The faces x = 0 and x c of a slab 0 0. (a) After writing...

  

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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/T) 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 %3! n?m?k u(x, t) = E b, exp c2 n-1 where 2 b, sin dx (n = 1,2,...). 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/T) 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 %3! n?m?k u(x, t) = E b, exp c2 n-1 where 2 b, sin dx (n = 1,2,...). 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/T) 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 %3! n?m?k u(x, t) = E b, exp c2 n-1 where 2 b, sin dx (n = 1,2,...). 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/T) 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 %3! n?m?k u(x, t) = E b, exp c2 n-1 where 2 b, sin dx (n = 1,2,...).