Fundamentals of heat transfer

I. Introduction to Heat Transfer

Heat transfer is the process of exchanging thermal energy between two or more systems due to a temperature difference. It is a fundamental concept that is crucial in various fields such as engineering, physics, chemistry, and biology. Understanding the fundamentals of heat transfer is essential in designing efficient thermal systems, predicting temperature distributions, and ensuring safety in numerous applications.

Modes of Heat Transfer

There are three main modes of heat transfer: conduction, convection, and radiation.

1. Conduction

Conduction is the transfer of heat through a material or between two materials that are in contact with each other. The heat transfer occurs due to the collision of atoms or molecules in the material. Conduction is primarily dependent on the thermal conductivity of the material, which is the ability of the material to conduct heat.

The rate of heat transfer by conduction is given by Fourier's law of heat conduction:

q = -kA(dT/dx)

where q is the rate of heat transfer per unit time, k is the thermal conductivity of the material, A is the cross-sectional area, and (dT/dx) is the temperature gradient in the direction of heat flow.

2. Convection

Convection is the transfer of heat through a fluid (gas or liquid) due to the motion of the fluid. Convection occurs due to the difference in density of the fluid at different temperatures. Hot fluids are less dense than cold fluids, and they rise while the cold fluids sink. This movement of fluids transfers heat from one place to another.

The rate of heat transfer by convection is given by Newton's law of cooling:

q = hA(Ts - Tf)

where q is the rate of heat transfer per unit time, h is the convective heat transfer coefficient, A is the surface area, Ts is the temperature of the surface, and Tf is the temperature of the fluid.

3. Radiation

Radiation is the transfer of heat through electromagnetic waves without the need for a medium. All objects with a temperature above absolute zero emit electromagnetic waves, which carry thermal energy. The rate of radiation heat transfer depends on the temperature and emissivity of the surfaces involved.

The rate of heat transfer by radiation is given by Stefan-Boltzmann's law:

q = σAε(Ts^4 - Tf^4)

where q is the rate of heat transfer per unit time, σ is the Stefan-Boltzmann constant, A is the surface area, ε is the emissivity of the surface, Ts is the temperature of the surface, and Tf is the temperature of the surroundings.

Importance of Heat Transfer

Heat transfer is crucial in various applications such as:

1. HVAC systems: Heating, ventilation, and air conditioning systems rely on heat transfer to maintain a comfortable indoor environment.
2. Power generation: Heat transfer is essential in power plants, where thermal energy is converted into electrical energy.
3. Aerospace engineering: Heat transfer is essential in the design of aircraft and spacecraft, where temperature control is crucial.
4. Food industry: Heat transfer is critical in cooking, baking, and food preservation.
5. Medical field: Heat transfer is essential in medical imaging and the design of medical devices.

 

II. Conduction Heat Transfer

A. Introduction to Conduction Heat Transfer

Conduction heat transfer is the transfer of heat through a medium by means of molecular collisions. It occurs when there is a temperature gradient within a material or between two materials in contact with each other. The direction of heat flow is always from high temperature to low temperature.

Conduction is an essential mode of heat transfer in various applications, including thermal insulation, electronics cooling, and building construction. In this section, we will discuss the mathematical equations and principles that govern conduction heat transfer.

B. Fourier's Law of Heat Conduction

The rate of heat transfer through a medium due to conduction is given by Fourier's law of heat conduction, which states that the heat flux q (rate of heat transfer per unit area) is proportional to the temperature gradient in the direction of heat flow:

q = -kA(dT/dx)

where k is the thermal conductivity of the medium, A is the cross-sectional area of heat transfer, and (dT/dx) is the temperature gradient in the direction of heat flow. The negative sign indicates that the heat flow is always from high temperature to low temperature.

C. Thermal Conductivity

Thermal conductivity is a property of the material that measures its ability to conduct heat. It is defined as the rate of heat transfer per unit area per unit temperature gradient:

k = q/(A*dT/dx)

Thermal conductivity is dependent on the material properties such as density, specific heat, and thermal diffusivity. The higher the thermal conductivity, the more effective the material is at conducting heat.

D. One-Dimensional Steady-State Conduction

One-dimensional steady-state conduction occurs when the temperature gradient within a medium is constant and unchanging with time. This occurs in situations where the heat flow is steady and there is no change in the boundary conditions.

In one-dimensional steady-state conduction, Fourier's law of heat conduction can be simplified to:

q = -kA(T1 - T2)/L

where T1 and T2 are the temperatures at the two ends of the medium, L is the length of the medium, and A is the cross-sectional area.

E. Two-Dimensional Steady-State Conduction

Two-dimensional steady-state conduction occurs when there is a constant temperature gradient within a medium in two dimensions. This occurs in situations where there is a steady heat flow, and the boundary conditions remain constant over time.

In two-dimensional steady-state conduction, the heat transfer rate can be calculated using Laplace's equation:

(d^2T/dx^2) + (d^2T/dy^2) = 0

where T is the temperature, and x and y are the two spatial coordinates.

F. Unsteady-State Conduction

Unsteady-state conduction occurs when the temperature within a medium is changing with time. This occurs in situations where there is a change in the boundary conditions or the initial conditions of the system.

The heat transfer rate in unsteady-state conduction can be calculated using the heat diffusion equation:

(dT/dt) = α(d^2T/dx^2)

where α is the thermal diffusivity of the medium, and t is time.

 

III. Convection Heat Transfer

A. Introduction to Convection Heat Transfer

Convection heat transfer is the transfer of heat by means of the movement of a fluid (liquid or gas). The fluid can either be in motion naturally or forced to move by an external force such as a fan or pump. Convection heat transfer is a dominant mode of heat transfer in many engineering applications, including HVAC systems, automotive cooling systems, and aerospace applications.

In this section, we will discuss the types of convection, boundary layer concepts, Nusselt number, dimensional analysis, and empirical correlations that govern convection heat transfer.

B. Types of Convection

There are two types of convection: natural convection and forced convection.

1. Natural Convection

Natural convection occurs when a fluid is heated, and the density of the fluid decreases, causing it to rise. This upward movement of the fluid creates a flow pattern that transfers heat from the source to the surrounding environment. Natural convection occurs without the aid of external forces such as fans or pumps and is a common mode of heat transfer in many industrial and natural systems.

2. Forced Convection

Forced convection occurs when a fluid is forced to flow over a surface by an external force such as a fan or pump. The velocity of the fluid in forced convection is higher than that in natural convection, resulting in a more efficient heat transfer process.

C. Boundary Layer Concepts

In convection heat transfer, a boundary layer is the region of fluid near a surface where the velocity of the fluid is significantly affected by the presence of the surface. The boundary layer plays a critical role in heat transfer since it is the region where the bulk of the heat transfer occurs.

D. Nusselt Number

The Nusselt number (Nu) is a dimensionless parameter used to quantify the efficiency of heat transfer in convective systems. It is defined as the ratio of convective heat transfer to conductive heat transfer:

Nu = hL/k

where h is the convective heat transfer coefficient, L is the characteristic length of the system, and k is the thermal conductivity of the fluid.

E. Dimensional Analysis and Empirical Correlations

Dimensional analysis is a technique used to relate physical parameters of a system based on their dimensions. By using this technique, engineers can derive equations that describe the behavior of the system without having to know the underlying physics.

Empirical correlations are derived by using experimental data to determine the relationship between different parameters in a system. These correlations are often expressed in the form of dimensionless parameters and can be used to predict the behavior of similar systems.

F. Heat Transfer Coefficient

The heat transfer coefficient (h) is a measure of the effectiveness of heat transfer between a solid surface and a fluid. It is defined as the ratio of the convective heat transfer rate to the temperature difference between the surface and the fluid:

q = hA(Ts - Tf)

where q is the heat transfer rate, A is the surface area, Ts is the temperature of the surface, and Tf is the temperature of the fluid.

 

IV. Radiation Heat Transfer

A. Introduction to Radiation Heat Transfer

Radiation heat transfer is the transfer of energy in the form of electromagnetic waves, without the need for a physical medium. Unlike conduction and convection, which require a material medium, radiation can occur in a vacuum or in a medium that is transparent to the radiation. Radiation heat transfer plays a significant role in many natural and engineering systems, including thermal radiation in the earth's atmosphere, heat transfer in space, and thermal radiation in furnaces and combustion systems.

In this section, we will discuss the laws of radiation, blackbody radiation, and gray and non-gray surfaces that govern radiation heat transfer.

B. Laws of Radiation

There are three fundamental laws of radiation that govern the behavior of electromagnetic waves and their interaction with matter.

1. Planck's Law

Planck's law describes the spectral distribution of electromagnetic radiation emitted by a blackbody at a given temperature. It states that the intensity of radiation emitted by a blackbody is proportional to the frequency of the radiation and the temperature of the blackbody.

2. Stefan-Boltzmann Law

The Stefan-Boltzmann law relates the total radiant heat energy emitted per unit area per unit time by a blackbody to its absolute temperature. It states that the radiant heat energy emitted by a blackbody is proportional to the fourth power of its absolute temperature.

3. Wien's Displacement Law

Wien's displacement law states that the peak wavelength of the spectral distribution of electromagnetic radiation emitted by a blackbody is inversely proportional to its absolute temperature.

C. Blackbody Radiation

A blackbody is an idealized object that absorbs all radiation incident upon it and emits radiation according to Planck's law. The spectral distribution of radiation emitted by a blackbody is independent of its shape, size, and composition and depends only on its absolute temperature. The emissivity of a blackbody is unity, and its absorptivity is also unity at all wavelengths.

D. Gray and Non-Gray Surfaces

In radiation heat transfer, the emissivity of a surface determines the amount of radiation it emits at a given temperature. A gray surface is one that emits and absorbs radiation with the same spectral emissivity at all wavelengths. A non-gray surface, on the other hand, emits and absorbs radiation with different spectral emissivities at different wavelengths.

 

V. Heat Exchangers

A. Introduction to Heat Exchangers

A heat exchanger is a device that is used to transfer heat from one fluid to another. Heat exchangers are widely used in various industrial and engineering applications, such as power plants, chemical processing plants, and refrigeration systems. The basic principle of a heat exchanger is to facilitate the transfer of heat from a high-temperature fluid to a low-temperature fluid, without allowing the two fluids to mix.

B. Types of Heat Exchangers

There are different types of heat exchangers, and the choice of a particular type depends on the specific application, the flow rates of the fluids, and the desired temperature change. Some of the common types of heat exchangers are:

1. Shell and Tube Heat Exchangers

Shell and tube heat exchangers are the most commonly used type of heat exchangers in industrial applications. They consist of a shell, which contains a bundle of tubes, through which the fluids flow. One fluid flows through the tubes, and the other fluid flows through the shell, around the tubes. This arrangement provides a large surface area for heat transfer and is suitable for high-pressure and high-temperature applications.

2. Plate Heat Exchangers

Plate heat exchangers are compact and efficient heat exchangers that are suitable for low to medium flow rates. They consist of a series of thin, corrugated plates that are stacked together with gaskets in between. One fluid flows through the channels formed between the plates, and the other fluid flows through the alternate channels. This arrangement provides a large surface area for heat transfer, and the high turbulence created by the corrugated plates enhances the heat transfer coefficient.

3. Double-Pipe Heat Exchangers

Double-pipe heat exchangers consist of two pipes, one inside the other. The fluids flow in opposite directions, with one fluid flowing through the inner pipe and the other fluid flowing through the annular space between the two pipes. Double-pipe heat exchangers are simple in design and are suitable for low flow rate and low-temperature applications.

C. Effectiveness-NTU Method

The effectiveness-NTU method is a widely used method for analyzing the performance of heat exchangers. The effectiveness of a heat exchanger is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate. The NTU (Number of Transfer Units) is a dimensionless quantity that is used to quantify the heat transfer capacity of a heat exchanger. The effectiveness-NTU method is used to determine the heat transfer rate, the outlet temperatures of the fluids, and the overall heat transfer coefficient of a heat exchanger.

VI. Boiling and Condensation

 

A. Introduction to Boiling and Condensation

Boiling and condensation are two important processes in heat transfer that occur during phase change. Boiling is a process in which a liquid is converted into a vapor due to the transfer of heat. Condensation is the opposite process, in which a vapor is converted into a liquid due to the transfer of heat. Boiling and condensation play important roles in many engineering applications, such as power generation, refrigeration, and air conditioning.

 

B. Pool Boiling

Pool boiling is a process in which a heated surface is in contact with a pool of liquid. The heat is transferred from the heated surface to the liquid, causing it to boil and form vapor bubbles. The vapor bubbles detach from the surface and rise to the liquid surface, where they collapse and release their latent heat of vaporization to the surrounding liquid. Pool boiling can be classified into several regimes, including nucleate boiling, transition boiling, and film boiling.

 

C. Flow Boiling

Flow boiling is a process in which a heated fluid flows over a heated surface. The heat is transferred from the heated surface to the fluid, causing it to boil and form vapor bubbles. Unlike pool boiling, the vapor bubbles are carried away by the flowing fluid and do not accumulate on the heated surface. Flow boiling can also be classified into several regimes, including nucleate boiling, transition boiling, and film boiling.

 

D. Condensation

Condensation is a process in which a vapor is converted into a liquid due to the transfer of heat. The heat is transferred from a cooler surface to the vapor, causing it to condense into a liquid. Condensation can occur in several modes, including film condensation and dropwise condensation. In film condensation, the liquid film forms on the surface and grows until it covers the entire surface. In dropwise condensation, the vapor condenses into droplets that fall off the surface, leaving behind a dry surface that promotes further condensation.

 

E. Heat Transfer Coefficients

Heat transfer coefficients are important parameters in boiling and condensation. They represent the rate of heat transfer per unit area between the heated surface and the fluid or vapor. In boiling, the heat transfer coefficient depends on the boiling regime, the properties of the fluid, and the geometry of the heated surface. In condensation, the heat transfer coefficient depends on the mode of condensation, the properties of the vapor and the surface, and the flow rate of the vapor. Heat transfer coefficients can be determined experimentally or through analytical or numerical methods.

 

VII. Heat Transfer with Phase Change

 

A. Introduction to Heat Transfer with Phase Change

Heat transfer with phase change is a process in which a substance undergoes a phase change, such as melting, freezing, vaporization, or condensation, during the transfer of heat. During phase change, a substance undergoes a latent heat transfer, which is the transfer of heat without a change in temperature. Heat transfer with phase change is important in many engineering applications, such as refrigeration, air conditioning, and energy storage.

 

B. Latent Heat

Latent heat is the amount of heat required to change the phase of a substance without changing its temperature. During a phase change, such as melting or vaporization, energy is absorbed by the substance to break the intermolecular bonds between the molecules. This results in an increase in potential energy, without a corresponding increase in kinetic energy, which causes the temperature to remain constant during the phase change. The latent heat is released when the substance undergoes a reverse phase change, such as freezing or condensation.

 

C. Thermal Energy Storage

Thermal energy storage is a method of storing thermal energy for later use. One way to store thermal energy is by using materials that undergo a phase change, such as melting or solidification, during the storage and release of thermal energy. During the charging process, thermal energy is added to the material to melt it, and during the discharging process, the material releases the stored thermal energy by solidifying. Thermal energy storage can be used to store energy from renewable sources, such as solar and wind power, and to reduce energy consumption during peak hours.

 

D. Heat Transfer in Melting and Freezing

Heat transfer during melting and freezing involves the transfer of heat between a substance and its surroundings during a phase change. During melting, energy is transferred from the surroundings to the substance to break the intermolecular bonds and change the substance from a solid to a liquid. During freezing, energy is transferred from the substance to the surroundings to form intermolecular bonds and change the substance from a liquid to a solid. The rate of heat transfer during melting and freezing depends on the properties of the substance, the temperature difference between the substance and its surroundings, and the rate of heat transfer through the substance.

 

E. Heat Transfer in Vaporization and Condensation

Heat transfer during vaporization and condensation involves the transfer of heat between a substance and its surroundings during a phase change. During vaporization, energy is transferred from the surroundings to the substance to break the intermolecular bonds and change the substance from a liquid to a vapor. During condensation, energy is transferred from the substance to the surroundings to form intermolecular bonds and change the substance from a vapor to a liquid. The rate of heat transfer during vaporization and condensation depends on the properties of the substance, the temperature difference between the substance and its surroundings, and the rate of heat transfer through the substance.

 

VIII. Heat Transfer in Solids and Porous Media

Heat transfer in solids and porous media is an essential topic in the field of engineering and science. The following sections will provide an overview of the fundamentals of heat transfer in solids and porous media.

A. Introduction to Heat Transfer in Solids and Porous Media

Heat transfer in solids and porous media refers to the transfer of thermal energy through materials that are not fluids. It is an important area of study in many engineering applications, such as the design of electronic devices, heat exchangers, and energy storage systems.

B. Thermal Diffusivity

Thermal diffusivity is a measure of how quickly heat can diffuse through a material. It is defined as the ratio of thermal conductivity to specific heat capacity and density. The thermal diffusivity of a material determines the rate at which heat can be conducted through the material.

C. Heat Conduction in Composite Materials

Heat conduction in composite materials is an important topic in heat transfer. Composite materials are made up of two or more materials with different thermal properties. The thermal conductivity of a composite material depends on the properties of each individual material and the arrangement of the materials within the composite.

D. Heat Transfer in Porous Media

Heat transfer in porous media is an important area of study in many engineering applications, such as geothermal systems, catalytic reactors, and fuel cells. Porous media is made up of a solid matrix with interconnected voids or pores. The heat transfer in porous media is influenced by the geometry of the porous structure, the properties of the solid matrix and the fluid flowing through the pores, and the convective and conductive heat transfer mechanisms.

The study of heat transfer in porous media is complex and requires the use of advanced mathematical models to describe the complex interactions between the solid matrix and the fluid flowing through the pores. Analytical and numerical methods, such as the finite element method and computational fluid dynamics, are often used to model heat transfer in porous media.

 

IX. Heat Transfer in Microchannels

 

A. Introduction to Heat Transfer in Microchannels

Heat transfer in microchannels has become an area of great interest in recent years, as they offer several advantages over conventional heat exchangers. Microchannels are channels with hydraulic diameters less than 1 mm and offer high surface area-to-volume ratios, making them highly efficient heat transfer devices. Additionally, microchannels can handle high heat fluxes with low pressure drop, making them ideal for applications in electronics cooling, chemical reactors, and microreactors.

 

B. Microchannel Heat Transfer Fundamentals

The heat transfer mechanisms in microchannels are the same as those in conventional heat transfer devices, including convection, conduction, and radiation. However, the high surface area-to-volume ratios in microchannels mean that convective heat transfer dominates, and the heat transfer coefficient is much higher than that in conventional devices. The governing equations for microchannel heat transfer are the same as those for conventional heat transfer, but the boundary conditions are different due to the high surface area-to-volume ratios.

 

C. Boiling and Condensation in Microchannels

Boiling and condensation in microchannels have been of great interest due to their applications in electronics cooling and chemical processes. Boiling in microchannels occurs when the heat flux exceeds a certain limit, resulting in the formation of a thin liquid film or dry spots on the heated surface. Condensation in microchannels is also of interest due to its potential use in microscale heat pumps and refrigeration systems. The heat transfer coefficients for boiling and condensation in microchannels are much higher than those in conventional devices, making them attractive for high-performance applications.

 

D. Applications of Microchannel Heat Transfer

Microchannel heat transfer has several applications, including electronics cooling, chemical reactors, microreactors, and energy systems. In electronics cooling, microchannels can be integrated into microprocessors to improve their cooling efficiency and reduce their size. In chemical reactors and microreactors, microchannels can be used to enhance heat transfer and improve reaction rates. In energy systems, microchannels can be used for thermal management in fuel cells and batteries, as well as in solar collectors.

 

X. Heat Transfer Enhancement Techniques

Heat transfer enhancement techniques are used to improve the rate of heat transfer between two surfaces. These techniques are applied in various industrial applications where high heat transfer rates are required. In this section, we will discuss some of the commonly used heat transfer enhancement techniques.

 

A. Introduction to Heat Transfer Enhancement Techniques

Heat transfer enhancement techniques are methods used to improve the rate of heat transfer between two surfaces. These techniques are employed to increase the efficiency of heat transfer equipment and reduce the size of heat transfer equipment. The primary objective of heat transfer enhancement techniques is to achieve a higher rate of heat transfer while maintaining low pressure drop and high thermal performance.

 

B. Ribbed Surfaces

Ribbed surfaces are commonly used in heat transfer applications to increase the surface area of heat transfer. Ribbed surfaces consist of a series of ribs or grooves on a flat surface. The ribs increase the surface area and create turbulence in the fluid flow, resulting in enhanced heat transfer. The ribs can be made in various shapes and sizes, depending on the application.

 

C. Extended Surfaces

Extended surfaces, also known as fins, are used in heat transfer applications to increase the surface area for heat transfer. Extended surfaces are commonly used in applications where space is limited, and high heat transfer rates are required. The fins increase the surface area and create turbulence in the fluid flow, resulting in enhanced heat transfer.

 

D. Porous Media

Porous media are used in heat transfer applications to enhance heat transfer by increasing the surface area and creating turbulence in the fluid flow. Porous media can be made of various materials such as metals, ceramics, and polymers. The porous media can be designed to have different pore sizes, shapes, and orientations, depending on the application.

 

E. Forced Mixing Techniques

Forced mixing techniques are used in heat transfer applications to enhance heat transfer by increasing the mixing of fluids. Forced mixing techniques can be achieved by using different devices such as baffles, swirl generators, and static mixers. These devices create turbulence in the fluid flow, resulting in enhanced heat transfer.

 

XI. Heat Transfer in Industrial Processes

 

Heat transfer plays a critical role in numerous industrial processes, including power generation, manufacturing, and food processing. In this section, we will explore some of the applications of heat transfer in industrial processes.

 

A. Introduction to Heat Transfer in Industrial Processes

Industrial processes often involve the transfer of heat between fluids or between fluids and solid surfaces. Heat exchangers are a common tool used in industrial processes to facilitate this heat transfer. Other processes, such as combustion, also involve heat transfer.

 

B. Heat Exchangers in Industrial Processes

Heat exchangers are used in a wide range of industrial processes to transfer heat between fluids. They can be found in power plants, chemical processing plants, and oil refineries, among other applications. The design of a heat exchanger will depend on the specific application and the properties of the fluids involved. Some common types of heat exchangers used in industrial processes include shell and tube heat exchangers, plate heat exchangers, and double-pipe heat exchangers.

 

C. Thermal Processing of Foods

Heat transfer is critical in the thermal processing of foods, such as pasteurization, sterilization, and cooking. The goal of thermal processing is to destroy harmful microorganisms and enzymes while preserving the nutritional quality of the food. The specific thermal processing parameters, such as temperature and time, will depend on the type of food being processed and the desired level of microbial reduction.

 

D. Heat Transfer in Combustion Processes

Heat transfer is also critical in combustion processes, such as those used in power generation and industrial furnaces. Combustion involves the rapid oxidation of fuel, which releases heat. This heat is then transferred to a working fluid, such as steam or air, which can be used to generate electricity or heat industrial processes.

 

E. Heat Transfer in Nuclear Reactors

Nuclear reactors generate heat through nuclear fission reactions. This heat is then transferred to a working fluid, such as water or gas, which is used to generate electricity. The design of a nuclear reactor will depend on many factors, including the type of fuel used and the desired level of safety.