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Foundations of Heat Transfer
Lumped Integral and Differential Formulations
Steady OneDimensional Problems Bessel Functions
8 other sections not shown
ambient temperature Tx approximate solution assumed axial conduction Bessel functions boundary conditions cartesian cartesian geometry characteristic functions characteristic values consider constant control volume convection convenient coordinate corresponding cosh cylindrical differential equation differential formulation evaluated extended surfaces Find the steady finite fluid foregoing form of Eq Fourier Fourier's law geometry given by Eq gives heat flux q heat transfer coefficient heater homogeneous initial temperature Inserting Eq insulated integral formulation internal energy interval Introducing Eq inversion theorem Kantorovich profile Laplace transforms law of thermodynamics lumped method nodal points nonhomogeneous Note obtained one-dimensional orthogonal parameter plate polynomials procedure product solution radius readily respectively result Ritz profile separation of variables shown in Fig sinh solid solution of Eq spherical geometry steady periodic steady temperature temperature distribution thermal conductivity thickness tion tube two-dimensional unsteady problems variational variational calculus velocity wish to find x-direction yields zero