## Boundary Value Problem , triangular plate

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 dont know if this helps at all.

$$u_{x}(x,0,t) = 50$$ ; 0<x<10
$$u(0,y,t) = 0$$ ; 0<y<5
now for the slanted side i dont know if this is right
$$u(x,y,t) = 2y + x - 10 = 0$$

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?
 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks