##### Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields I

Physical Science International Journal, Page 1-20
DOI: 10.9734/psij/2021/v25i1030284

Two classes of three-dimensional metric spaces are identified. They are the conventional three-dimensional metric space and a new ‘three-dimensional’ absolute intrinsic metric space. Whereas an initial flat conventional proper metric space IE′3 can transform into a curved three-dimensionalRiemannian metric space IM′3 without any of its dimension spanning the time dimension (or in the absence of the time dimension), in conventional Riemann geometry, an initial flat ‘three-dimensional’ absolute intrinsic metric space ∅IˆE3 (as a flat hyper-surface) along the horizontal, evolves into a curved ‘three-dimensional’ absolute intrinsic metric space ∅IˆM3, which is curved (as a curved hyper-surface) toward the absolute intrinsic metric time ‘dimension’ along the vertical, and it is identified as ‘three-dimensional’ absolute intrinsic Riemannian metric space. It invariantly projects a flat ‘three-dimensional’ absolute proper intrinsic metric space ∅IE′3ab along the horizontal, which is made manifested outwardly in flat ‘three-dimensional’ absolute proper metric space IE′3ab, overlying it, both as flat hyper-surfaces along the horizontal. The flat conventional three-dimensional relative proper metric space IE′3 and its underlying flat three-dimensional relative proper intrinsic metric space ∅IE′3 remain unchanged. The observers are located in IE′3. The projective ∅IE′3ab is imperceptibly embedded in ∅IE′3 and IE′3ab in IE′3. The corresponding absolute intrinsic metric time ‘dimension’ is not curved from its vertical position simultaneously with ‘three-dimensional’ absolute intrinsic metric space. The development of absolute intrinsic Riemannian geometry is commenced and the conclusion that the resulting geometry is more all-encompassing then the conventional Riemannian geometry on curved conventional metric space IM′3 only is reached.

##### Habitat Cooling by a Canadian Well in Ouagadougou (Burkina Faso): Numerical Approach

Boureima Kaboré, Germain Wende Pouiré Ouedraogo, Moctar Ousmane, Vincent Zoma, Belkacem Zeghmati, Xavier Chesneau, Sié Kam, Dieudonné Joseph Bathiébo

Physical Science International Journal, Page 21-28
DOI: 10.9734/psij/2021/v25i1030285

In the Sahelian zone, air cooling in house by air-soil heat exchanger is an alternative in the context of insufficient of electrical energy. This work is about cooling of a habitat in Ouagadougou by numerical approach. Numerical results provided a better understanding of the influence of parameters such as tube length, air velocity and soil temperature on the thermal efficiency of this system. We analyze the effects of parameters such as renewal air flow rate, soil temperature and number of tubes. The results show that during the hot periods of the day, the Canadian well cool air in habitat.

##### Thermal Performance Assessment of a Box-type Solar Cooker with an Inclined Collecting Surface and Kapok Wool Insulation

Jacques Nébié, Sidiki Zongo, Augustin S. Zongo, Guy C. Tubreoumya, Zacharie S. Kam, Serge W. Igo, Tizane Daho, Ilyassé Konkobo, Antoine Béré, Belkacem Zeghmati

Physical Science International Journal, Page 29-38
DOI: 10.9734/psij/2021/v25i1030286

The present work reports the thermal performance of a box-type solar cooker insulated with kapok wool, a local plant with a low thermal conductivity. The experimental results obtained indicate that the absorber plate reached a maximum temperature of 155.2 °C. Moreover, the maximum power of the cooker was 87.5 W with an efficiency of 35.45 %. The first and second figure of merit parameters performed are 0.15 and 0.298 respectively. The cooking test carried out on eggs and rice was conclusive. And it appears that this solar cooker can cook an average of 464 meals per year thanks to the solar energy available in Burkina Faso corresponding to a reduction of 67.62 % in household fuel wood consumption.

##### Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields II

Physical Science International Journal, Page 39-77
DOI: 10.9734/psij/2021/v25i1030287

The geometry of curved ‘three-dimensional’ absolute intrinsic metric space (an absolute intrinsic Riemannian metric space) $$\varnothing\hat{\mathbb{M}}^3$$, which is curved (as a curved hyper-surface) toward the absolute time/absolute intrinsic time ‘dimensions’ (along the vertical), and projects a flat three-dimensional absolute proper intrinsic metric space $$\varnothing\hat{\mathbb{E}}^\prime$$ab3 and its outward manifestation namely, the flat absolute proper 3-space $$\hat{\mathbb{E}}^\prime$$ab3, both as flat hyper-surfaces along the horizontal, isolated in the first part of this paper, is subjected to graphical analysis. Two absolute intrinsic metric tensor equations, one of which is of the form of Einstein free space field equations and the other which is a tensorial statement of absolute intrinsic local Euclidean invariance (A$$\varnothing$$LEI) on $$\varnothing\hat{\mathbb{M}}^3$$, are derived. Simultaneous (algebraic) solution to the equations yields the absolute intrinsic metric tensor and the absolute intrinsic Ricci tensor of absolute intrinsic Riemann geometry on the curved $$\varnothing\hat{\mathbb{M}}^3$$, in terms of a derived absolute intrinsic curvature parameter. A superposition procedure that yields the resultant absolute intrinsic metric tensor and the resultant absolute intrinsic Ricci tensor, when two or a larger number of absolute intrinsic Riemannian metric spaces co-exist (or are superposed) is developed.

The fact that a curved ‘three-dimensional’ absolute intrinsic metric space $$\varnothing\hat{\mathbb{M}}^3$$ is perfectly isotropic and is consequently contracted to a ‘one-dimensional’ isotropic absolute intrinsic metric space, denoted by $$\varnothing\hatρ^3$$, which is curved toward the absolute time/absolute intrinsic time ’dimensions’ ($$\hat{c}$$$$\hat{t}$$/$$\varnothing$$$$\hat{c}$$$$\varnothing$$$$\hat{t}$$) along the vertical is derived.

##### Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields III

A curved two-dimensional' absolute intrinsic metric spacetime ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$) on the vertical intrinsic spacetime hyperplane; its invariantly projected flat ‘two-dimensional' absolute proper intrinsic metric spacetime ($$\varnothing$$$${\rho}^\prime$$ab,$$\varnothing$$$${c}$$sab$$\varnothing$$$${t}^\prime$$ab)  and a flat two-dimensional' absolute proper metric spacetime ($${\rho}^\prime$$ab,$${c}$$sab$${t}^\prime$$ab) as the outward manifestation of the latter, evolve from a flat four-dimensional' absolute metric spacetime ($$\hat{\mathbb{E}}^3$$,$$\hat{c}_s$$$$\hat{t}$$) and its underlying flat two-dimensional' absolute intrinsic metric spacetime ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$), in all finite neighborhood of the source of a long-range metric force field. The flat four-dimensional relative proper metric spacetime ($$\varnothing{\mathbb{E}}^\prime$$3, $${c}_s$$$$t^\prime)$$ and its underlying flat two-dimensional relative proper intrinsic metric spacetime ($$\varnothing$$$${\rho}^\prime$$,$$\varnothing$$c$$_s$$$$\varnothing$$$${t}^\prime$$), remain unchanged within the field. The geometry is valid with respect to 3-observers located in the relative proper Euclidean 3-space $${\mathbb{E}}^\prime$$3.
A pair of absolute intrinsic metric tensor equations derived on the curved ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$) are solved algebraically to obtain the absolute intrinsic metric tensor and absolute intrinsic Ricci tensor on the curved ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$) in terms of an isolated absolute intrinsic geometrical parameter, referred to as absolute intrinsic static flow' speed, which the source of a long-range absolute intrinsic metric force field causes to be established on the extended curved ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$) from its location. This third part of this paper is the conclusion of the development of absolute intrinsic Riemann geometry on the curved two-dimensional' ($$\varnothing$$$$\hat{\rho}$$,$$\varnothing$$$$\hat{c}_s$$$$\varnothing$$$$\hat{t}$$) at the first stage of evolutions of spacetime and intrinsic spacetime in long-range metric force fields, started in the first and second parts. The first stage shows up as a numerical evolution. Extension to the second stage shall be done in the fourth and final part of this paper. Particularization to the gravitational field shall then follow in another article.