... of thermal boundary and initial conditions [ 1–4 ]. heat equation semi-analytical numerical methods Fourier series Green’s functions Duhamel’s integrals Classical Green’s and Duhamel’s integral formulas are enforced for the solution of one dimensional heat conduction in a slab, under...

... technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated. 11 03 2010 17 09 2010 13 01 2011 13 01 2011 Fourier analysis...

... heat flux. Those functions, which contain more high-frequency components of Fourier series, are more sensitive to the increase in the Reynolds number. This work was supported by the National Natural Science Foundation of China (Grant No. 50636050) and the Fundamental Project of R&D in China...

...A. G. Ostrogorsky Based on the one-term Fourier series solution, a simple equation is derived for low Biot number transient conduction in plates, cylinders, and spheres. In the 0 < Bi < 0.3 range, the solution gives approximately three times less error than the lumped capacity solution...

...-dependent term in the boundary condition, Duhamel’s theorem is used to solve the problem for a periodic boundary condition. The boundary condition is decomposed by Fourier series. In order to check the validity of the results, the technique was also applied to a solid sphere under harmonic boundary...

...Kamel Hooman; Ali A. Merrikh A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series...

...A. Haji-Sheikh This is a theoretical and numerical study of fully developed forced convection in various rectangular ducts. Each duct is filled with porous materials and the Brinkman model describes the laminar fluid flow inside this fully saturated porous passage. A Fourier series solution...

... on the motion of the flux. The working function of the intermittent heat source with respect to time is evaluated by using the Fourier series and temperature profile of each point heat source is derived by using the Duhamel’s theorem. Finally, by superposition of the temperature fields over all the point heat...

... are such that axial symmetry does not occur and temperature does not change in the axial direction. The dimensionless local balance equations are solved analytically by means of the Fourier series expansion method. The analytical expressions of the dimensionless temperature field, of the dimensionless velocity field...