Fourier’s Law, Heat Transfer by Conduction, Convection and Radiation

Fourier's Law

Using Fourier's law of thermal conduction, heat is transferred through a material in a specific proportion to its negative gradient of temperature and to its area (perpendicular to the gradient).

The rate equations describe heat transfer processes. In thermal conduction, Fourier's law of thermal conduction is used to calculate the rate equation. A negative gradient in area and temperature, where flow of heat occurs at 90 degrees to that gradient, directly relates to the rate of heat transfer across a solid substance.

According to Fourier's law, the differential form is:

q = - k ▽ T

∇T is the gradient of temperature (K.m-1)

A material's conductivity (W. m-1. K-1) is represented by k.

Heat flux density is expressed by q (W. m-2)

Essentially, the proportionality constant of a substance is what determines its thermal conductivity (k or λ). Thermal conductivity is determined by the rapid transfer of energy by conduction in a body. The value of K is also higher. The inverse relationship between geometry, temperature difference, and material thermal conductivity is used to find Fourier's law. The law was first presented by Joseph Fourier in 1822, who noted that: "the difference in heat flux between two surfaces depends on the magnitude and sign of the temperature gradient".

Heat Transfer by Conduction

In this process, heat is transferred from objects in higher temperatures to objects in lower temperatures.

A high kinetic energy area transfers thermal energy to a lower kinetic energy area. Due to the collision between high-speed particles and slow-moving particles, slow moving particles increase their kinetic energy. Physical contact transfers heat in this way. The term conduction itself is synonymous with heat transfer.

Conduction examples are as follows:

• Clothing can be ironed through conduction, in which heat is transferred from the iron to the clothing.
• Holding an ice cube in your hands results in the melting of the ice cube due to heat transfer.
• When the sand is hot, ice cubes melt. It is common during summer months. Sandy surfaces conduct heat very well.

Heat Transfer by Convection

As fluids move from high to low temperatures, molecules move from region to region.

Temperature increases cause the volume of the liquid to increase by the same factor, which is called displacement. Convection can be calculated using the following equation:

Q = hc . A . (Ts – Tf)

• A unit of heat transfer is Q
• Hc is the heat transfer coefficient for convection
• Heat transfer area A
• Temperature on the surface is Ts
• Temperature of fluid Tf

Convection can be characterized by:

• The molecules that are denser move to the bottom, and the molecules that are less dense move to the top, so that the water gets heated by the circular motion of molecules.
• Cool water at the poles flows towards the equator while warm water around the equator does the reverse.
• Convection is responsible for regulating the body temperature of warm-blooded animals by circulating their blood.

Heat Transfer by Radiation

All of us are exposed to radiant heat in some form or another on a daily basis. It is a form of thermal radiation. Radiant heat is a type of electromagnetic radiation. Electromagnetic waves remove energy from emitting bodies. The process of radiation involves the passage of a vacuum or transparent medium, either solid or liquid. Thermal radiation is produced by molecular motion. Emission of electromagnetic radiation occurs as a result of electron and proton motion. Radiation heat is measured by thermocouples. Temperature is measured by this device. Occasionally, a measurement error occurs in this device through radiation heat transfer.

With increased temperature, the wavelengths of the radiation emitted get shorter, resulting in shorter wavelengths. According to the Stefan-Boltzmann law, thermal radiation can be calculated as follows:

P = e ∙ σ ∙ A· (Tr – Tc)4

• Radiative power is referred to as P
• Radiation occurs in area A
• The temperature of a radiator is Tr
• The temperature of the environment is Tc
• Stefan's constant σ is emissivity and e is the emissivity

Radiation examples are as follows:

• An example of radiation is microwave radiation generated in the oven.
• Sunlight emitting UV rays is also an example of radiation.
• Radiation occurs when Uranium-238 decays into Thorium-234 and alpha particles are released.

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