Consider a rod of diameter D, thermal conductivity k, and length 2L that is perfectly insulated over one portion of its length, - L

(a) Sketch the temperature distribution on T – x coordinates and identify its key features. Assume that T1 > T3 > T∞.

(b) Derive an expression for the midpoint temperature T2 in terms of the thermal and geometric parameters of the system.

(c) For T1, = 200°C, T3 = 100°C, and the conditions provided in the schematic, calculate T 2 and plot the temperature distribution. Describe key features of the distribution and compare it to your sketch of part (a).

Transcribed Image Text:

R", = 4 x 10 m•K/W- Insulation -T3 Rod +L D= 5 mm T= 20°C L= 50 mm h= 500 Wim-K k= 100 Wim-K