PROBLEM 3.158
KNOWN: Dimensions and base temperature of an annular, aluminum fin of rectangular profile.
Ambient air conditions.
FIND: (a) Fin heat loss, (b) Heat loss per unit length of tube with 200 fins spaced at 5 mm increments.
SCHEMATIC:
ASSUMPTIONS
PROBLEM 3.116
KNOWN: Thermal conductivity, diameter and length of a wire which is annealed by passing an
electrical current through the wire.
FIND: (a) Steady-state temperature distribution along wire, (b) Maximum wire temperature, (c)
Average wire temper
PROBLEM 5.92
KNOWN: Thick oak wall, initially at a uniform temperature of 25C, is suddenly exposed to combustion
products at 800C with a convection coefficient of 20 W/m2K.
FIND: (a) Time of exposure required for the surface to reach an ignition temperatu
PROBLEM 5.116
KNOWN: A 0.12 m thick wall, with thermal diffusivity 1.5 10-6 m2/s, initially at a uniform
temperature of 85C, has one face suddenly lowered to 20C while the other face is perfectly insulated.
FIND: (a) Using the explicit finite-difference m
PROBLEM 5.119
KNOWN: Plane wall, initially at a uniform temperature To = 25C, has one surface (x = L) suddenly
exposed to a convection process with T = 50C and h = 1000 W/m2K, while the other surface (x = 0) is
&
maintained at To. Also, the wall suddenly
PROBLEM 5.133
KNOWN: Tantalum rod initially at a uniform temperature, 300K, is suddenly subjected to a
current flow of 80A; surroundings (vacuum enclosure) and electrodes maintained at 300K.
FIND: (a) Estimate time required for mid-length to reach 1000K,
PROBLEM 5.131
2
KNOWN: Plastic film on metal strip initially at 25C is heated by a laser (85,000 W/m for
ton = 10 s), to cure adhesive; convection conditions for ambient air at 25C with coefficient
2
of 100 W/m K.
FIND: Temperature histories at center and
PROBLEM 5.134
KNOWN: Support rod spanning a channel whose walls are maintained at Tb = 300 K. Suddenly the rod
is exposed to cross flow of hot gases with T = 600 K and h = 75 W/m2K. After the rod reaches steadystate conditions, the hot gas flow is termina
PROBLEM 5.135
KNOWN: Thin metallic foil of thickness, w, whose edges are thermally coupled to a sink at temperature,
Tsink, initially at a uniform temperature Ti = Tsink, is suddenly exposed on the top surface to an ion beam
heat flux, q , and experiences
PROBLEM 5.136
KNOWN: Stack or book of steel plates (sp) and circuit boards (b) subjected to a prescribed
platen heating schedule Tp(t). See Problem 5.46 for other details of the book.
FIND: (a) Using the implicit numerical method with x = 2.36mm and t = 6
PROBLEM 5.137
KNOWN: Thin, circular-disc subjected to induction heating causing a uniform heat
generation in a prescribed region; upper surface exposed to convection process.
FIND: (a) Transient finite-difference equation for a node in the region subjecte
PROBLEM 5.138
KNOWN: An electrical cable experiencing uniform volumetric generation; the lower half is well
insulated while the upper half experiences convection.
FIND: (a) Explicit, finite-difference equations for an interior node (m,n), the center node
PROBLEM 5.139
KNOWN: Initial temperature distribution in two bars that are to be soldered together; interface
contact resistance.
FIND: (a) Explicit FDE for T4,2 in terms of Fo and Bi x/k R ; stability criterion, (b) T4,2
t,c
one time step after contact i
PROBLEM 5.141
KNOWN: Electrical heating elements embedded in a ceramic plate as described in Problem
4.86; initially plate is at a uniform temperature and suddenly heaters are energized.
FIND: Time required for the difference between the surface and initi
PROBLEM 5.132
KNOWN: Insulated rod of prescribed length and diameter, with one end in a fixture at 200C, reaches a
uniform temperature. Suddenly the insulating sleeve is removed and the rod is subjected to a convection
process.
FIND: (a) Time required for
PROBLEM 5.127
KNOWN: One-dimensional convective heating and cooling of a plane slab with Bi1 = 10 (for Heating
Phase 1, beginning at Fo = 0 and ending at Fo = Fo1 = 0.1), Bi2 = 1 (for Cooling Phase 2, beginning at
Fo = Fo1).
FIND: (a) Dimensionless form o
PROBLEM C5.121
KNOWN: Dimensions and properties of acrylic and steel plates. Initial temperatures.
FIND: Time needed to bring external surface of the acrylic to its softening temperature. Plot of the
average acrylic and steel plate temperatures and acryli
PROBLEM 5.123
KNOWN: Thickness, initial temperature, speed and thermophysical properties of steel in a thin-slab
continuous casting process. Surface convection conditions.
FIND: Time required to cool the outer surface to a prescribed temperature. Correspo
PROBLEM 5.124
KNOWN: Thickness and thermal diffusivity of a plane wall. Initial and boundary conditions.
FIND: (a) Temperature distribution at t = 30 min using an explicit finite difference technique with a
time step of 600 s and a space increment of 30 m
PROBLEM 5.122
KNOWN: Conditions associated with heat generation in a rectangular fuel element with surface
cooling. See Example 5.11.
FIND: (a) The temperature distribution 1.5 s after the change in operating power; compare your
results with those tabulat
PROBLEM 5.125
KNOWN: Very thick plate, initially at a uniform temperature, Ti, is suddenly exposed to a
convection cooling process (T,h).
FIND: Temperatures at the surface and a 45mm depth after 3 minutes using finite-difference
method with space and time
PROBLEM 5.126
KNOWN: Sudden exposure of the surface of a thick slab, initially at a uniform temperature,
to convection and to surroundings at a high temperature.
FIND: (a) Explicit, finite-difference equation for the surface node in terms of Fo, Bi, Bir,
PROBLEM 5.128
KNOWN: Thick slab of copper, initially at a uniform temperature, is suddenly exposed to a constant
net radiant flux at one surface. See Example 5.12.
FIND: (a) The nodal temperatures at nodes 00 and 04 at t = 120 s; that is, T00(0, 120 s) an
PROBLEM 5.130
KNOWN: Dimensions and properties of a steel-reinforced concrete pillar. Initial, ambient and
surroundings temperatures. Values of convection heat transfer coefficient and contact resistance.
FIND: (a) Temperature of the exposed concrete surf
PROBLEM 5.129
KNOWN: Plane wall of thickness 2L, initially at a uniform temperature, is suddenly subjected to
convection heat transfer.
FIND: The mid-plane, T(0,t), and surface, T(L,t), temperatures at t = 50, 100, 200 and 500 s, using
the following metho
PROBLEM 5.142
KNOWN: Conditions associated with heat generation in a rectangular fuel element with surface
cooling. See Example 5.11.
FIND: (a) The temperature distribution 1.5 s after the change in the operating power; compare results
with those tabulate
PROBLEM 5.143
KNOWN: Thick slab of copper as treated in Example 5.12, initially at a uniform temperature, is
suddenly exposed to large surroundings at 1000C (instead of a net radiant flux).
FIND: (a) The temperatures T(0, 120 s) and T(0.15 m, 120s) using
PROBLEM 5.140
KNOWN: Flue of square cross-section, initially at a uniform temperature is suddenly exposed to hot
flue gases. See Problem 4.92.
FIND: Temperature distribution in the wall 5, 10, 50 and 100 hours after introduction of gases using
the implici
PROBLEM 5S.7
KNOWN: Diameter and initial temperature of hailstone falling through warm air.
FIND: (a) Time, tm, required for outer surface to reach melting point, T(ro,tm) = Tm = 0C,
(b) Centerpoint temperature at that time, (c) Energy transferred to the
PROBLEM 5S.9
KNOWN: Steel (plain carbon) billet of square cross-section initially at a uniform
temperature of 30C is placed in a soaking oven and subjected to a convection heating process
with prescribed temperature and convection coefficient.
FIND: Time