Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat - Softcover

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...V COS V O.V Jo a I tf Jo 4. Show that /' is the ordinate of a broken line running parallel to the axis of x from #=0 to x = a, and from.r = 6 to.r=x, and inclined to the axis of x at an angle a between x--a. and x = l. PART II. THE MATHEMATICAL THEORY OF THE CONDUCTION OF HEAT IN SOLIDS. CHAPTER IX. THE DIFFERENTIAL EQUATIONS OF THE MATHEMATICAL THEORY OF THE CONDUCTION OF HEAT. §70. Introductory. When different parts of a body are at different temperatures, heat flows from the hotter to the colder. Consider the metal rod A BCD Fig. 20. and suppose that it is heated at the end A from some external source. For some time the temperature of the rod gradually rises, the parts near A being heated first, but no change takes place at CD till BC has had its temperature raised. Ultimately, if the end A is heated long enough it is found that a steady state of temperature is reached, in which, while the temperature may vary from point to point, it remains the same at eacli point as the time changes. This transference of heat from the hotter portions of a body to the colder is called Conduction of Heat. It must be distinguished from Convection, on the one hand, and Radiation, on the other. In Convection the transference of heat is due to the motion of the heated body itself, as, for example, when the different parts of a liquid are at different temperatures, currents are produced by means of which a uniform temperature is reached. In Radiation the hotter body loses heat and the colder body gains it by means of a process occurring in some intervening medium. §71. Conductivity. There are two different methods of establishing the Mathematical Theory of the Conduction of Heat. The one which Fourier adopted and by means of which he was led to the discovery of the ...

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