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Unformatted text preview: IND: The finitedifference equation for nodal point on this boundary when (a) insulated;
compare result with Eq. 4.42, and when (b) subjected to a constant heat flux.
SCHEMATIC: ASSUMPTIONS: (1) Twodimensional, steadystate conduction with no generation, (2)
Constant properties, (3) Boundary is adiabatic.
ANALYSIS: (a) Performing an energy balance on the control volume, (∆x/2)⋅∆y, and using
the conduction rate equation, it follows that Note that there is no heat rate across the control volume surface at the insulated boundary.
Recognizing that ∆x =∆y, the above expression reduces to the form
The Eq. 4.42 of Table 4.2 considers the same configuration but with the boundary subjected
to a convection process. That is, Note that, if the boundary is insulated, h = 0 and Eq. 4.42 reduces to Eq. (4).
(b) If the surface is exposed to a constant heat flux, the energy balance has the form
and the finite difference equation becomes COMMENTS: Equation (4) can be obtained by using the “interior node” finitedifferenc...
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This note was uploaded on 01/24/2014 for the course CHE 306 taught by Professor Deng during the Fall '12 term at NMSU.
 Fall '12
 Deng
 Mass Transfer

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