Solved: Find the steady- ~tate temperature in the plate in

Chapter 12, Problem 12.1.106

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A laterally insulated bar of length 10 cm and constant cross-sectional area \(1 \mathrm{~cm}^{2}\), of density \(10.6 \mathrm{gm} / \mathrm{cm}^{3}\), thermal conductivity \(1.04 \mathrm{cal} /\left(\mathrm{cm} \quad \mathrm{sec}{ }^{\circ} \mathrm{C}\right)\), and specific heat \(0.056 \mathrm{cal} /\left(\mathrm{gm}^{\circ} \mathrm{C}\right)\) (this corresponds to silver, a good heat conductor) has initial temperature f) and is kept at \(0^{\circ} \mathrm{C}\) at the ends x = 0 and x = 10. Find the temperature u(x, t) at later times. Here, f(x) equals:

\(f(x)=0.2 x \text { if } 0<x<5 \text { and } 0 \text { otherwise }\)

Text Transcription:

1 cm^2

10.6 gm/cm^3

1.04 cal/(cm sec degree C)

0.056 cal/(gm degree C)

0 degree C

f(x)=0.2x if 0 < x < 5 and 0 otherwise