CHEMENG 3A04 Lecture 4: ChE 3A04 L4 2D Conduction
24 Jan 2016
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Document Summary
For many heat transfer problems engineers must solve, the effect of the object"s ends, corners, etc. can be neglected without significant error (semi-infinite assumption). a 2d or 3d problem becomes 1d. However, other problems cannot be simplified to a 1-d system without incorporating large amounts of error or missing some critical phenomena. For 2d conduction at steady state, no internal heat generation and assuming constant properties (constant k): The laplace equation can be solved analytically by the method of separation of variables. Basic trick: assume that the solution can be expressed as the product of a function of x and a function of y, Since t = x * y, differentiate: yyxxt = dt dx dt dy. Since x and y are independent, the the equation can only hold for all x, y values if l. h. s. =r. h. s. =constant= - 2. Consequently, the solution of the original pde (laplace) reduces to the solution of the two following odes:
