Thermal Analysis
Glossary Of Terms

Absorption is defined as the process in which radiation intercepted by matter is converted into internal thermal energy. It is the portion of the incident radiation that is absorbed by the material. This can be characterized by directional, hemispherical, spectral, and total absorption coefficients.

An adiabatic condition is a process or boundary condition in which no heat transfer occurs. In the context of heat transfer, an adiabatic condition implies that there is no heat exchange between the system and its surroundings. This is important because it allows for the analysis of heat transfer processes under specific conditions, such as when insulation prevents heat from entering or leaving the system.

Assuming adiabatic conditions can simplify the calculation of heat transfer rates and temperature distributions. By considering adiabatic conditions, one can focus on specific aspects of heat transfer—such as conduction, convection, or radiation—without the added complexity of heat exchange with the environment.

Advection refers to the transport of a substance through the bulk motion of a fluid. It is specifically associated with the movement of a large number of molecules collectively or as aggregates in the fluid. When there is a temperature gradient, this collective movement contributes to heat or mass transfer. In the context of heat transfer, advection is synonymous with the bulk fluid motion that contributes to the total heat transfer, in addition to random molecular motion (diffusion).

The Biot number, denoted as Bi, is a dimensionless number that plays a fundamental role in conduction problems involving surface convection effects. It is defined as the ratio of the internal thermal resistance of a solid body to the thermal resistance at the solid–fluid interface. Mathematically, it is expressed as:

$$Bi = \frac{h L}{k}$$

Where:

• h is the convective heat transfer coefficient [W/m².K]
• L is a characteristic length (such as the thickness of the solid body) [m]
• k is the thermal conductivity of the solid body [W/m.K]

The Biot number provides a measure of the temperature drop within the solid body relative to the temperature difference between the surface of the solid and the surrounding fluid. It is used to evaluate the significance of convective heat transfer in comparison to conductive heat transfer in a given system.

A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of wavelength and direction. It also emits the maximum amount of radiation possible for a given temperature and wavelength. The radiation emitted by a black body is a function of wavelength and temperature, but it is independent of direction, making it a diffuse emitter. No real surface exhibits the exact properties of a black body, but the black body concept serves as a standard against which the radiative properties of real surfaces can be compared.

Boiling is the process in which evaporation occurs at a solid–liquid interface. It happens when the temperature of the surface exceeds the saturation temperature corresponding to the fluid pressure. Heat is transferred from the solid surface to the liquid, leading to the formation of vapor bubbles that grow and detach from the surface. Boiling can occur under various conditions, such as pool boiling, forced convection boiling, subcooled boiling, and saturated boiling, each with distinct characteristics. The boiling process is influenced by factors such as superheat (temperature excess), surface properties, the thermophysical properties of the liquid, and buoyant forces.

A boundary layer is a thin layer of fluid that develops near a surface when a fluid flows over that surface. It is characterized by a gradual transition in fluid velocity (velocity boundary layer) and other properties, such as temperature (thermal boundary layer), from the surface to the outer free stream. The boundary layer is typically defined by its thickness and is important in problems involving convective heat transfer.

Buoyancy refers to the upward force exerted by a fluid on an object submerged in it. This force results from the pressure difference between the top and bottom of the object and is directly related to the density of the fluid. When an object is placed in a fluid, it displaces a portion of that fluid, and the weight of the displaced fluid exerts an upward force on the object—this is known as the buoyant force.

In the context of fluid mechanics, buoyant forces play a significant role in driving fluid motion during free convection, where density variations caused by temperature differences lead to the generation of buoyant forces. These forces drive the movement of the fluid, resulting in phenomena such as natural circulation and heat transfer in various engineering and environmental applications.

Condensation is the process in which a substance changes from its gaseous state to its liquid state. It is a crucial phenomenon in heat and mass transfer, as it involves the transfer of thermal energy (heat) and the transfer of mass from the vapor phase to the liquid phase.

Conduction is the transfer of energy within a medium as a result of a temperature gradient, and it occurs due to random atomic or molecular activity. This type of heat transfer is governed by Fourier’s law, which describes the heat flux in relation to the temperature distribution within the medium. Conduction can occur in various scenarios, including steady-state and transient conduction, and in both one-dimensional and multidimensional systems. Moreover, conduction is the only form of heat transfer in a medium where the temperature distribution is governed by the heat diffusion equation.

Convection refers to the form of heat transfer that involves both energy transport through the bulk motion of the fluid ((advection)) and the random motion of fluid molecules (conduction or diffusion). It occurs when a moving fluid comes into contact with a surface at a different temperature, resulting in the transfer of heat. The interaction between the fluid and the surface leads to the development of a boundary layer in the fluid, where the velocity varies from zero at the surface to a finite value associated with the flow.

Diffusion is the movement of molecules from a region of high concentration to a region of low concentration. It is a process in which molecules spread and mix with other molecules due to their random motion. In the context of mass transfer, diffusion refers to the movement of a component within a mixture as a result of a concentration difference. This process is governed by Fick’s law, which describes the diffusive flux of a component in terms of the concentration gradient and the binary diffusion coefficient.

Diffusivity is a measure of how quickly a substance will spread or diffuse. It can be defined as the proportionality constant between the flux of a substance and its concentration gradient. In the context of mass transfer, diffusivity specifically refers to the rate at which a particular component within a mixture will spread or diffuse.

Dynamic viscosity, denoted by the symbol μ, is defined as the measure of a fluid's resistance to shear or angular deformation. It quantifies the internal friction within the fluid during flow and is a key property that determines how the fluid behaves under shear stress. In the context of a Newtonian fluid, dynamic viscosity is directly proportional to the shear deformation. It is measured in units of [Pa·s] in the SI system. Alternative units include [lbm/ft·h] and [lbf·h/ft²].

The electromagnetic spectrum encompasses all forms of electromagnetic radiation, ranging from high-energy gamma rays and X-rays to ultraviolet (UV) radiation, visible light, and infrared radiation, to longer wavelengths such as microwaves and radio waves. It covers wavelengths from approximately 0.1 to 100 μm. This spectrum is important in various fields such as high-energy physics, nuclear engineering, electrical engineering, and atmospheric science due to the diverse properties and interactions of the different types of radiation.

Emission refers to the process by which a material releases thermal energy in the form of radiation. This radiation is emitted as electromagnetic waves, and the intensity and spectral distribution of the emitted radiation depend on the temperature and properties of the emitting material. Emission can be characterized by parameters such as total emissive power, spectral emissive power, emissivity, and directional emissivity, which describe the amount and characteristics of the radiation emitted by a surface.

Enthalpy H is a thermodynamic property of a system. It represents the total internal energy of a system, including the amount of energy associated with the system's pressure and volume. Enthalpy is defined as H = U + PV, where U is the internal energy of the system, P is the pressure, and V is the volume. In the context of fluid mechanics and heat transfer, enthalpy is often used to describe the total energy of a fluid, including both the internal energy and the energy associated with pressure and volume.

Evaporation is the process in which a liquid changes into a gas or vapor. This occurs when the molecules in a liquid gain enough energy to break free from the liquid phase and enter the gas phase. The energy required for evaporation typically comes from the surroundings, and the process results in a cooling effect on the remaining liquid. In the context of heat and mass transfer, evaporation is an important aspect of processes such as evaporative cooling, where the transfer of energy and mass between a liquid and its environment is crucial.

Forced convection is the process of heat transfer in which fluid motion is caused by external means, such as a fan, a pump, or wind. An example of forced convection is using a fan to provide air cooling for hot electrical components on circuit boards. In forced convection, the flow is driven by external forces rather than natural buoyant forces.

In forced convection boiling, the majority of heat transfer occurs through direct transfer from the hot surface to the liquid. This is similar to a form of forced convection in the liquid phase, where fluid motion is induced by the rising vapor bubbles. The process of forced convection boiling significantly affects heat transfer characteristics, and correlations are used to understand and predict these effects.

Fouling refers to the accumulation of unwanted material on solid surfaces, especially in heat exchangers. This buildup can reduce the efficiency of heat transfer and increase resistance to fluid flow, leading to decreased performance of the heat exchanger. Fouling can be caused by various factors, such as the deposition of solids, precipitation of dissolved salts, biological growth, or chemical reactions. It is a common issue in industrial processes and can be mitigated through regular cleaning and maintenance of heat exchanger surfaces.

The fouling factor, denoted as R_f, is a measure of the resistance to heat transfer caused by the accumulation of deposits on a heat transfer surface. It represents the additional thermal resistance due to fouling and is typically expressed in [m² · K/W]. Higher fouling factors indicate greater resistance to heat transfer as a result of fouling.

The Fourier number, often denoted as Fo, is a dimensionless time parameter used to characterize transient conduction problems. It is defined as the ratio of the rate of heat conduction within a solid to the rate of thermal energy storage within the solid. Mathematically, it is expressed as:

$$Fo = \frac{\alpha \cdot t}{L^2}$$

• α is the thermal diffusivity of the solid
• t is time
• L is a characteristic length of the solid

The Fourier number is used to determine the relative significance of conduction within a solid over a given period of time. It helps in understanding the behavior of temperature distribution within the solid during transient conduction. For example, a small Fourier number indicates that the conduction process is relatively fast compared to the rate of heat storage, resulting in a rapidly changing temperature distribution. Conversely, a large Fourier number suggests that the rate of heat storage within the solid is significant compared to the rate of heat conduction, leading to a slower change in temperature distribution over time.

Fourier’s law is a fundamental principle that governs heat conduction and expresses the relationship between heat flux (the rate of heat transfer per unit area) and the temperature gradient (the rate of change of temperature with distance) in a material. It is given by the equation:

$$q = -k \nabla T$$

Where:

• q de warmtestroom is [W/m²]
• k de thermische geleidbaarheid van het materiaal is [W/m·K]
• ∇T de temperatuurgradiënt vertegenwoordigt [K/m]

Fourier’s law states that the heat flux is proportional to the negative of the temperature gradient, and it applies to all forms of matter, including solids, liquids, and gases. The law provides a means to calculate heat transfer within a material based on the temperature distribution and is essential for understanding and analyzing conductive heat transfer in various physical systems.

Natural convection is a type of fluid motion that occurs within a fluid as a result of buoyancy, without any external driving conditions. It arises when a body force—usually gravity—acts on a fluid with density gradients, leading to the development of free convection currents. This type of convection is driven by the presence of a temperature gradient, which causes buoyant forces and the formation of free convection boundary layers. Natural convection plays an important role in various systems and applications, influencing heat transfer, temperature distributions, and environmental processes.

The Froude number (Fr) is a dimensionless number used to quantify the influence of gravity on fluid motion. It is defined as the ratio of inertial forces to gravitational forces and is given by the equation:

$$Fr = \frac{V}{\sqrt{gL}}$$

• V is the characteristic velocity [m/s]
• g is the gravitational acceleration [m/s²]
• L is the characteristic length [m]

In the context of fluid flow, the Froude number is particularly important in the analysis of open channel flow and in determining the type of flow regime, such as subcritical, critical, or supercritical flow.

The Grashof number is a dimensionless number that relates buoyant forces to viscous forces in free convection heat transfer. It is defined as:

$$Gr = \frac{g \cdot \beta \cdot \Delta T \cdot L^3}{\nu^2}$$

Where:

• g is the gravitational acceleration
• β is the coefficient of volumetric expansion
• ΔT is the temperature difference between the surface and the surrounding fluid
• L is a characteristic length
• ν is the kinematic viscosity

The Grashof number plays a crucial role in free convection, similar to the role the Reynolds number plays in forced convection. It is a measure of the influence of buoyant forces on the heat transfer process.

A gray body is a theoretical concept used in thermal radiation and heat transfer. It refers to a surface that emits and absorbs radiation with an emissivity and absorptivity that are independent of the wavelength of the radiation. This means a gray body emits and absorbs radiation equally well at all wavelengths—in other words, it has a constant emissivity and absorptivity across the entire electromagnetic spectrum.

Heat flux, denoted by the symbol q'', is the rate of heat transfer per unit area. It is a measure of the amount of thermal energy passing through a surface per unit time. Mathematically, it is defined as the heat transfer per unit time per unit area and is expressed in units of watts per square meter [W/m²].

An ideal gas is a theoretical gas composed of a large number of molecules that have no volume and no intermolecular forces. In an ideal gas, the molecules are in constant, random motion and undergo perfectly elastic collisions with each other and with the walls of the container. The behavior of an ideal gas is described by the ideal gas law, which relates pressure, volume, temperature, and the number of moles of gas. This law is represented by the equation:

$$P V = n R T$$

Where:

• P is the pressure
• V is the volume
• n is the number of moles
• R is the ideal gas constant
• T is the temperature

Irradiation refers to the radiant energy incident on a surface per unit area. It is related to radiative heat transfer, as it determines how much radiation is absorbed by a surface. The irradiation received by a surface influences the rate at which the surface gains or loses thermal energy through radiation. In the context of radiative heat transfer, irradiation plays a crucial role because it affects the heat exchange between surfaces and the surrounding environment.

Kinematic viscosity, denoted by the symbol ν, is a fluid property defined as the ratio of dynamic viscosity (measured in [Pa·s]) to mass density ρ,measured in [kg/m³]. It has units of [m²/s]. Kinematic viscosity is a measure of a fluid’s resistance to flow under the influence of gravity and provides insight into the fluid’s internal friction and ability to deform. In the context of fluid dynamics, kinematic viscosity plays a crucial role in determining the behavior of boundary layers, diffusion, and the overall flow characteristics of a fluid.

Laminar flow is a type of fluid flow in which the fluid moves in parallel layers with minimal mixing between them. In laminar flow, the fluid flows smoothly in an orderly manner, and the velocity of the fluid at each point remains constant over time. This type of flow is characterized by well-defined streamlines and low velocity gradients within the fluid. Laminar flow typically occurs at lower flow velocities and is distinguished by its organized and predictable behavior.

Latent heat refers to the energy associated with a phase change of a substance, such as from solid to liquid, liquid to gas, or vice versa. This energy is not related to a change in temperature but rather to the change in the physical state of the substance. For example, when a liquid evaporates and turns into a gas, or when a gas condenses into a liquid, the energy involved in this phase change is called latent heat. It is important to note that this energy is not directly related to the temperature of the substance but to the transformation in its physical state.

The lumped capacitance method is a simplified approach used to analyze transient conduction problems in which a solid body undergoes a sudden change in its thermal environment. The method assumes that the temperature within the solid is spatially uniform at any given moment during the transient process, meaning that temperature gradients inside the solid are considered negligible.

To determine the validity of the lumped capacitance method, a criterion is used to assess whether the method can be applied with reasonable accuracy. This criterion involves calculating the Biot number, which compares the convective heat transfer at the surface of the solid to the conductive heat transfer within the solid. If the Biot number is less than a certain threshold (typically 0.1), the lumped capacitance method is considered valid for the given problem.

The characteristic length, denoted as L_c, plays a crucial role in determining the method's validity. It is defined as the ratio of the volume of the solid to its surface area and facilitates the calculation of L_c for solids of various shapes. Additionally, the Fourier number, another dimensionless parameter, is used alongside the Biot number to characterize transient conduction problems.

Overall, the lumped capacitance method provides a simple and convenient way to analyze transient heating and cooling problems under specific conditions and is often used as a first approximation for such scenarios.

Newton’s law of cooling is a fundamental principle in heat transfer. It states that the rate of heat transfer between a surface and a fluid is proportional to the temperature difference between the surface and the fluid. Mathematically, it can be expressed as:

$$q'' = h \cdot \left( T_s - T_{\infty} \right)$$

Where:

• q'' is the heat flux [W/m²]
• h is the convective heat transfer coefficient [W/m²⋅K]
• T_s is the surface temperature [K]
• T_∞ is the fluid temperature far from the surface [K]

This law is essential for understanding the heat transfer process between a surface and a fluid, and it provides a foundation for analyzing convective heat transfer in various engineering applications.

Learn more about Newton's Law of Cooling.

A phase change refers to the transition of a substance from one state of matter to another, such as from solid to liquid, liquid to gas, or vice versa. During a phase change, the energy associated with the substance can be divided into sensible energy, which is primarily related to temperature changes, and latent energy (or latent heat), which is associated with the phase transition.

For example, when a material changes from solid to liquid (melting) or from liquid to gas (vaporization, evaporation, boiling), latent energy increases. Conversely, when the phase change occurs from gas to liquid (condensation) or from liquid to solid (solidification, freezing), latent energy decreases.

Pool boiling is a process that occurs when the temperature of a solid surface exceeds the saturation temperature corresponding to the fluid pressure. Heat is transferred from the solid surface to the liquid, leading to the formation of vapor bubbles that then detach from the surface.

Pool boiling typically occurs under conditions where the liquid is stationary, and the motion near the surface is due to natural convection and mixing caused by the growth and detachment of bubbles. It can be classified as either subcooled or saturated, depending on the temperature of the liquid. In subcooled boiling, most of the liquid is below the saturation temperature, whereas in saturated boiling, the liquid temperature is slightly above the saturation temperature.

The Prandtl number, denoted as Pr, is a dimensionless number that represents the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity in a fluid. It provides a measure of the relative effectiveness of momentum and energy transfer by diffusion in the velocity and thermal boundary layers, respectively.

In laminar boundary layers, the value of the Prandtl number significantly affects the relative thickness of the velocity boundary layers and the thermal boundary layers. Specifically, the Prandtl number influences the relative growth of the velocity and thermal layers: higher Prandtl numbers lead to greater development of the thermal boundary layer compared to the velocity boundary layer.

See Thermal Radiation.

Radiative intensity refers to the directional distribution of radiation either leaving a surface or incident upon a surface from various directions. It is mathematically defined using the spherical coordinate system, where the differential solid angle is used to measure the directional distribution of radiation. The intensity of radiation emitted or received by a surface is typically expressed in terms of the rate at which radiative energy is emitted or incident at a specific wavelength, in a specific direction, and per unit area of the emitting or receiving surface. This concept is crucial for understanding the directional effects of radiation and for determining the net radiative heat transfer rate.

Reflection is the process by which incident radiation is bounced back from the surface of a material. In the context of radiative heat transfer, reflection plays an important role in determining the amount of thermal energy absorbed by a material. The reflectivity of a surface—defined as the ratio of reflected radiation to incident radiation—affects how much energy is absorbed by the material. A surface with high reflectivity will reflect a greater portion of the incident radiation, resulting in lower absorption of thermal energy. Conversely, a surface with low reflectivity will absorb more of the incident radiation, increasing the material's thermal energy.

The Reynolds number, denoted as Re, is a dimensionless quantity used in fluid mechanics to predict flow patterns in different fluid flow situations. It represents the ratio of inertial forces to viscous forces within a fluid. The Reynolds number is calculated using the formula:

$$Re = \frac{ρ · u · L}{μ}$$

Where:

• ρ is the density of the fluid [kg/m³]
• u is the velocity of the fluid [m/s]
• L is a characteristic length (such as the diameter of a pipe or the distance from the leading edge in flow over a flat plate) [m]
• μ is the dynamic viscosity of the fluid [Pa·s].

When the Reynolds number is low, viscous forces dominate, and the flow remains laminar. Conversely, when the Reynolds number is high, inertial forces dominate, leading to turbulent flow. The critical value at which the transition from laminar to turbulent flow occurs varies depending on the specific flow situation.

Saturated boiling occurs when the temperature of the liquid is slightly above the saturation temperature. Bubbles that form at the surface are then propelled through the liquid by buoyant forces and eventually escape at a free surface. This type of boiling is characterized by the presence of bubbles and their movement through the liquid due to buoyancy.

Solar radiation refers to the electromagnetic radiation emitted by the sun. It is essential for sustaining life on Earth, as it serves as the primary energy source for processes such as photosynthesis, which provides food, fiber, and fuel for humans. Solar radiation also has the potential to provide significant amounts of heat and electricity through thermal and photovoltaic processes. The solar radiation flux at the outer edge of Earth's atmosphere is measured at 1368 W/m², and it varies depending on factors such as geographic latitude, time of day, and season. This radiation carries energy and plays a crucial role in determining the temperature of Earth’s surface and atmosphere.

Subcooled boiling occurs when the temperature of the bulk liquid is lower than the saturation temperature. In this boiling mode, bubbles that form at the surface can condense within the liquid. The heat flux in subcooled boiling typically increases as $\left( T_s - T_l\right)^n$ of $\left( \Delta T_e + \Delta T_{sub} \right)^n$, where 5/4 ≤ n ≤ 4/3, depending on the geometry of the heated surface. The effect of subcooling is generally considered negligible in the nucleate boiling regime, where the maximum heat flux occurs. The subcooled boiling process involves natural convection and mixing induced by bubble formation and detachment, and it significantly influences the heat transfer coefficient.

A thermal boundary layer develops when there is a temperature difference between the free stream of the fluid and the surface over which the fluid flows. This boundary layer is fundamental in problems involving heat transfer and convective transport. It is important to engineers due to its relationship with surface temperature, surface friction effects, and heat transfer rates. The thickness of the thermal boundary layer is influenced by various factors, such as the Prandtl number and the distance from the leading edge of the surface.

Thermal radiation refers to the electromagnetic energy emitted by matter as a result of its temperature. It is concentrated in the spectral range of approximately 0.1 to 100 μm. The emission of thermal radiation is associated with the oscillations or transitions of the many electrons that make up matter, driven by the internal energy and temperature of the material. All forms of matter emit thermal radiation, and it is a significant factor in the transfer of heat energy between surfaces and their surroundings. This process is crucial for understanding the cooling of hot solids, energy balance at surfaces, and the radiative balance of the environment—including the impact of solar radiation on the Earth's atmosphere.

Transmission refers to the process of transferring thermal energy as a result of a spatial temperature difference. Whenever there is a temperature variation within a medium or between different media, heat transfer occurs. This energy transfer can take place through conduction, convection, or thermal radiation, each governed by its own physical principles and rate equations.

Turbulent flow is a chaotic and disordered fluid motion characterized by irregular fluctuations in velocity and pressure. It is distinguished by the presence of turbulent eddies and vortices, leading to mixing of fluid particles. In turbulent flow, the transport of momentum, energy, and species is enhanced by turbulent mixing, resulting in increased transfer rates.

The transition from laminair to turbulent flow is influenced by triggering mechanisms such as natural flow structures or disturbances within the fluid. Within a turbulent boundary layer, three regions can be identified based on the distance from the surface: a viscous sublayer, a buffer layer, and a turbulent core. These regions exhibit different characteristics in terms of transport mechanisms and velocity profiles.

Vaporization is the transformation of a substance from a liquid or solid state into a vapor or gas phase. This can occur through boiling, which is rapid vaporization that happens at the liquid’s boiling point, or through evaporation, a slower process that takes place at the surface of a liquid below its boiling point.

A velocity boundary layer develops when fluid flows over a surface. This boundary layer is characterized by a thin region of fluid where velocity gradients and shear stresses are significant, while outside this region, velocity gradients and shear stresses are negligible. The thickness of the boundary layer, denoted as δ, is the distance from the surface at which the fluid velocity reaches 99% of the free-stream velocity.As the distance from the leading edge increases, the effects of viscosity penetrate further into the free stream, causing the boundary layer to grow. The velocity boundary layer is fundamentally important in problems involving convective transport and is related to surface temperature and friction effects.

View factors, also known as configuration or shape factors, are a concept used to quantify the exchange of radiation between surfaces. They represent the fraction of radiation leaving one surface that is intercepted by another surface. View factors are determined by the geometry of the surfaces and are used to calculate radiative heat transfer between them. They are important in the context of thermal radiation and play a crucial role in determining energy exchange in various engineering and physical systems.