PROBLEM 2.12
KNOWN: Plane wall with prescribed thermal conductivity, thickness, and surface temperatures.
FIND: Heat flux, q , and temperature gradient, dT/dx, for the three different coordinate systems
x
shown.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional
PROBLEM 2.9
KNOWN: Irradiation and absorptivity of aluminum, glass and aerogel.
FIND: Ability of the protective barrier to withstand the irradiation in terms of the temperature
gradients that develop in response to the irradiation.
SCHEMATIC:
G = 10 x 106
PROBLEM 2.7
KNOWN: End-face temperatures and temperature dependence of k for a truncated cone.
FIND: Variation with axial distance along the cone of q x , q , k, and dT / dx.
x
SCHEMATIC:
r
ASSUMPTIONS: (1) One-dimensional conduction in x (negligible temp
PROBLEM 2.6
KNOWN: Rod consisting of two materials with same lengths. Ratio of thermal conductivities.
FIND: Sketch temperature and heat flux distributions.
SCHEMATIC:
T1
T2
T1 < T2
A
x
0.5 L
B
L
ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimension
PROBLEM 2.5
KNOWN: Symmetric shape with prescribed variation in cross-sectional area, temperature
distribution and heat rate.
FIND: Expression for the thermal conductivity, k.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduc
PROBLEM 2.4
KNOWN: A spherical shell with prescribed geometry and surface temperatures.
FIND: Sketch temperature distribution and explain shape of the curve.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction in radial (sp
PROBLEM 2.3
KNOWN: Hot water pipe covered with thick layer of insulation.
FIND: Sketch temperature distribution and give brief explanation to justify shape.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional (radial) conduction, (3)
PROBLEM 2.2
KNOWN: Axisymmetric object with varying cross-sectional area and different temperatures at
its two ends, insulated on its sides.
FIND: Shapes of heat flux distribution and temperature distribution.
SCHEMATIC:
T1
T2
T1 > T2
dx
x
L
ASSUMPTIONS:
PROBLEM 2.1
KNOWN: Steady-state, one-dimensional heat conduction through an axisymmetric shape.
FIND: Sketch temperature distribution and explain shape of curve.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, one-dimensional conduction, (2) Constant properties
PROBLEM 1.62
KNOWN: Elapsed times corresponding to a temperature change from 15 to 14C for a reference
sphere and test sphere of unknown composition suddenly immersed in a stirred water-ice mixture.
Mass and specific heat of reference sphere.
FIND: Specif
PROBLEM 1.7
KNOWN: Inner and outer surface temperatures of a glass window of prescribed dimensions.
FIND: Heat loss through window.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
conditions, (3) Constant proper
PROBLEM 1.20
KNOWN: Inner and outer surface temperatures of a wall. Inner and outer air temperatures and
convection heat transfer coefficients.
FIND: Heat flux from inner air to wall. Heat flux from wall to outer air. Heat flux from wall to
inner air. Whe
PROBLEM 1.11
KNOWN: Heat flux at one face and air temperature and convection coefficient at other face of plane
wall. Temperature of surface exposed to convection.
FIND: If steady-state conditions exist. If not, whether the temperature is increasing or de
PROBLEM 1.9
KNOWN: Width, height, thickness and thermal conductivity of a single pane window and
the air space of a double pane window. Representative winter surface temperatures of single
pane and air space.
FIND: Heat loss through single and double pane
PROBLEM 1.8
KNOWN: Net power output, average compressor and turbine temperatures, shaft dimensions and
thermal conductivity.
FIND: (a) Comparison of the conduction rate through the shaft to the predicted net power output of
the device, (b) Plot of the rat
PROBLEM 1.6
KNOWN: Heat flux and surface temperatures associated with a wood slab of prescribed
thickness.
FIND: Thermal conductivity, k, of the wood.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
conditions,
PROBLEM 1.4
KNOWN: Dimensions, thermal conductivity and surface temperatures of a concrete slab. Efficiency
of gas furnace and cost of natural gas.
FIND: Daily cost of heat loss.
SCHEMATIC:
ASSUMPTIONS: (1) Steady state, (2) One-dimensional conduction, (3
PROBLEM 1.3
KNOWN: Inner surface temperature and thermal conductivity of a concrete wall.
FIND: Heat loss by conduction through the wall as a function of outer surface temperatures ranging from
-15 to 38C.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional condu
PROBLEM 1.2
KNOWN: Thickness and thermal conductivity of a wall. Heat flux applied to one face and
temperatures of both surfaces.
FIND: Whether steady-state conditions exist.
SCHEMATIC:
L = 10 mm
T2 = 30C
q = 20 W/m2
T1 = 50C
qcond
k = 12 W/mK
ASSUMPTIONS
PROBLEM 1.1
KNOWN: Thermal conductivity, thickness and temperature difference across a sheet of rigid
extruded insulation.
FIND: (a) The heat flux through a 2 m 2 m sheet of the insulation, and (b) The heat rate
through the sheet.
SCHEMATIC:
A = 4 m2
k =
ME 4210-HEAT TRANSFER LABORATORY #1
Free and Forced Convection Experiments
I. Objectives
To review the following convection heat transfer concepts, practice related measurements and
data analyses, and compare measured results against predictions:
1. Funda
ME 4150, Fall 2013
HW #2 (due on 09/25/13)
Use material properties from Table A-5 to solve following problems.
1. Sketch a free-body diagram of each element in the figure. Compute the magnitude and
direction of each force using an algebraic or vector meth