The steady-state expression for heat conduction through a plane wall is q =(kA/L) ΔT as given by equation (17-4). For steady-state heat conduction through a hollow cylinder, an

expression similar to equation (17-4) is

where AÌ… is the €œlog-mean€ area defined as

a. Show that AÌ… as defined above satisfies the equations for steady-state radial heat transfer in a hollow cylindrical element.
b. If the arithmetic mean area, π (r_o - r_i), is used rather than the logarithmic mean, calculate the resulting percent error for values of r_o/r_i of 1.5, 3, and 5.

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T1 T2 Case dT|dx Ях (K/m) (W/m²) 350 K 275 K 300 K -2000 350 K 3 -300 250 K 4 200 kA .ΔΤ ri Το η