Heat transfer chapter 2 solutions

PROBLEM 2.12 KNOWN: Plane wall with prescribed thermal conductivity, thickness, and surface temperatures. FIND: Heat flu

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PROBLEM 2.12 KNOWN: Plane wall with prescribed thermal conductivity, thickness, and surface temperatures. FIND: Heat flux, q x , and temperature gradient, dT/dx, for the three different coordinate systems shown. SCHEMATIC:

ASSUMPTIONS: (1) One-dimensional heat flow, (2) Steady-state conditions, (3) No internal generation, (4) Constant properties. ANALYSIS: The rate equation for conduction heat transfer is

q x   k

dT , dx

(1)

where the temperature gradient is constant throughout the wall and of the form

dT T  L   T  0   . dx L

(2)

Substituting numerical values, find the temperature gradients,

(a)

dT T2  T1  600  400  K    2000 K/m dx L 0.100m