The faces x = 0 and x = c of a slab 0 0. (a) After...
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The faces x = 0 and x = c of a slab 0 <x < c, which is initially at temperatures f(x), are kept at temperature zero. Use the following method to derive an expression for the temperatures u = u(x, t) throughout the slab when i > 0. (a) After writing the boundary value problem for the temperatures, make the substitution s = Tx/c to show that u, = (km?/c?)u ,,, u = 0 when s 0 and s = T, and u = f(cs/7) when t= 0. (b) By referring to the solution (5), with coefficients (7), of the problem in Example 1, Sec. 32, write an expression for u in terms of s and t. Then, with the aid of the relation s = Tx/c that was used in part (a), show that n'm?k u(x, 1) = E b, exp sin %3D n=1 where 2 b, dx (n = 1,2,...). %3D The faces x = 0 and x = c of a slab 0 <x < c, which is initially at temperatures f(x), are kept at temperature zero. Use the following method to derive an expression for the temperatures u = u(x, t) throughout the slab when i > 0. (a) After writing the boundary value problem for the temperatures, make the substitution s = Tx/c to show that u, = (km?/c?)u ,,, u = 0 when s 0 and s = T, and u = f(cs/7) when t= 0. (b) By referring to the solution (5), with coefficients (7), of the problem in Example 1, Sec. 32, write an expression for u in terms of s and t. Then, with the aid of the relation s = Tx/c that was used in part (a), show that n'm?k u(x, 1) = E b, exp sin %3D n=1 where 2 b, dx (n = 1,2,...). %3D
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Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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