COM_Q2_16-17

Question 2 The two-dimensional heat transfer in an isotropic medium may be expressed in terms of a potential formulation. The temperature T may be found by minimising the functional subject to the boundary conditions T-T"(x,y) on S where S1+ S2 S total boundary Q-internal heat generation Tspecified temperature on boundary q specified heat flux on boundary nx, nydirection cosines of outward normal to boundary kx, kycomponents of thermal conductivity Show that the element stiffness matrix and element load vector for an r-noded finite element may be written as FON,ddy+N,ds20 marks) Question 2 The two-dimensional heat transfer in an isotropic medium may be expressed in terms of a potential formulation. The temperature T may be found by minimising the functional subject to the boundary conditions T-T"(x,y) on S where S1+ S2 S total boundary Q-internal heat generation Tspecified temperature on boundary q specified heat flux on boundary nx, nydirection cosines of outward normal to boundary kx, kycomponents of thermal conductivity Show that the element stiffness matrix and element load vector for an r-noded finite element may be written as FON,ddy+N,ds20 marks)