A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two types of exchange function are defined: the direct exchange function and the total exchange function. Certain integral equations relating total exchange functions to direct exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exchange factors.
The unsteady surface element method is a powerful numerical technique for solution of linear transient two- and three-dimensional heat transfer problems. Its development originated with the need of solving certain transient problems for which similar or dissimilar bodies are attached one to the other over a part of their surface boundaries. In this paper a multinode unsteady surface element (MUSE) method for two arbitrary geometries contacting over part of their surface boundaries is developed and formulated. The method starts with Duhamel’s integral (for arbitrary time and space variable boundary conditions) which is then approximated numerically in a piecewise manner over time and the boundaries of interest. To demonstrate the capability of the method, it is applied to the problem of two semi-infinite bodies initially at two different temperatures suddenly brought into perfect contact over a small circular region. The results show excellent agreement between the MUSE solution and the other existing solutions.
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