Finite Element Analysis by Mike Fagan

By Mike Fagan

This article treats the basic ideas of the strategy in an easy, logical demeanour, putting the emphasis at the functional purposes of the tactic in these components the place it's most ordinarily used, and so permitting the scholar to strengthen a legitimate figuring out of the topic. utilizing easy, comprehensible arithmetic, sponsored up by means of functional modelling information and labored examples, the writer explains the idea after which introduces the reader to the extra complex functions and amenities provided via advertisement finite applications.

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Analysis The molar rate of transfer of species ,,4 can be calculated from the expression iZA = oW/o L NA~ fx=o dzdy (I) 32 CHAPTER 2. MOLECULAR AND CONVECTIVE TRANSPORT where the total molar flux of species jt at the interface, NAxI~=o, is given by , [~=0 = - DAB \ OX ] ~=0 NA~ [~=o- JAx (2) By the application of the chain rule, Eq. , Eq. 4-3) in Appendix A, as dcA dv = CAo e _773 r(4/3) (5) Substitution of Eqs. (~) and (5) into Eq. (3) yields NA~ Ix=0 -- F(4/3) 9 ~DABZ (6) Finally, the use of Eq.

0023 ( m o l / m 3 ) / c m . 5 Concentration of species ,4 as a function of position. 6. 6 Concentration of species ,4 as a function of position. CHAPTER 2. 6 that a straight line represents the data fairly well. The equation of this line can be determined by the method of least squares in the form y-mx+b (2) where y = log CA (3) To determine the values of m and b from Eqs. (A. 6-10) and (A. 6-11) in Appendix A, the required values are calculated as follows: Yi xi x 2. 76) - ( 1 5 0 ) ( - 6 . 0087 ( - 6 .

2 Energy generation rate per unit volume as a result of fission within a spherical reactor of radius R is given as a function of position as (;) ] where r is the radial distance measured from the center of the sphere. Cooling fluid at a temperature of Too flows over the reactor. If the average heat transfer coe]ficient (h} at the surface of the reactor is known, determine the surface temperature of the reactor at steady-state. Solution System: Reactor Analysis The inventory rate equation for energy becomes Rate of energy out = Rate of energy generation (1) The rate at which energy leaves the sphere by convection is given by Newton's law of cooling as Rate of energy out = (47rR2)(h)(T~ - Too) (2) where Tw is the surface temperature of the sphere.

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