Question

formulate complete PDE problems (specify the equation, space domain, time interval, boundary, and initial conditions) for the following model situations:

a) Conduction heat transfer occurs in a thin rod of length L with insulated side walls. Temperature is initially constant T(0) = T₀. We are asked to find the temperature distribution in the time period 0 < t < t₁, during which the left end of the rod is kept at the temperature T₀, and the right end is subject to cooling with the constant heat transfer rate q.

b) We are asked to find equilibrium temperature distribution in a rectangular metal plate 0 is less than or equal to x is less than or equal to L_x, 0 is less than or equal to y is less than or equal to L_y. The boundaries x = 0 and x = L_x are kept at constant temperatures T₁ and T₂. The boundaries y = 0 and y = L_y are thermally insulated

c) One-dimensional string stretched between the points (x,y) = (0,0) and (x,y) = (L_x, 0) oscillates elastically during the time period 0 < t < t₁. At the initial moment t = 0, the deiation of the string from the horizontal and its velocity are given by function f(x) and g(x), respectively.

Answer 1

cf CP 2 u preset case, s u

しレ Lt 8 c Ll