. | |||||

Polystyrene (PS) | Common insulating material, used in packaging and insulation. | |||||

Concrete | Construction material with good heat storage capacity. |

### Notes on Properties:

- The provided values are approximate and may vary depending on temperature, pressure, and purity of materials. It is always recommended to consult specific sources or technical literature for accurate values.
**Thermal conductivity**is essential for determining how a material can transfer heat.**Specific heat capacity**indicates the amount of energy needed to change the temperature of a unit mass of material.**Density**is important for calculating the weight and volume of a material in engineering applications.**Viscosity**affects the flow of liquids and gases and, therefore, heat transfer in convection systems.**Emissivity**is a key factor in thermal radiation, affecting how a material emits and absorbs thermal radiation.