Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

FOURIER’S LAW OF HEAT CONDUCTION

France, 1822. The rate of heat flow between two points in a material is proportional to the difference in the temperatures of the points and inversely proportional to the distance between the two points.

CROSS REFERENCE: RENÉ DESCARTES, LORD KELVIN, NICOLAS DE CARITAT CONDORCET, ANTOINE LAVOISIER, AND OLIVER HEAVISIDE.

In 1822, Jean-François Champollion revealed his first successful
attempts at deciphering Egyptian hieroglyphs through the use of
the Rosetta Stone. English mathematician and mechanical engi-
neer Charles Babbage proposed the construction of a Difference
Engine—a special-purpose mechanical digital calculator. Alas,
this first model would have required nearly 25,000 parts, and he
did not complete the construction.

If we place one end of a metal spoon into a hot cup of tea, the temperature at the end of the handle of the spoon begins to rise. This heat transfer is caused by molecules at the hot end exchanging their kinetic and vibrational energies with adjacent regions of the spoon through random motions. The energy is always transported from the tea to the spoon tip, that is, from high to low temperature, through a process known as conduction.

Fourier’s Law of Heat Conduction is concerned with the transmission of heat in materials. The law states that the heat flux, Q, which is the flow of heat per unit area and per unit time, is proportional to the gradient of temperature difference:

The law is often applied to objects such as a slab of material, a body of water, or insulated wires. Here, A is the surface area for heat transfer; Δx is the thickness of the matter through which the heat is passing; K is a conductivity constant, which is dependent on the nature of the material and its temperature; and ΔT is the temperature difference through which the heat is being transferred. The minus sign is placed before the conductivity constant to indicate that heat flows in the direction of decreasing temperature. Note that although the heat conduction equation refers to one-dimensional conduction, the formula can be generalized to three dimensions by observing that heat flow may be a vector quantity with x, y, and z components.

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