Abstract
In this work a new developed dimensionless finite difference technique for 2-D transient heat conduction is developed and presented. The technique is then applied to predict the time development of temperature profiles in a convectively cooled rectangular fin. In addition, a corrected analytical form that reduces the 2-D problem to a 1-D one is developed. Results prove that the numerical technique is simple and fast, while the 1-D reduced analytical solution is valid only for early time, small Biot number, and thin fins.
Highlights
The obtalned scot o f algebraic equa tions aY e solved U~ ln9 the simple explicit sch e me
Applying the bc.undal"y c>:.n{jit'iofl of Eq.6b, on e finds that the 50illtic·n ilO st ~, ble if the foll ow ing cc·ndition is 6.:1tisfied
Fio Fo urier n umberUsing t he proper t y 'cd orthe'gconality [1) , the! e c'ef licients (9 ) a n m.a y he ,:", l .:u l ."l\;ed by the e xpr e!Osi e.n :
Summary
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