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y =2 (0,0) u(x,0) = 0 means that in a two-dimensional heat flow, at any point along the x-axis, the temperature equals(4). u( y) = 0 means that any point along the (5) axis, the temperature equals (6) In a one-dimensional heal flow Kving homogeneous boundary conditions, the solution -'at the to the heat equation is u(x, t) = (7) at temp. cond. I 18)

y =2 (0,0) u(x,0) = 0 means that in a two-dimensional heat flow, at any point along the x-axis, the temperature equals(4). u( y) = 0 means that any point along the (5) axis, the temperature equals (6) In a one-dimensional heal flow Kving homogeneous boundary conditions, the solution -'at the to the heat equation is u(x, t) = (7) at temp. cond. I 18)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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y y =2 (0,0) u(x,0) = 0 means that in a two-dimensional heat flow, at any point along the x-axis, the temperature equals (4). ut : y) = 0 means that any point along the (5)_ axis, the temperature equals (6) In a one-dimensional heal flow kaving homogeneous boundary conditions, the solution -iattemp cond. 18) L'at the to the heat equation is u(x, t) : (7)
Transcribed Image Text:y y =2 (0,0) u(x,0) = 0 means that in a two-dimensional heat flow, at any point along the x-axis, the temperature equals (4). ut : y) = 0 means that any point along the (5)_ axis, the temperature equals (6) In a one-dimensional heal flow kaving homogeneous boundary conditions, the solution -iattemp cond. 18) L'at the to the heat equation is u(x, t) : (7)
In the Laplace (or potential) equation: uxx + uyy = 0, the solutior u(x, y), which represarts temperature at a point is usefui in solving partial differential equations relating to two-dirmensional heat flow. The potential does not depend on time as implied in the equation; thus no (1). _state temperature condition is required. The Laplace equation is a pure boundary-value problem. If the value of the solution is given around the boundary of the region, the BVP is a Dirichlet problem summarized as follows: (Uxx + uyy = 0; 0<x<1, 0sys2 u(x,0) = 0, u(x, 2) = x(1 – x), 0gx<1 u(0, y) = 0, u(1, y) = 0, 0Ky<2 The summary indicates that a = (2) and b = (3) as indicated in the figure below.
Transcribed Image Text:In the Laplace (or potential) equation: uxx + uyy = 0, the solutior u(x, y), which represarts temperature at a point is usefui in solving partial differential equations relating to two-dirmensional heat flow. The potential does not depend on time as implied in the equation; thus no (1). _state temperature condition is required. The Laplace equation is a pure boundary-value problem. If the value of the solution is given around the boundary of the region, the BVP is a Dirichlet problem summarized as follows: (Uxx + uyy = 0; 0<x<1, 0sys2 u(x,0) = 0, u(x, 2) = x(1 – x), 0gx<1 u(0, y) = 0, u(1, y) = 0, 0Ky<2 The summary indicates that a = (2) and b = (3) as indicated in the figure below.
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