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jc2009

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This exercise deal with the temperature u(x,y,t) in a homogeneous and thin plate. We assume that the top and bottom of the plate are insulated and the material has diffusivity k. Write the BVP .

Problem: The plate is triangular , picture this as a right triangle with this coordinates, (0,0) ,

(0,5) , ( 10,0) , with the hypotenuse(slanted) side being insulated the vertical side with 0 degrees and the horizontal side with 50 degrees.

THe initial temperature is 100 degrees throughout.

Solution: what i did first is to get the equation of the slanted side which is y = -(1/2)x + 5

or 2y + x - 10 = 0 i don't know if this helps at all.

[tex]u_{x}(x,0,t) = 50 [/tex] ; 0<x<10

[tex]u(0,y,t) = 0[/tex] ; 0<y<5

now for the slanted side i don't know if this is right

[tex]u(x,y,t) = 2y + x - 10 = 0 [/tex]

any help/hints would be appreciated.

NOTE: the use of u(x,t) and confuses me , sometimes i see that they use u_x for the vertical side or BVP problems and sometimes they use u_x for the horizontal . can you help me to clarify this notation issue?

Problem: The plate is triangular , picture this as a right triangle with this coordinates, (0,0) ,

(0,5) , ( 10,0) , with the hypotenuse(slanted) side being insulated the vertical side with 0 degrees and the horizontal side with 50 degrees.

THe initial temperature is 100 degrees throughout.

Solution: what i did first is to get the equation of the slanted side which is y = -(1/2)x + 5

or 2y + x - 10 = 0 i don't know if this helps at all.

[tex]u_{x}(x,0,t) = 50 [/tex] ; 0<x<10

[tex]u(0,y,t) = 0[/tex] ; 0<y<5

now for the slanted side i don't know if this is right

[tex]u(x,y,t) = 2y + x - 10 = 0 [/tex]

any help/hints would be appreciated.

NOTE: the use of u(x,t) and confuses me , sometimes i see that they use u_x for the vertical side or BVP problems and sometimes they use u_x for the horizontal . can you help me to clarify this notation issue?

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