The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the

The effects of T-shaped fins on the improvement of phase change materials (PCM) melting are numerically investigated in vertical triple-tube storage containment. The PCM is held in the middle pipe of a triple-pipe heat exchanger while the heat transfer fluid flows through the internal and external pipes. The dimension effects of the T-shaped fins on the melting process of the PCM are investigated to determine the optimum case. Results indicate that while using T-shaped fins improves the melting performance of the PCM, the improvement potential is mainly governed by the fin’s body rather than the head. Hence, the proposed T-shaped fin did not noticeably improve melting at the bottom of the PCM domain; additionally, a flat fin is ad

In this paper we introduce the basic of definitions of groups for geometric figures; we describe some of geometric figures by using the properties of groups. The classification of some geometric figures by using the properties of some algebraic structures.

In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2)   are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory. 

the regional and spatial dimension of development planning must be taken as a point of departure to the mutual of the spatial structure of the economy , development strategy and policies applied 'therein such as the location principles and regional development coordination of the territorial problems with the national development planning and timing of regional vis-a-vis national development plan_. Certain balance and integration is of sound necessity' between national _regional and local development objectives through which the national development strategy should have to represent the guidelines of the local development aspirations and goals. The economic development exerts an impact on the spatial evolution, being itself subje

In the present paper, we have introduced some new definitions On D- compact topological group and D-L. compact topological group for the compactification in topological spaces and groups, we obtain some results related to D- compact topological group and D-L. compact topological group.

The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.