By George S. Monk
New york 1937-1st McGraw Hill. 8vo., 477pp., illus., index. VG, no DJ.
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2 Boundary or Surface Conditions Various surface conditions may arise. The following surface conditions are most frequent. No Heat Flux at the Surface From a practical point of view, this case is very extreme, as perfect thermal insulators do not really exist. However, from a theoretical point of view, the case is of interest, because mathematical treatment is often possible. At all points on the surface, the differentiation of temperature in the n direction of the outward normal to the surface is equal to zero.
2 Heat Conduction Through a Semi-infInite Medium The problem of heat conduction through a semi-infinite medium is considered, when the boundary is kept at a constant temperature Too, and the initial temperature is To within this medium. 39) According to the principle shown in Eq. 37), the left-hand side, for x > 0, becomes pT(x, p) - To The right-hand side of Eq. 40) Eq. 41') ax which can be written as a2 T2 ax (x, p) = E. (T(X, ll' p The general solution of Eq. 43) The boundary condition (Eq. 42) becomes To -; x) T = - + Too - To exp (-.
83) is a solution of the problem, by considering the method of separation of variables. 87) where wns are the positive roots of Eq. 86), and Ans are constants to be determined, is a solution which satisfies the equation of heat conduction within the sheet and the boundary conditions. J n=1 (w~ + h2)L + 2h L X exp(-w~(l't) Jo f(y)(wncoswny Sheet Located Between the Abscissae -Rand R, and the Initial Temperature [(x) The Eq. 93) As Eq. 95) When Wn is a root of Eq. 96) f is an even function, Eq.