Heat Transfer in a Composite Medium

Now we can transform the model relations into dimensionless forms. For this purpose, we use the dimensionless temperature as a measure of a local excess with respect to the adjacent medium Tp = (t —tj)/ the dimensionless time 

Region 2 overlay a second region in left half  

The above-mentioned trend occurs in spite of the different conditions that characterize the calculation of each curve. As is known, the dimensionless time that characterizes cooling depends on the width of each brick. However, this dimensionless value has not changed in the simulations used for dratving Figs. 3.50 and 3.51. Consequently, these figures are characterized by the same dimensionless time axis division. In addition, the heat transfer surface used for the simulation also has the same value. Indeed, both figures are reported to use the same base of comparison. 

In the third simulation example, we carried out an analysis of some of the aspects that characterize the case of the mass transfer of species through a membrane which is composed of two layers (the separative and the support layers) with the same thickness but with different diffusion coefficients of each entity or species. To answer this new problem the early model has been modified as follows (i) the term corresponding to the source has been eliminated (u) different conditions for bottom and top surfaces have been used for example, at the bottom surface, the dimensionless concentration of species is considered to present a unitary value while it is zero at the top surface (iii) a new initial condition is used in accordance with this case of mass transport through a two-layer membrane (iv) the values of the four thermal diffusion coefficients from the original model are replaced by the mass diffusion coefficients of each entity for both membrane layers (v) the model is extended in order to respond correctly to the high value of the geometric parameter 1/L. 

It is clear that, for this problem, the normal trend is to use the monodimensional and unsteady state model, which is represented by the assembly of relations (3.152)-(3.156). It accepts a very simple numerical solution or an analytical solution made of one of the methods classically recommended such as the variable separation method  

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