Consider a one-dimensional plane wall of thickness 2L. The surface at x=–L is subjected to convective conditions characterized by T_∞,1, h₁, while the surface at x =  + L is subjected to conditions T_∞,2, h₂. The initial temperature of the wall is T_o = (T_∞,1 + T_∞,2)/2 where T_∞,1 > T_∞,2.

(a) Write the differential equation, and identify the boundary and initial conditions that could be used to determine the temperature distribution T(x, t) as a function of position and time.

(b) On T – x coordinates, sketch the temperature distributions for the initial condition, the steady-state condition, and for two intermediate times for the case h₁ = h₂.

(c) On q"_x – t coordinates, sketch the heat flux at the planes x = 0,– L, and + L.

(d) The value of h1 is now doubled with all other conditions being identical as in parts (a) through (c). On T – x coordinates drawn to the same scale as used in part (b), sketch the temperature distributions for the initial condition, the steady-state condition, and for two intermediate times. Compare the sketch to that of part (b).

(e) Using the doubled value of h₁, sketch the heat flux q"_x (x,t) at the planes x = 0,–L, and  + L on the same plot you prepared for part (c). Compare the two responses.

Transcribed Image Text:

To h₁, T1 T1 > T2 X 2L 1₂, 2