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PROBLEM 1.1 KNOWN: Heat rate, q, through one-dimensional wall of area A, thickness L, thermal conductivity k and inner temperature, T1. FIND: The outer temperature of the wall, T2. SCHEMATIC: ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state conditions, (3) Constant properties. ANALYSIS: The rate equation for conduction through the wall is given by Fourier’s law, q cond 〓 q x 〓 q ′′ ? A 〓 -k x Solving for T2 gives T ?T dT ? A 〓 kA 1 2 . dx L T2 〓 T1 ? q cond L . kA Substituting numerical values, find T2 〓 415 C - 3000W × 0.025m 0.2W / m ? K × 10m2 T2 〓 415 C - 37.5 C T2 〓 378 C. COMMENTS: Note direction of heat flow and fact that T2 must be less than T1. [ PROBLEM 1.2 KNOWN: Inner surface temperature and thermal conductivity of a concrete wall. FIND: Heat loss by conduction through the wall as a function of ambient air temperatures ranging from -15 to 38°C. SCHEMATIC: ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (…
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