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Heat Transfer: Modes and Conservation of Energy

Handout
University (Grade 14)
English

Heat Transfer: Modes and Conservation of Energy

Introduction to Heat Transfer

From the study of thermodynamics, we understand that energy can be transferred as work and heat. Thermodynamics primarily focuses on the end states of a process, providing no information about the nature or rate of energy interaction. Heat transfer, however, extends this analysis by studying the modes of heat transfer and developing relations to calculate heat transfer rates.

What is Heat Transfer?

Heat transfer is defined as thermal energy in transit due to a spatial temperature difference. Whenever a temperature difference exists within a medium or between media, heat transfer will occur.

1. Modes of Heat Transfer

Heat transfer occurs through three primary modes: conduction, convection, and radiation. Understanding the physical mechanisms behind these modes and the rate equations that quantify energy transfer per unit time is crucial for engineers.

1.1 Conduction

Conduction is the transfer of energy from more energetic particles to less energetic particles of a substance due to interactions between them. This mode is sustained by atomic and molecular activity. In gases, it involves random translational motion and collisions. In liquids, molecules are more closely spaced with stronger interactions. In solids, conduction is attributed to lattice vibrations (lattice waves) and, in electrical conductors, also to the translational motion of free electrons. Conduction occurs in a stationary medium (solid or fluid) when a temperature gradient exists, leading to a net transfer of energy in the direction of decreasing temperature.
Fourier's Law of Conduction: For one-dimensional heat conduction through a plane wall, the rate equation is known as Fourier's Law:

Where:
  • 
    is the heat flux (W/m²), representing the heat transfer rate per unit area perpendicular to the direction of transfer.
  • 
    is the thermal conductivity (W/m·K), a transport property characteristic of the material.
  • 
    is the temperature gradient in the x-direction.
The minus sign indicates that heat is transferred in the direction of decreasing temperature. For steady-state conditions with a linear temperature distribution across a wall of thickness

with temperatures

and

at its surfaces, the temperature gradient can be expressed as

. Thus, the heat flux becomes:

The total heat rate by conduction,

(W), through a plane wall of area

is then

.
Example 1.1: Conduction through a Furnace Wall
Known: A fireclay brick furnace wall (0.15 m thick,

W/m·K) has inner and outer surface temperatures of 1400 K and 1150 K, respectively. The wall is 0.5 m by 1.2 m. Find: Rate of heat loss through the wall. Assumptions: Steady-state, one-dimensional conduction, constant thermal conductivity. Analysis: Using Fourier's Law, the heat flux is:

The total heat rate

is then:

Comments: Heat flows from higher to lower temperature. The distinction between heat flux (per unit area) and heat rate (total energy per time) is important.

1.2 Convection

Convection heat transfer involves two mechanisms: energy transfer due to random molecular motion (diffusion) and energy transfer by the bulk, or macroscopic, motion of the fluid. This combined transport is termed convection, while transport due to bulk fluid motion alone is advection.
Convection heat transfer is particularly relevant between a fluid in motion and a bounding surface at different temperatures. When fluid flows over a heated surface, a hydrodynamic (velocity) boundary layer develops, where velocity varies from zero at the surface to a finite value in the outer flow. Similarly, a thermal boundary layer forms if surface and fluid temperatures differ, where temperature varies from the surface temperature

to the outer fluid temperature

.
Types of Convection:
  • Forced Convection: Fluid motion is caused by external means (e.g., fan, pump, atmospheric winds).
  • Natural (Free) Convection: Fluid motion is induced by buoyancy forces resulting from density differences caused by temperature variations.
  • Mixed Convection: Both forced and natural convection mechanisms are significant.
  • Convection with Phase Change: Involves latent heat exchange during boiling (liquid to vapor) or condensation (vapor to liquid).
Newton's Law of Cooling: Regardless of the specific nature of the convection process, the heat transfer rate equation is:

Where:
  • 
    is the convective heat flux (W/m²).
  • 
    is the convection heat transfer coefficient (W/m²·K), which depends on boundary layer conditions, fluid properties, and surface geometry.
  • 
    is the surface temperature and
    
    is the fluid temperature far from the surface.
Typical values of

vary significantly depending on the process:
  • Free convection: Gases (2-25 W/m²·K), Liquids (50-1000 W/m²·K)
  • Forced convection: Gases (25-250 W/m²·K), Liquids (100-20,000 W/m²·K)
  • Convection with phase change (Boiling or condensation): (2500-100,000 W/m²·K)
Example 1.2: Heat Loss from an Uninsulated Steam Pipe
Known: An uninsulated pipe (70 mm diameter,

,

°C) passes through a room where air and walls are at

°C. The free convection coefficient is

W/m²·K. Find: 1. Surface emissive power and irradiation. 2. Pipe heat loss per unit length,

. Assumptions: Steady-state, radiation exchange between small surface and large enclosure,

.
Analysis:
  1. Surface Emissive Power (
    
    ) and Irradiation (
    
    ): Temperature must be in Kelvin:
    
    K,
    
    K. Stefan-Boltzmann constant
    
    W/m²·K⁴. Emissive power
    
    . Irradiation
    
    .
  1. Heat Loss per Unit Length (q'): Total heat loss is by convection and radiation. For a pipe of length
    
    and diameter
    
    , the surface area is
    
    . The heat loss per unit length,
    
    , is:

Substituting values (

m,

°C,

°C,

°C):


Comments: Temperatures must be in Kelvin for radiation terms. Convection and radiation heat transfer rates are comparable in this case.

1.3 Radiation

Thermal radiation is energy emitted by matter at a non-zero temperature, due to changes in electron configurations. This energy is transported by electromagnetic waves (photons) and, unlike conduction and convection, does not require a material medium; it is most efficient in a vacuum.
Surface Emissive Power (

): The rate at which energy is released per unit area (W/m²) from a surface. The upper limit is prescribed by the Stefan-Boltzmann law for an ideal radiator (blackbody):

Where

is the absolute temperature (K) of the surface and

is the Stefan-Boltzmann constant (

W/m²·K⁴).
For a real surface, the heat flux emitted is less than that of a blackbody and is given by:

Where

is the emissivity, a radiative property (

) that measures how efficiently a surface emits energy relative to a blackbody.
Irradiation (

): Radiation incident on a surface from its surroundings (W/m²). A portion of this irradiation may be absorbed, increasing the thermal energy of the material. The rate of absorbed radiant energy per unit surface area is

, where

is the absorptivity (

). If

, portions may be reflected or transmitted.
Net Radiation Heat Transfer: For a small surface at

completely surrounded by a much larger, isothermal surface at

, the net rate of radiation heat transfer from the surface per unit area (assuming

) is:

This can be linearized using a radiation heat transfer coefficient,

:

Where

.
If a surface simultaneously transfers heat by convection to an adjoining gas, the total rate of heat transfer from the surface is the sum of convection and radiation components:


2. Conservation of Energy Requirement

The first law of thermodynamics, or the law of conservation of energy, is a fundamental tool in heat transfer analysis. It states that the total energy of a system is conserved, and energy can only change if it crosses system boundaries.

2.1 Conservation of Energy for a Control Volume

For a closed system (fixed mass), energy crosses boundaries via heat transfer (

) and work (

). The first law states:

Where

is the change in total energy stored,

is net heat transferred to the system, and

is net work done by the system.
For a control volume (open system, where mass can cross boundaries), energy can also be transferred by energy advection (mass carrying energy). The first law for a control volume over a time interval

states:
Thermal and Mechanical Energy Equation over a Time Interval (

) The increase in stored thermal and mechanical energy in the control volume equals the amount of thermal and mechanical energy entering, minus the amount leaving, plus the amount generated within the control volume.
Symbolically:

For an instant in time

, using rates:

Where:
  • 
    is the sum of thermal and mechanical energy stored (thermal energy
    
    , kinetic energy
    
    , potential energy
    
    ). In heat transfer, changes in KE and PE are often negligible.
  • 
    is the rate of thermal energy generation (e.g., exothermic chemical reactions, electrical resistance heating) within the control volume.
  • 
    and
    
    are rates of energy entering and leaving the control volume, including heat transfer (conduction, convection, radiation), work interactions, and energy advected by mass flow.
Simplified Steady-Flow Thermal Energy Equation: For steady-state conditions (

), no latent energy changes, and no thermal energy generation, the steady-flow thermal energy equation for an ideal gas or incompressible liquid simplifies to:

Where

is the net rate of heat transfer,

is the mass flow rate,

is the specific heat, and

,

are outlet and inlet temperatures.
Example 1.3: Heating of an Electrical Rod
Known: A conducting rod of diameter

and electrical resistance per unit length

is initially in thermal equilibrium with ambient air and surroundings. Electrical current

is passed through the rod. Find: Equation for the variation of rod temperature with time. Assumptions: Uniform rod temperature, constant properties, radiation exchange between small surface and large enclosure. Analysis: Apply the first law on a rate basis to a control volume of length

around the rod:

Where:
  • Generation:
    
    (Ohmic heating).
  • Outflow:
    
    (convection + radiation).
  • Storage change:
    
    .
Substituting these into the energy balance yields:

Rearranging to solve for

:

Comments: This differential equation can be integrated numerically to find

. At steady-state,

, leading to an algebraic equation for

.
Example 1.5: Melting Ice in a Cubical Container
Known: Mass

of ice at fusion temperature

°C in a cubical container (width

, wall thickness

, thermal conductivity

). Outer surface heated to

. Find: Expression for the time

needed to melt the entire mass of ice. Assumptions: Inner surface at

, constant properties, steady-state one-dimensional conduction through each wall, conduction area of one wall is

. Analysis: Apply the first law over the time interval

to a control volume around the ice-water mixture:

Where:
  • Energy inflow (conduction through 6 walls):
    
    .
  • Change in stored latent energy:
    
    (where
    
    is latent heat of fusion).
Substituting and solving for

:


Comments: Complications arise if ice is subcooled initially. Units of K and °C cancel when used in temperature differences.

2.2 The Surface Energy Balance

Often, the conservation of energy is applied at the surface of a medium. In this special case, the control surfaces enclose no mass or volume. Therefore, generation and storage terms are irrelevant, and the conservation requirement simplifies to:

Even with thermal energy generation within the medium, it does not affect the energy balance at the control surface. This applies to both steady-state and transient conditions.
On a unit area basis, the surface energy balance for conduction from the medium to the surface (

), convection from the surface to a fluid (

), and net radiation exchange from the surface to the surroundings (

) is:

Example 1.6: Human Thermoregulation in Air and Water
Known: A person with a skin/fat layer (thickness

mm,

W/m·K, area

m², emissivity

) has an inner skin temperature of

°C (308 K). Find: Skin surface temperature (

) and heat loss rate (

) when in: 1. Still air (

K,

W/m²·K). 2. Water (

K,

W/m²·K). Assumptions: Steady-state, one-dimensional conduction, uniform thermal conductivity, radiation exchange small surface to large enclosure, water opaque to thermal radiation.
Analysis (Part 1: In Air): Energy balance at skin surface: Conduction into surface = Convection out + Radiation out.

This equation is solved iteratively for

. Estimating

with a guessed

K gives

W/m²·K. Then, solving for

:

Substituting numerical values:

Heat loss rate

(W):

Analysis (Part 2: In Water): Water is opaque to thermal radiation, so heat loss is by convection only (set

). Using

W/m²·K:

Heat loss rate

(W):

Comments: Radiation is significant in air due to low convection coefficient. Heat loss in water is much higher due to water's higher thermal conductivity, leading to a colder skin temperature.

3. Analysis of Heat Transfer Problems: Methodology

Solving heat transfer problems systematically enhances understanding and confidence. A recommended procedure includes:
  1. Known: State briefly and concisely what is known from the problem statement.
  1. Find: State briefly and concisely what needs to be determined.
  1. Schematic: Draw a physical system schematic, indicating control surfaces with dashed lines and relevant heat transfer processes with labeled arrows.
  1. Assumptions: List all pertinent simplifying assumptions.
  1. Properties: Compile necessary property values and their sources.
  1. Analysis: Apply conservation laws and rate equations. Develop the analysis completely before substituting numerical values. Perform calculations.
  1. Comments: Discuss results, critique assumptions, and infer implications.

4. Relevance of Heat Transfer

Heat transfer principles are vital in diverse fields, from engineering to biology.
  • Energy Conversion & Production: Crucial for optimizing gas turbine engines (cooling blades), designing fuel cells (temperature control to prevent failure, water management), and managing thermal loads in nuclear reactors.
  • Electronics Cooling: Essential for microprocessors, data centers, and other electronic devices. Advances in heat transfer engineering enable higher performance and reliability by maintaining low operating temperatures, often using heat sinks and forced convection.
  • Biological Systems (Thermoregulation): Heat transfer processes (convection, radiation, evaporation) regulate body temperature, preventing conditions like hypothermia or heat stroke. Blood flow also plays a critical role in internal heat transport.
  • Biomedical Engineering: Applied in laser surgery (destroying cancerous lesions with heat), cryosurgery (destroying diseased tissue with extreme cold), and drug delivery (controlling temperature distribution during chemotherapies).

5. Units and Dimensions

Physical quantities in heat transfer are specified by dimensions, measured in units. The four basic dimensions are length (

), mass (

), time (

), and temperature (

).
The International System of Units (SI) is the worldwide standard. Key SI base units include:
  • Length: meter (m)
  • Mass: kilogram (kg)
  • Time: second (s)
  • Thermodynamic Temperature: kelvin (K)
  • Electric Current: ampere (A)
  • Amount of Substance: mole (mol)
Derived SI units, such as newton (N) for force (kg·m/s²), pascal (Pa) for pressure (N/m²), joule (J) for energy (N·m), and watt (W) for power (J/s), are consistently used. While Celsius (°C) is common, temperatures in radiation equations must be in Kelvin. Temperature differences are equivalent for both scales (

).

Introduction to Heat Transfer

Introduction to Heat Transfer

From the study of thermodynamics, we understand that energy can be transferred as work and heat. Thermodynamics primarily focuses on the end states of a process, providing no information about the nature or rate of energy interaction. Heat transfer, however, extends this analysis by studying the modes of heat transfer and developing relations to calculate heat transfer rates.

What is Heat Transfer?

Heat transfer is defined as thermal energy in transit due to a spatial temperature difference. Whenever a temperature difference exists within a medium or between media, heat transfer will occur.

1. Modes of Heat Transfer

Heat transfer occurs through three primary modes: conduction, convection, and radiation. Understanding the physical mechanisms behind these modes and the rate equations that quantify energy transfer per unit time is crucial for engineers.

1.1 Conduction

Conduction is the transfer of energy from more energetic particles to less energetic particles of a substance due to interactions between them. This mode is sustained by atomic and molecular activity. In gases, it involves random translational motion and collisions. In liquids, molecules are more closely spaced with stronger interactions. In solids, conduction is attributed to lattice vibrations (lattice waves) and, in electrical conductors, also to the translational motion of free electrons. Conduction occurs in a stationary medium (solid or fluid) when a temperature gradient exists, leading to a net transfer of energy in the direction of decreasing temperature.
Fourier's Law of Conduction: For one-dimensional heat conduction through a plane wall, the rate equation is known as Fourier's Law:

Where:
  • 
    is the heat flux (W/m²), representing the heat transfer rate per unit area perpendicular to the direction of transfer.
  • 
    is the thermal conductivity (W/m·K), a transport property characteristic of the material.
  • 
    is the temperature gradient in the x-direction.
The minus sign indicates that heat is transferred in the direction of decreasing temperature. For steady-state conditions with a linear temperature distribution across a wall of thickness

with temperatures

and

at its surfaces, the temperature gradient can be expressed as

. Thus, the heat flux becomes:

The total heat rate by conduction,

(W), through a plane wall of area

is then

.
Example 1.1: Conduction through a Furnace Wall
Known: A fireclay brick furnace wall (0.15 m thick,

W/m·K) has inner and outer surface temperatures of 1400 K and 1150 K, respectively. The wall is 0.5 m by 1.2 m. Find: Rate of heat loss through the wall. Assumptions: Steady-state, one-dimensional conduction, constant thermal conductivity. Analysis: Using Fourier's Law, the heat flux is:

The total heat rate

is then:

Comments: Heat flows from higher to lower temperature. The distinction between heat flux (per unit area) and heat rate (total energy per time) is important.

1.2 Convection

Convection heat transfer involves two mechanisms: energy transfer due to random molecular motion (diffusion) and energy transfer by the bulk, or macroscopic, motion of the fluid. This combined transport is termed convection, while transport due to bulk fluid motion alone is advection.
Convection heat transfer is particularly relevant between a fluid in motion and a bounding surface at different temperatures. When fluid flows over a heated surface, a hydrodynamic (velocity) boundary layer develops, where velocity varies from zero at the surface to a finite value in the outer flow. Similarly, a thermal boundary layer forms if surface and fluid temperatures differ, where temperature varies from the surface temperature

to the outer fluid temperature

.
Types of Convection:
  • Forced Convection: Fluid motion is caused by external means (e.g., fan, pump, atmospheric winds).
  • Natural (Free) Convection: Fluid motion is induced by buoyancy forces resulting from density differences caused by temperature variations.
  • Mixed Convection: Both forced and natural convection mechanisms are significant.
  • Convection with Phase Change: Involves latent heat exchange during boiling (liquid to vapor) or condensation (vapor to liquid).
Newton's Law of Cooling: Regardless of the specific nature of the convection process, the heat transfer rate equation is:

Where:
  • 
    is the convective heat flux (W/m²).
  • 
    is the convection heat transfer coefficient (W/m²·K), which depends on boundary layer conditions, fluid properties, and surface geometry.
  • 
    is the surface temperature and
    
    is the fluid temperature far from the surface.
Typical values of

vary significantly depending on the process:
  • Free convection: Gases (2-25 W/m²·K), Liquids (50-1000 W/m²·K)
  • Forced convection: Gases (25-250 W/m²·K), Liquids (100-20,000 W/m²·K)
  • Convection with phase change (Boiling or condensation): (2500-100,000 W/m²·K)
Example 1.2: Heat Loss from an Uninsulated Steam Pipe
Known: An uninsulated pipe (70 mm diameter,

,

°C) passes through a room where air and walls are at

°C. The free convection coefficient is

W/m²·K. Find: 1. Surface emissive power and irradiation. 2. Pipe heat loss per unit length,

. Assumptions: Steady-state, radiation exchange between small surface and large enclosure,

.
Analysis:
  1. Surface Emissive Power (
    
    ) and Irradiation (
    
    ): Temperature must be in Kelvin:
    
    K,
    
    K. Stefan-Boltzmann constant
    
    W/m²·K⁴. Emissive power
    
    . Irradiation
    
    .
  1. Heat Loss per Unit Length (
    
    ): Total heat loss is by convection and radiation. For a pipe of length
    
    and diameter
    
    , the surface area is
    
    . The heat loss per unit length,
    
    , is:

Substituting values (

m,

°C,

°C,

°C):


Comments: Temperatures must be in Kelvin for radiation terms. Convection and radiation heat transfer rates are comparable in this case.

1.3 Radiation

Thermal radiation is energy emitted by matter at a non-zero temperature, due to changes in electron configurations. This energy is transported by electromagnetic waves (photons) and, unlike conduction and convection, does not require a material medium; it is most efficient in a vacuum.
Surface Emissive Power (

): The rate at which energy is released per unit area (W/m²) from a surface. The upper limit is prescribed by the Stefan-Boltzmann law for an ideal radiator (blackbody):

Where

is the absolute temperature (K) of the surface and

is the Stefan-Boltzmann constant (

W/m²·K⁴).
For a real surface, the heat flux emitted is less than that of a blackbody and is given by:

Where

is the emissivity, a radiative property (

) that measures how efficiently a surface emits energy relative to a blackbody.
Irradiation (

): Radiation incident on a surface from its surroundings (W/m²). A portion of this irradiation may be absorbed, increasing the thermal energy of the material. The rate of absorbed radiant energy per unit surface area is

, where

is the absorptivity (

). If

, portions may be reflected or transmitted.
Net Radiation Heat Transfer: For a small surface at

completely surrounded by a much larger, isothermal surface at

, the net rate of radiation heat transfer from the surface per unit area (assuming

) is:

This can be linearized using a radiation heat transfer coefficient,

:

Where

.
If a surface simultaneously transfers heat by convection to an adjoining gas, the total rate of heat transfer from the surface is the sum of convection and radiation components:


2. Conservation of Energy Requirement

The first law of thermodynamics, or the law of conservation of energy, is a fundamental tool in heat transfer analysis. It states that the total energy of a system is conserved, and energy can only change if it crosses system boundaries.

2.1 Conservation of Energy for a Control Volume

For a closed system (fixed mass), energy crosses boundaries via heat transfer (

) and work (

). The first law states:

Where

is the change in total energy stored,

is net heat transferred to the system, and

is net work done by the system.
For a control volume (open system, where mass can cross boundaries), energy can also be transferred by energy advection (mass carrying energy). The first law for a control volume over a time interval

states:
Thermal and Mechanical Energy Equation over a Time Interval (

) The increase in stored thermal and mechanical energy in the control volume equals the amount of thermal and mechanical energy entering, minus the amount leaving, plus the amount generated within the control volume.
Symbolically:

For an instant in time

, using rates:

Where:
  • 
    is the sum of thermal and mechanical energy stored (thermal energy
    
    , kinetic energy
    
    , potential energy
    
    ). In heat transfer, changes in KE and PE are often negligible.
  • 
    is the rate of thermal energy generation (e.g., exothermic chemical reactions, electrical resistance heating) within the control volume.
  • 
    and
    
    are rates of energy entering and leaving the control volume, including heat transfer (conduction, convection, radiation), work interactions, and energy advected by mass flow.
Simplified Steady-Flow Thermal Energy Equation: For steady-state conditions (

), no latent energy changes, and no thermal energy generation, the steady-flow thermal energy equation for an ideal gas or incompressible liquid simplifies to:

Where

is the net rate of heat transfer,

is the mass flow rate,

is the specific heat, and

,

are outlet and inlet temperatures.
Example 1.3: Heating of an Electrical Rod
Known: A conducting rod of diameter

and electrical resistance per unit length

is initially in thermal equilibrium with ambient air and surroundings. Electrical current

is passed through the rod. Find: Equation for the variation of rod temperature with time. Assumptions: Uniform rod temperature, constant properties, radiation exchange between small surface and large enclosure. Analysis: Apply the first law on a rate basis to a control volume of length

around the rod:

Where:
  • Generation:
    
    (Ohmic heating).
  • Outflow:
    
    (convection + radiation).
  • Storage change:
    
    .
Substituting these into the energy balance yields:

Rearranging to solve for

:

Comments: This differential equation can be integrated numerically to find

. At steady-state,

, leading to an algebraic equation for

.
Example 1.5: Melting Ice in a Cubical Container
Known: Mass

of ice at fusion temperature

°C in a cubical container (width

, wall thickness

, thermal conductivity

). Outer surface heated to

. Find: Expression for the time

needed to melt the entire mass of ice. Assumptions: Inner surface at

, constant properties, steady-state one-dimensional conduction through each wall, conduction area of one wall is

. Analysis: Apply the first law over the time interval

to a control volume around the ice-water mixture:

Where:
  • Energy inflow (conduction through 6 walls):
    
    .
  • Change in stored latent energy:
    
    (where
    
    is latent heat of fusion).
Substituting and solving for

:


Comments: Complications arise if ice is subcooled initially. Units of K and °C cancel when used in temperature differences.

2.2 The Surface Energy Balance

Often, the conservation of energy is applied at the surface of a medium. In this special case, the control surfaces enclose no mass or volume. Therefore, generation and storage terms are irrelevant, and the conservation requirement simplifies to:

Even with thermal energy generation within the medium, it does not affect the energy balance at the control surface. This applies to both steady-state and transient conditions.
On a unit area basis, the surface energy balance for conduction from the medium to the surface (

), convection from the surface to a fluid (

), and net radiation exchange from the surface to the surroundings (

) is:

Example 1.6: Human Thermoregulation in Air and Water
Known: A person with a skin/fat layer (thickness

mm,

W/m·K, area

m², emissivity

) has an inner skin temperature of

°C (308 K). Find: Skin surface temperature (

) and heat loss rate (

) when in: 1. Still air (

K,

W/m²·K). 2. Water (

K,

W/m²·K). Assumptions: Steady-state, one-dimensional conduction, uniform thermal conductivity, radiation exchange small surface to large enclosure, water opaque to thermal radiation.
Analysis (Part 1: In Air): Energy balance at skin surface: Conduction into surface = Convection out + Radiation out.

This equation is solved iteratively for

. Estimating

with a guessed

K gives

W/m²·K. Then, solving for

:

Substituting numerical values:

Heat loss rate

(W):

Analysis (Part 2: In Water): Water is opaque to thermal radiation, so heat loss is by convection only (set

). Using

W/m²·K:

Heat loss rate

(W):

Comments: Radiation is significant in air due to low convection coefficient. Heat loss in water is much higher due to water's higher thermal conductivity, leading to a colder skin temperature.

3. Analysis of Heat Transfer Problems: Methodology

Solving heat transfer problems systematically enhances understanding and confidence. A recommended procedure includes:
  1. Known: State briefly and concisely what is known from the problem statement.
  1. Find: State briefly and concisely what needs to be determined.
  1. Schematic: Draw a physical system schematic, indicating control surfaces with dashed lines and relevant heat transfer processes with labeled arrows.
  1. Assumptions: List all pertinent simplifying assumptions.
  1. Properties: Compile necessary property values and their sources.
  1. Analysis: Apply conservation laws and rate equations. Develop the analysis completely before substituting numerical values. Perform calculations.
  1. Comments: Discuss results, critique assumptions, and infer implications.

4. Relevance of Heat Transfer

Heat transfer principles are vital in diverse fields, from engineering to biology.
  • Energy Conversion & Production: Crucial for optimizing gas turbine engines (cooling blades), designing fuel cells (temperature control to prevent failure, water management), and managing thermal loads in nuclear reactors.
  • Electronics Cooling: Essential for microprocessors, data centers, and other electronic devices. Advances in heat transfer engineering enable higher performance and reliability by maintaining low operating temperatures, often using heat sinks and forced convection.
  • Biological Systems (Thermoregulation): Heat transfer processes (convection, radiation, evaporation) regulate body temperature, preventing conditions like hypothermia or heat stroke. Blood flow also plays a critical role in internal heat transport.
  • Biomedical Engineering: Applied in laser surgery (destroying cancerous lesions with heat), cryosurgery (destroying diseased diseased tissue with extreme cold), and drug delivery (controlling temperature distribution during chemotherapies).

5. Units and Dimensions

Physical quantities in heat transfer are specified by dimensions, measured in units. The four basic dimensions are length (

), mass (

), time (

), and temperature (

).
The International System of Units (SI) is the worldwide standard. Key SI base units include:
  • Length: meter (m)
  • Mass: kilogram (kg)
  • Time: second (s)
  • Thermodynamic Temperature: kelvin (K)
  • Electric Current: ampere (A)
  • Amount of Substance: mole (mol)
Derived SI units, such as newton (N) for force (kg·m/s²), pascal (Pa) for pressure (N/m²), joule (J) for energy (N·m), and watt (W) for power (J/s), are consistently used. While Celsius (°C) is common, temperatures in radiation equations must be in Kelvin. Temperature differences are equivalent for both scales (

).