Find the finite difference equation for nodal point

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Unformatted text preview: IND: The finite-difference 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) Two-dimensional, steady-state 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” finite-differenc...
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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.

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