# Boundary Value Problem , triangular plate

by jc2009
Tags: boundary, plate, triangular
 P: 14 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