Fundamentals of Heat and Mass Transfer [Frank P.Incropera - David P.DeWitt] Solution Manual - CH2.pdf

PROBLEM
KNOWN: Electrical heater attached to backside of plate while front surface is exposed to
convection process (T¥,h); initially plate is at a uniform temperature of the ambient air and suddenly
heater power is switched on providing a constant q.¢¢o
FIND: (a) Sketch temperature distribution, T(x,t), (b) Sketch the heat flux at the outer surface,
q¢¢x (L,t) as a function of time.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction, (2) Constant properties, (3) Negligible heat
loss from heater through insulation.
ANALYSIS: (a) The temperature distributions for four time conditions including the initial
distribution, T(x,0), and the steady-state distribution, T(x,¥), are as shown above.
Note that the temperature gradient at x = 0, -dT/dx)x=0, for t > 0 will be a constant since the flux,
q¢¢x (0,) is a constant. Noting that To = T(0,¥), the steady-state temperature distribution will be
linear such that
To ­¥T(L, )
q¢¢o =k=hTéù(L,¥­) T.¥
L ëû
(b) The heat flux at the front surface, x = L, is given by q¢¢ L,t=­kdT/dx. From the
x ( ) ( )x=L
temperature distribution, we can construct the heat flux-time plot.
COMMENTS: At early times, the temperature and heat flux at x = L will not change from their
initial values. Hence, we show a zero slope for q¢¢x (L,t) at early times. Eventually, the value of
q¢¢x (L,t) will reach the steady-state value which is q.¢¢o
PROBLEM
KNOWN: Plane wall whose inner surface is insulated and outer surface is exposed to an
airstream at T∞. Initially, the wall is at a uniform temperature equal to that of the airstream.
′′
Suddenly, a radiant source is switched on applying a uniform flux, q,o to the outer surface.
FIND: (a) Sketch temperature distribution on T-x coordinates for initial, steady-state, and
′′
two intermediate times, (b) Sketch heat flux at the outer surface, qx () L,t , as a function of
time.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction, (2) Constant properties, (3) No int