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Practical engineering problems in heat transfer and fluid flow involve one or more governing equations, together with some boundary conditions over the domain. The restoration of boundary condition in two-dimensional steady heat conduction problems is described using BEM. Boundary Integral Equation is derived from a combination of Laplace Equation, Divergence Theorem, Green's Identities, Dirac Delta and Heaviside functions.In the formulation, the boundary conditions are represented by linear relation between the temperature and heat flux. The temperature inside the solution domain of diesel engine, together with the space of environment surrounding the heat conduction, is found from addition boundary temperature and fluxes. The BEM implementation is performed using FORTRAN 77 software. To validate the technique, solution to two non-linear problems are presented and space dependence results are in agreement with the computed analytical solutions.