PROBLEM 4.79
KNOWN
:
Bottom half of an Ibeam exposed to hot furnace gases.
FIND
:
(a) The heat transfer rate per unit length into the beam using a coarse nodal network (5
×
4)
considering the temperature distribution across the web is uniform and (b) Assess the reasonableness of
the uniform webflange interface temperature assumption.
SCHEMATIC
:
ASSUMPTIONS
:
(1) Steadystate, twodimensional conduction, and (2) Constant properties.
ANALYSIS
:
(a) The symmetrical section of the Ibeam is shown in the Schematic above indicating the
webflange interface temperature is uniform, T
w
= 100
°
C.
The nodal arrangement to represent this system
is shown below.
The nodes on the line of symmetry have been shown for convenience in deriving the
nodal finitedifference equations.
Using the
IHT FiniteDifference Equations Tool
, the set of nodal equations can be readily formulated.
The temperature distribution (
°
C) is tabulated in the same arrangement as the nodal network.
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 Spring '10
 LEE,J.S.
 Heat, Heat Transfer, Thermal conductivity, TW, webflange interface

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