# Which method is used to write the basic heat transfer equation in the following form using weighted residuals? $\int_v \left(\frac{\partial q_x}{\partial x}+\frac{\partial q_y}{\partial y}+\frac{\partial q_z}{\partial z}-Q+ \rho c \frac{\partial T}{\partial t}\right)$ N<sub>i</sub> dV = 0

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Which method is used to write the basic heat transfer equation in the following form using weighted residuals?

$\int_v \left(\frac{\partial q_x}{\partial x}+\frac{\partial q_y}{\partial y}+\frac{\partial q_z}{\partial z}-Q+ \rho c \frac{\partial T}{\partial t}\right)$ N<sub>i</sub> dV = 0

(a) Galerkin method

(b) Jacobi method

(c) Rayleigh Ritz method

(d) Delaunay method

The question was posed to me during an internship interview.

I would like to ask this question from Single Variable Problems topic in section Single Variable Problems of Finite Element Method

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Correct answer is (a) Galerkin method

For explanation I would say: Finite element equations are obtained using Galerkin method. Rayleigh Ritz method does not use interpolation functions, Ni whereas Galerkin method uses interpolation functions, Ni and thus, is used in FEM. Jacobi is used for Eigen value problems. Delaunay method is used to generate mesh for triangular elements.

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