Research Article
Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows
Doglas Ambani Onchere*
,
Mathew Ngugi Kinyanjui,
Phineas Roy Kiogora
Issue:
Volume 15, Issue 1, February 2026
Pages:
1-12
Received:
17 October 2025
Accepted:
27 October 2025
Published:
8 January 2026
DOI:
10.11648/j.acm.20261501.11
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Abstract: This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.
Abstract: This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the...
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Research Article
Investigating the Effects of Joule Heating on Chemically Reactive Williamson Fluid over an Inclined Rotating Surface
Tabitha Kerubo Ong’au*,
Johanna Kibet Sigey,
Viona Nakhulo Ojiambo,
Moffat Chamuchi
Issue:
Volume 15, Issue 1, February 2026
Pages:
13-25
Received:
30 September 2025
Accepted:
7 November 2025
Published:
15 January 2026
DOI:
10.11648/j.acm.20261501.12
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Abstract: This study focuses on the analysis of the flow behaviour of a chemically reacting Williamson fluid over an inclined rotating surface, taking into account the combined effects of Coriolis force and Joule heating. A mathematical model is developed to describe the fluid dynamics by integrating the equations of momentum, energy, and species concentration under the influence of these physical phenomena. The governing partial differential equations have been non-dimensionalised and transformed into a system of ordinary differential equations by introducing similarity transform. The resulting ODEs are written as a truncated series whose coefficients are obtained by using the collocation numerical technique on the resulting equations. The flow variables are determined and presented in profile and tabular form. The results were validated by comparing with MATLAB bvp4c and the error ranges between 0.09% and 0.61%, indicating that the method of solution is admissible. It is established that the Coriolis force enhances fluid velocity while simultaneously reducing both temperature and concentration. In contrast, Joule heating increases temperature but decreases fluid velocity and concentration. Additionally, chemical reactions lead to a reduction in velocity and concentration due to the consumption of reactive species, while simultaneously increasing temperature due to exothermic effects.
Abstract: This study focuses on the analysis of the flow behaviour of a chemically reacting Williamson fluid over an inclined rotating surface, taking into account the combined effects of Coriolis force and Joule heating. A mathematical model is developed to describe the fluid dynamics by integrating the equations of momentum, energy, and species concentrati...
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Research Article
Modeling and Analysis of Flow Problems in Aquifer Systems Involving Nonlinear Source-terms: Application of Schauder’s Fixed Point Theorem
Daniel. Bandji,
Obaker Clément. Nzonda Noussi,
Durel Wilfried. Wopiwo,
Abdou. Njifenjou*
Issue:
Volume 15, Issue 1, February 2026
Pages:
26-34
Received:
15 November 2025
Accepted:
6 December 2025
Published:
15 January 2026
DOI:
10.11648/j.acm.20261501.13
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Abstract: This work deals with two mathematical aspects of subsurface flow problems within aquifer systems, namely Mathematical Modeling and Theoretical Analysis. Concerning the Mathematical Modeling, the classical challenges for this class of problems are a rigorous description of diverse interactions that may take place between different involved aquifers. Recall that the main challenge at this stage is a realistic description of the flows from one aquifer to another passing necessarily through an aquitard which is a porous layer with small permeability coefficient and small thickness (compared with the mean thickness of involved aquifers. In the same way as most of flow phenomena, the governing equations of subsurface flows are based upon conservation laws.) To address the mathematical modeling of water exchange between different aquifers separated by aquitards we expose a mathematical approach based upon the Taylor expansion. Introducing the concept of observers located inside the aquitard and the neighboring aquifers, the mass conservation law has been applied and has led to one mass balance equation for each aquifer. Thanks to this original approach we have recovered the well-known mass balance equations exposed in the literature for flow problems in aquifer systems. Due to the assumptions of small thickness and homogeneity of the absolute permeability of aquitards for our framework the water flow is supposed vertical in aquitards and so we deal with one-dimensional flows there. This is the reason why the Taylor expansion deployed there concerns only the vertical space variable. The flux continuity has been applied to get the coupling of flow equations in the two aquifers. Since the flows in aquifers are supposed horizontal it is clear that the interface aquitard/aquifer flux acts as an additional source-term for each aquifer (and not a boundary term). Concerning the Theoretical Analysis of the global system of elliptic equations (as the flow is supposed to be submitted to a steady state) the Schauder Fixed Point Theorem has been applied for facing the nonlinearity of the right-hand sides of the system. This is the way we have got the existence of a solution to the system, but not the uniqueness. Thanks to a monotonicy assumption on the right-hand side vector-function we get the uniqueness of the solution. Finally the stability of that solution has been established under appropriate conditions.
Abstract: This work deals with two mathematical aspects of subsurface flow problems within aquifer systems, namely Mathematical Modeling and Theoretical Analysis. Concerning the Mathematical Modeling, the classical challenges for this class of problems are a rigorous description of diverse interactions that may take place between different involved aquifers....
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