The air inside a chamber at T_∞,i = 50°C is heated convectively with h; = 20 W/m² ∙ K by a 200-mm-thick wall having a thermal conductivity of 4 W/m ∙ K and a uniform heat generation of 1000 W/m³. To prevent any heat generated within the wall from being lost to the outside of the chamber at T_∞,o = 25°C with h_o = 5 W/m² ∙ K, a very thin electrical strip heater is placed on the outer wall to provide a uniform heat flux, q_o.

(a) Sketch the temperature distribution in the wall on T -x coordinates for the condition where no heat generated within the wall is lost to the outside of the chamber.

(b) What are the temperatures at the wall boundaries, T (0) and T (L), for the conditions of part (a)?

(c) Determine the value of q”_o that must be supplied by the strip heater so that all heat generated within the wall is transferred to the inside of the chamber.

(d) If the heat generation in the wall were switched off while the heat flux to the strip heater remained constant, what would be the steady-state temperature, T (0), of the outer wall surface?

Transcribed Image Text:

Strip heater, q" -Wall, k, ġ 11 Outside chamber Inside chamber