Browsing by Author "Mukalazi, Herbert"

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Couple-stress nanofluid flow comprised of titanium alloy subject to Hall current and Joule heating effects: Numerical investigation
(AIP Advances, 2024-11-01) Jubair, Sidra; Ali, Bilal; Rafique, Khadija; Ansari, Mushtaq Ahmad; Mahmood, Zafar; Kumar, Abhinav; Mukalazi, Herbert; Alqahtani, Haifa
Nanofluid flowoverarotating disk has several applications in engineering and industrial sectors, such as in cooling systems, heat exchangers, aerospace systems, and renewable energy systems. In the current analysis, the couple stress nanofluid flow over a rotating disk is reported. The nanofluid consists of ethylene glycol and titanium aluminum vanadium (Ti6Al4V) nanoparticles (NPs). The unique properties of Ti6Al4V-NPs, such as biocompatibility, high strength, high boiling point (1604–1660○C), and high corrosion resistance, make them more suitable for automobile industries. For the heat and mass transfer, the Cattaneo–Christov concept is introduced. In addition, the fluid flow is subjected to magnetic field, Hall current, thermal radiation, and Joule heating. The modeled equations are restructured into the dimensionless system of ordinary differential equations (ODEs) by using the similarity approach. The system of ODEs is further numerically solved through a MATLABpackagebased on the finite difference method (BVP4c). The results are presented in figures. It has been observed that the energy and curves of the nanofluid decline with the influence of thermal and solutal time relaxation parameters, respectively.
Exploring the wave’s structures to the nonlinear coupled system arising in surface geometry
(Scientific Reports, 2025-04-04) Farooq, Khizar; Hussain, Ejaz ; Younas, Usman ; Mukalazi, Herbert ; Khalaf, Tamer M. ; Mutlib, Abdul ; Shah, Syed Asif Ali
In the area of scientific inquiry, scientists are increasingly intrigued by the subtle dynamics of natural occurrences. Leveraging cutting-edge approaches and procedures, they attempt to decode these complexities with more accuracy and insight. An important tool in this effort is the use of partial differential equations (PDEs) to create models that correctly capture these events. The expanding capacity of 3D visualization plays a crucial role in boosting researchers’ knowledge and analysis of such occurrences. By applying PDEs, scientists are able to reveal the complicated patterns controlling physical processes and give greater insights into their behavior. A soliton is an isolated solitary wave that propagates over a material without wasting energy or altering its shape due to contact with other waves. Solitons are distinct from regular wave occurrences due to their strong localization and remarkable stability and endurance. Soliton plays a crucial role in several disciplines of study such as nonlinear optics1,2, mechanics3, plasma physics4, engineering5, hydrodynamics6, communication systems7, optical fiber8, biology9, fluid dynamics10,11. Nonlinear partial differential equations (NLPDEs) grow as exceptionally crucial assets in this scientific pursuit. NLPDEs provide sophisticated insights into a wide range of fields, including optics, acoustics, plasma dynamics, and condensed matter physics. They not only increase our comprehension of the researched events but also allow scientists to make precise estimates about their future proliferation. As a result, many academics have committed to analyzing diverse NLPDEs, seeking to expand their comprehension of the exhibited behavior in the examined natural occurrences. Recent assessments have involved inquiries into the Batman–Burger equation12,13, Schrodinger equation14–18, Date–Jimbo–Kashiwara–Miwa equation19–21, thin film ferroelectric material equation22–25, Benjamin–Bona–Mahony equation26–28, Boussinesq equation29 generalized Calogero-Bogoyavlenskii-schiff equation33,34, Buckmaster equation35, non-linear non classical Sobolev-type wave model36, and different other37–49. T he study of the single-wave solutions of NLPDEs is significant for giving better views and understanding of the underlying process and useful uses. Therefore, numerous researchers have created new ways to study these NLPDEs answers. Plenty of strong techniques such as,exp (−χ expansion method50, extend mapping method51, homotopy perturbation method52, Darboux transformation53, exp-function method54, generalized Kudryashov method55, extended trial equation method56, Hirota bilinear method57, extended jacobian method58, extended direct algebric method59, improved extended fan-sub equation method60, modified extended tanh method, Backlund transform method61, Novel (G′ G expansion method62, extended auxiliary equation mapping method63, extended simple equation method64 and many more methods65–71.
Stability analysis of a nonlinear malaria transmission epidemic model using an effective numerical scheme
(Scientific Reports, 2024-07-29) Jian, Jun He; Abeer, Aljohani; Shahbaz, Mustafa; Ali, Shokri; Khalsaraei, Mohammad Mehdizadeh; Mukalazi, Herbert
Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R (o) was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R0 ≤ 1. The endemic equilibrium is investigated for stability when R0 ≥ 1. All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.