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The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium.

The methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm.

The effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain.

The present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization.

It is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media.

The novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.

Small businesses growth has become an important area of study in the field of entrepreneurship. This paper aims to extend the inquiry by investigating whether there is a significant difference in growth between firms from the formal sector and the informal sector in the least developing countries (LDCs), particularly Tanzania.

A survey strategy as well as non-probability sampling are used. The sampling included 50 formal and 61 informal small businesses from the furniture industry. Data collected were evaluated using chi square and compounded annual growth rate (CAGR) techniques.

The results indicate that firms from the formal sector do not grow faster than firms from the informal sector. on the contrary, our tests reveal that firms from the informal sector predominantly grow faster than firms from the formal sector.

The study was conducted in Tanzania which is just one of the 48 LDCs in the world. Second, the literature that is used predominantly applies to developed countries. Third, the field work dependent on the respondent’s perception. Finally, change of measurement scale from five to three is ought to have contributed to mixed findings.

The overall implications are that external factors like inadequate regulatory tax systems may affect growth of formal small businesses and thus influence market opportunities for informal small businesses. Further, internal factors like inefficiencies of workers from formal enterprises may affect growth and therefore create more opportunities for informal enterprises.

Exploring differences between firms from the formal sector and the informal sector, and the way five scales were aggregated into three scales in the methodology.