A finite element mesh consisting of a linear triangular element (element 1), a linear quadrilateral element (element 2) and 5 nodes is shown in the figure below. Unit of the nodal coordinate is meter. Temperature boundary condition T = 20°C is applied to the left and bottom edges. Heat flux boundary condition q̅ = 10y W/m is applied to the right edge. Heat flux boundary condition q̅ = 5 W/m is applied to the top edge. Isotropic thermal conductivity of material in the triangular element 1 is k₁ = 5 W /°C. Isotropic thermal conductivity of material in the quadrilateral element 2 is k₂ 10 W/°C. Heat source through the whole domain is uniform and constant s = 2 W/m². Please calculate the conductance matrix

  

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K = = √e B²T Dª Bºdſ and flux matrix fe = f₁ + f₁ = − Sre NºTādr + Se NºT sd. of element 1. ne q=5 Ď T = 20 T = 20 Node 3 (0, 3) Node 1 (0, 0)¹ Node 5 - (3, 4) a = 10y Node 4 - (3, 2) q = 10y Node 2- (3, 1) K = = √e B²T Dª Bºdſ and flux matrix fe = f₁ + f₁ = − Sre NºTādr + Se NºT sd. of element 1. ne q=5 Ď T = 20 T = 20 Node 3 (0, 3) Node 1 (0, 0)¹ Node 5 - (3, 4) a = 10y Node 4 - (3, 2) q = 10y Node 2- (3, 1)

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