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Unformatted text preview: Chapter 2 Heat Conduction Equation ( a ) Heat transfer is transient, ( b ) it is onedimensional, ( c ) there is no heat generation, and ( d ) the thermal conductivity is constant. 227 For a medium in which the heat conduction equation is given in its simplest by r d T dr dT dr 2 2 + = : ( a ) Heat transfer is steady, ( b ) it is onedimensional, ( c ) there is heat generation, and ( d ) the thermal conductivity is constant. 228 We consider a small rectangular element of length Δ x , width Δ y , and height Δ z = 1 (similar to the one in Fig. 221). The density of the body is ρ and the specific heat is C. Noting that heat conduction is two dimensional and assuming no heat generation, an energy balance on this element during a small time interval Δ t can be expressed as ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ Δ + Δ − ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ element the of content energy the of change of Rate and + at surfaces at the conduction...
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Conductivity, Mass, Heat

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