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1. A 2-D, transient heat conduction problem in a rectangular body, illustrated by the figurebelow, is to be investigated using a numerical solution. There is no heat generation presentin this dimensionless constant property problem with = 1.0. The plate has a width W = 2.0and a height H = 1.0. It is insulated on all sides except over one-half of the top side whichhas a constant heat addition flux q₁ = 1.0. The initial condition is T(x,y,0) = 0.

a. Show the describing PDE and the boundary conditions for the problem analytically. b. The body is to be divided into a number of elements. Construct a figure for the problem showing a set of elements with a finite number of ºx's and ºy's (but °x need not equalºy) and label the nodes. Place nodes on the sides and corners. Specify the actual number of nodes and the resulting number of algebraic equations that you recommend for the numerical solution. c. Use appropriate finite-difference approximations (i.e., central, forward, or backward differences) for the spatial derivatives to derive finite-difference equations for: i.a typical interior node. ii. an edge node that includes heating. d. Employ a forward-difference approximation for the time derivative. Chose an explicitor implicit scheme for the solution; note any stability restriction(s).

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