ARTICLE:

• ON THE INTEGRAL TRANSFORM SOLUTION OF THE HEAT DIFFUSION EQUATION IN A SLAB WITH RADIANT FLUX AT THE OUTER SURFACE  download article

C. M. Hackenberg
PEQ/COPPE/UFRJ, Chem. Eng. Dept., C.P. 68502,21945-970-Rio de Janeiro-RJ, Brazil

A. G. Oliveira Filho
Military Institute of Engineering (IME), Chem. Eng. Dept, Praça Gen. Tibúrcio 80,22290-270-Rio de Janeiro-RJ, Brazil

ABSTRACT

Although many applications are found in the literature that utilize classical lumped analysis solutions to describe the transient behavior of the surface temperature of a slab exposed to convective and radiant heat transfer at the outer surface one, should realize that those solutions will not provide accurate results when a considerable amount of radiation is present due to the heat diffusion inside the solid. When diffusive transient behavior plays an important role, lumped parameter analysis and its simplifications must be replaced by a temperature field representation that ensures time and space dependence and also controls the surface temperature profile. In this paper, the heat diffusion equation in a solid slab is analytically solved with the convective-radiant flux at the outer boundary by an Integral Transform Technique and also by a functional method that uses the Basset-Duhamel Theorem. The linearized boundary condition is analyzed and it is shown that the solutions converge to the existing lumped parameter solutions for highly conductive materials. The nonlinear boundary condition is also treated, indicating that it is possible to determine the slab surface temperature by hybrid numerical-analytical methods.

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