H10: Suppose we wish to find the steady-state temperature u(x, y) in a rectangular plate whose vertical edges x= 0 and x

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H10 Suppose We Wish To Find The Steady State Temperature U X Y In A Rectangular Plate Whose Vertical Edges X 0 And X 1 (53.64 KiB) Viewed 28 times

H10: Suppose we wish to find the steady-state temperature u(x, y) in a rectangular plate whose vertical edges x= 0 and x= a are insulated, as shown in Figure below. When no heat escapes from the lateral faces of the plate, we solve the following boundary-value problem: au alu + = 0, 0<x<a, 0 < y<b (1) 012 Oy2 au ди = 0, axx=0 = 0, 0 < y<b (2) əxlx=a u(x, 0) = 0, u(x, b) = f(x), 0<x< a. (3) У. (a, b) Insulated Insulated H=0 Figure (1) Steady-state temperatures in a rectangular plate