 # Heat Transfer

The phrase “heat transfer” refers to the distribution and changes in temperature that result from the transport of heat (thermal energy) induced by temperature differences. The study of transport phenomena focuses on the interchange of momentum, energy, and mass through conduction, convection, and radiation.

These rules of momentum, energy, and mass conservation, along with constitutive laws—relations that characterize both the conservation and flow of the quantities involved in these phenomena—provide the foundation for these formulations. By giving the most exact descriptions of the aforementioned laws and constitutive relations, differential equations fulfil this purpose. It is efficient to examine systems and forecast their behavior by solving these equations.

## Heat Transfer – History

In the absence of any external work, heat will always move from hot objects to cold ones, according to the second rule of thermodynamics. This form of heat transport is referred to as heat flow.

In the early nineteenth century, scientists believed that caloric, an invisible fluid that moved from hot to cold items, was present in all living things. Calorie was given several qualities that turned out to be inconsistent with reality, such as having weight and not being able to be created or destroyed.

For instance, when we rub our hands together, both hands warm up even though they started off at a colder temperature. The heat would have flowed from one body (hotter) with more energy to another (colder) with less energy if it were coming from a fluid.

This caloric hypothesis was disproven by Thompson and Joule. Heat is a kind of kinetic energy at the molecular level rather than a substance as was once thought (so-called kinetic theory). The hands rubbing together in the preceding example are truly heated because friction has changed the kinetic energy of the action (rubbing) into heat.

## In nature, heat is always moving between many objects. Following are a few examples:

• In a climate-controlled space, heat is transferred from your heated body to the chilly air around you.
• Due to slight temperature differences, the air will move around the room in a buoyancy-driven motion known as convection.
• The Sun’s incredibly high temperature causes it to radiate heat over the wide emptiness of space.

These illustrations highlight the three heat transmission modes that are discussed in the next section.

Isothermal systems with uniform energy distribution and flawless insulation from all other systems in the environment would have to be the only ones free from heat flow. In the actual world, it is impossible to duplicate these circumstances.

• Conduction
• Convection

# Conduction

In 1822, Joseph Fourier created a thorough theory of heat conduction.

Fourier’s Law states that the quantity of heat flux (q) generated by thermal conduction is inversely proportional to the magnitude of the temperature gradient and flows in the opposite direction.

q=−kdTdx
Thermal conductivity, or k, is the name given to the proportionality constant and has the dimensions WmK or JmsK.

A vector quantity is the heat flow. According to the equation above, q will be positive, or flow in the positive x-direction, if temperature decreases with spatial x vector. Q will be negative and flow in the opposite direction of x if T rises with x.

In all scenarios, q will move from higher to lower temperatures. The one-dimensional representation of Fourier’s law is Equation (1). The analogous form in three dimensions is:

## One other approach to express Fourier’s law is in a simple scalar form:

Since q and T are both positive values, L is the distance along the direction of heat flow.

It is simpler to understand why gases have great heat conductivity when the gas molecules are seen as small particles.

Molecules exchange their internal energy by crashing against one other. Since low-temperature regions have less intrinsic thermal energy, they will absorb heat from hot molecules. The kinetic theory of gases and this hypothetical example may both be used to calculate thermal conductivity.

In an ideal gas, the average molecular kinetic energy is directly proportional to the absolute temperature, according to the formula T=23KNkB.

Pressure has no effect on the thermal conductivity, which increases with the square of temperature.

In solid substance, heat transmission by conduction is simpler. Heat is transferred by lattice vibrations in nonmetallic components (Phonon). Metals may convey heat through phonon thermal conductivity, but electrons with high thermal conductivity carry heat more effectively.

The theory behind the low thermal conductivity of air (or any other gas) serves as the foundation for the low thermal conductivity of insulating materials like polystyrene and glass wool.

## Analogous definitions

• Heat Transfer:

Heat flux density ∝ grad T (Thermal conductivity)

• Diffusion:

Partial current density ∝ grad x (Diffusion coefficient)

Current density ∝ grad Uel (Electric conductivity)

# Convection

Convection is a different method of heat transfer that particularly impacts fluids. Heat is transferred by convection as a fluid moves. A fluid that conducts heat may move under various conditions.

Depending on how the fluid motion is initiated, we may classify convection as either forced or natural convection. Natural convection is caused by the buoyancy effects of a fluid with a changeable temperature field that is under the influence of gravity. Warm fluid rises while cold fluid descends due to a difference in density. When a fluid is propelled by an external force, such as the wind, a fan, a pump, or a suction device, it is driven to flow by convection.

With forced convection, the fluid flow around a body can be caused by a wide range of natural occurrences or man-made technologies. The fluid from the target body does not move as a result of heating, in contrast to natural convection. The transfer of a solid into a fluid that generates fluid motion is another way to conceptualize forced convection. The circumstance in which a colder fluid with a temperature of Tin is flowing past a warmer body with a temperature of Toddy from a vast distance is generalized in the figure below:

The fluid encircles the body and forms the boundary layer, a constrained area of slower motion. Heat is conducted through this layer, transferred downstream, and integrated into the flow.

Isaac Newton (1701) considered the convection mechanism and suggested the following simple cooling formula:

T is the fluid’s temperature upon entry, therefore dTbodydt=Tbody-T. This sentence indicates that energy is leaving the body.

The steady-state formulation of Newton’s Law of Cooling, which establishes free convection, is given by the following formula:

## Q = h (-T)

where h is the heat transfer coefficient. The average over the surface of the body can be visualised as a bar with the symbol “h” to indicate this coefficient. h without a bar displays the “local” values of the coefficient.

A structure or a room’s temperature can change noticeably due to natural convection. Because some areas of the home are warmer than others, we can tell this. Forced convection produces a more even distribution of temperature, which makes the entire house seem cozy. As a result, there are fewer chilly areas within the home, which eliminates the need to raise the thermostat’s setting.

Radiation is the phenomenon of energy transfer or propagation from one body to another, regardless of whether there is a medium between the two bodies or not. In contrast, heat is transferred through or inside a body through conduction or convection.

All bodies, whether liquid or solid, continually generate electromagnetic radiation. Both the characteristics of the organism and the intensity of this energy stream are interdependent. The term “thermal radiation” is used to explain how heat energy is transferred. Based on the body’s surface characteristics and internal temperature. Radiant heat transfer from somewhat cooler bodies that you may regularly come into contact with is commonly disregarded in comparison to convection and conduction.

Electromagnetic radiation may be compared to a stream of photons carrying energy and moving in a wave-like pattern at the speed of light. Electromagnetic radiation may carry energy in a space devoid of substance. The photons in different electromagnetic radiations are categorised based on their photon energy. It’s crucial to remember that when a photon’s energy is discussed, the behavior can either be that of a wave or a particle known as a “wave-particle duality” of light.

### The electromagnetic (EM) spectrum:

The range of all forms of electromagnetic radiation is represented by this spectrum. Radiation is just energy that is moving and dispersing, like photons, from an energy source in a variety of electromagnetic (EM) forms, such as visible light, radio waves, X-rays, gamma rays, microwaves, and infrared light3.

Each instance of radiant radiation has a wavelength () and a frequency (v) associated with it. The connection between EM radiative energy, wavelength, and frequency may be described by the equations below:

## λ=cν

and that energy is equal to the frequency times the Planck constant, or

## E=h∗ν

where h is Planck’s constant (6,626070040∗10−34Js).

## Applications of Thermal Simulation

### Thermomechanical Analysis (Thermal-Structural)

The energy balance of the systems under study is taken into consideration through heat transfer. Investigations into thermomechanical components may also take into account structural deformations brought on by the effects of heat stresses on solids. Simulating the stress response to thermal loads and failure is essential for many industrial applications.. A printed circuit board’s thermal stress analysis is an illustration of an application.

### Conjugate Heat Transfer Analysis (Fluid-Solid)

Simulations of conjugate heat transfer (CHT) examine the linked heat transmission in solids and fluids. An essential aspect of CHT simulations is the prediction of fluid flow while investigating the heat transfer that occurs at the fluid/solid interface. It may be used for cooling electronics, among other things.

## Conduction Examples

When factors like a body’s geometric form and the material’s thermal conductivity are taken into consideration, conduction modelling may be used to directly analyse and visualise conduction, which is the heat transfer from a hot item to a cold object when they are in direct touch with one another. One or two examples are CFL lightbulbs.

## Convection Examples

The transport of heat without physical contact between two locations is referred to as convective heat transfer. When molecules begin to move after absorbing heat, convective currents develop. Without a direct simulation of the flow, it is challenging to anticipate both the convective cooling efficacy and the overall flow stream behavior, necessitating significant computational power to arrive at accurate answers. The cooling of a Raspberry Pi motherboard is one such use.

The source of heat transmission by radiation is electromagnetic waves. They frequently participate in hot environments. The kind of material’s surface determines how much heat is radiated from it. A common guideline is that radiation levels increase with surface area. Laser beam welding is one usage for radiation simulation technology.

### Structural Heat Transfer software is used when:

• We can suppose that the fluid temperature is uniform everywhere around the solid component.
• focusing mainly on how structural elements behave when heated
• examining the part’s stress and deformation brought on by the heat load (thermal stress analysis)

### Coupled Heat Transfer Analysis (Fluid-Solid) is used when:

• It is necessary to research the fluid distribution around the solid.
• investigating how the item affects the liquid
• examining induced or natural convection

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