Introduction to Thermal Transfer

Introduction to Thermal Transfer

Thermodynamics vs. Thermal Transfer

• The study of thermal phenomena involves exploring thermal transfer and thermodynamics
• Although closely related, thermodynamics and thermal transfer focus on different aspects of the science of heat.
• Thermodynamics helps understand the energy evolution of systems from an initial equilibrium state to a new equilibrium state
• Help to predicting the total amount of energy a system exchanges with its environment during a transition
• Lavoisier's quote summarizes the thermodynamics' first principle/ energy conservation principle: "Nothing is created, nothing is lost, everything is transformed."
• In an isolated system, the total energy remains constant during a transformation
• The second principle provides information on the direction of transformation; heat is transferred from a hot to a cold environment
• Thermodynamics not specify how energy exchanges occur or the mechanisms involved.
• Whereas Thermal transfers focus on heat transfer mechanisms between locations

Thermodynamics vs. Thermal Transfer Schematized

• Thermodynamics studies the energy evolution of systems (in the form of heat and work) from one equilibrium state to another
• Thermodynamics predict the total amount of energy a system exchanges with the exterior for transition
• Thermodynamics provides no indication on the mechanisms and dynamics of these exchanges
• Thermal approach focuses transfer of heat mechanisms
• Thermal transfer quantitatively describes the evolution of system characteristics, especially temperature, in space and time

Case of a Cup of Hot Coffee

• Consider hot coffee on a table to understand the two sciences

• Initially (t=0s), the cup of coffee is hot at temperature Tc

• In time, coffee cools and reaches ambient temperature

• Thermodynamics focuses on two equilibrium states: initial and final

• Thermal transfers describe temperature evolution over time

• Thermodynamics aids in understanding the overall system function

• Thermodynamics analyze the energy amount in the cup of coffee and study changes like heat loss over time

• Thermal transfer intervenes in heat propagation from the hot coffee cup to the environment due to a temperature difference

Importance of Science for Thermal Transfer

• Develop a deep understanding of thermal transfer mechanisms
• Predict and model these transfers
• Optimize industrial systems and processes
• Develop thermal insulation materials and techniques
• Enhance energy efficiency
• This knowledge is essential for diverse technological, industrial, and environmental applications

Thermal Transfer - Modes

• Heat transfer occurs in three modes:
  • Conduction
  • Convection ( a conduction particular case)
  • Radiation
• Heat energy at the microscopic level is agitation or vibration of molecules and free electrons
• Temperature is a macroscopic measure of this movement amplitude
• Agitation or vibration energy can be transmitted

Thermal Transfer - Modes - Definitions

• Conduction involves transmission from molecule to molecule through successive collisions
• Conduction requires a material support (solid, liquid, or gas); heat transfer occurs if a temperature gradient exists
• Radiation doesnt require material support; operates in a vacuum
• Transmission is through an electromagnetic wave
• A molecule in thermal agitation emits/absorbs electromagnetic waves (photons); found in solids, liquids, and some gases (H2O, CO2, etc.)
• Convection is a heat conduction phenomenon occurring within macroscopically moving fluids
• Heat transfer by molecular collisions (conduction) combines with the calorific energy displacement by molecules moving along speed field

Convection Types

• Based on the causes of fluid movement, there are three types of thermal convection:
  • Forced: Movement is independent of thermal causes (pump or fan-driven)
  • Natural: Movement is due to temperature gradients; fluid moves due to volumetric mass differences
  • Mixed: Movement combines forced and natural phenomena

Thermal Transfer - Modes - Summary

• Temperature: The fundamental parameter in thermal transfers:
  • Macroscopic parameter results from human sensation (touching hot bodies)
  • Microscopic parameter related to molecular agitation phenomena and degrees of heat.
• Contact physical and support material are between two materials: thermal transfers through conduction
• If there is an intermediate present such as a fluid like liquid then it's called transfers through convection
• Void separation or transparent environments between two environments: Thermal Transfers by radiation
• It's important to note the possibility of existence of 3 modes and two modes simultaneously

Thermal Examples

• Spoon
• Fan
• Sun

Part 1 - Conduction

• Conduction is also known as thermal diffusion and involves energy transfer in a material medium without macroscopic movement, involving:
  • Molecular collisions
  • Vibration transfers
• Heat will be transferred from a closer proximity by the collisions between the material parts (atoms/molecules)

Conduction Basis

• Heat transfer by conduction consider a solid bar with temperature varying only in direction x

• Assume temperature decreases as x increases

• Isothermal surfaces in solids are parallel and perpendicular to the x-axis like S

• Applying the second thermodynamic principle, heat is naturally transferred from the warmer surface S(x) to the cooler surface S(x+dx)

• Isothermal surface (ST) is a material medium surface with similar temperature at every surface point at an instant t

• Heat flux (Φ in Watts): The amount of heat crossing a given surface S(x) per unit of time

• Flux density (φ in W/m²): heat that crosses a surface in a given unit of time

Fourier's Law

• Fourier's law is the first fundamental law upon which thermal transfers are based
• Consider the solid bar to understand this law easily were the temperature is varied along the x direction
• This law states there's a proportionality with the flux of heat traversant and the variation of the spatial temperature which is the same as the surface that's being transferred to

Formulations

• The spatial variation rate of temperature as a function of x: gradient of temperature/ S(x)
• The math: φ=f(ΔΤ/Δx)
  • Φ = flux density vector, in W/m²
  • dT/dx = temperature gradient vector
• The coefficient of proportion denotes the the material of the conductor when regarding heat
• The law the minus sign is considered when the heat is being moved from hot to a warmer surface so consider the opposite direction

Law of Fourier: Unidirectional Case

• Defined as its traversant proportionally to the the gradient and how much is being put to

Law of Fourier: General Case

• In the solide form the repartition temperature to the space of quiconque type of law it is mathematically written that form

Basis Law for thermal conduction

• Measuring the capacity the material to conduct the hear through its unit based on these factors
• Physically measuring the capacity of a medium that moves based on the time
• The thermal conduction is expressed in watts / meters / kg
• Dependant on the structure such as : Chemical structure, Density and Temperature
• The higher thermal conductivity results in better conductivity and vs versa