Solution Manual for Fundamentals of Heat and Mass Transfer 8th Edition Bergman

SOLUTION MANUAL




SOLUTION MANUAL

, PROBLEM 1.1


KNOWN: Temperature distribution in wall of Example 1.1.

FIND: Heat fluxes and heat rates at x = 0 and x = L.

SCHEMATIC:




ASSUMPTIONS: (1) One-dimensional conduction through the wall, (2) constant thermal conductivity,
(3) no internal thermal energy generation within the wall.

PROPERTIES: Thermal conductivity of wall (given): k = 1.7 W/m·K.

ANALYSIS: The heat flux in the wall is by conduction and is described by Fourier’s law,

dT
q′′x = −k (1)
dx
Since the temperature distribution is T(x) = a + bx, the temperature gradient is

dT
=b (2)
dx

Hence, the heat flux is constant throughout the wall, and is


dT
q′′x =−k =−kb =−1.7 W/m ⋅ K × ( −1000 K/m ) =1700 W/m 2 <
dx

Since the cross-sectional area through which heat is conducted is constant, the heat rate is constant and is

qx =q′′x × (W × H ) =1700 W/m 2 × (1.2 m × 0.5 m ) =1020 W <

Because the heat rate into the wall is equal to the heat rate out of the wall, steady-state conditions exist. <

COMMENTS: (1) If the heat rates were not equal, the internal energy of the wall would be changing
with time. (2) The temperatures of the wall surfaces are T 1 = 1400 K and T 2 = 1250 K.

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