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There is an increasing industrial demand to improve the thermal characteristics of fluids as they flow over stretching/shrinking and rotating surfaces. Heat transfer liquids, thermal exchangers, and coolants in electronics are examples of applicable applications. The thermal transport characteristics of hybrid nanofluids are improved by the inclusion of composite nanoparticles. Because the hybrid nanofluids can improve thermal conductivity compared to traditional fluids. However, several investigations are still needed to fully comprehend its features. Hence, this study investigates the fluid flow and thermal transport properties of thermally radiated hybrid alumina-silica/methanol nanofluid in a three-dimensional domain through a permeable porous shrinking surface. The hybrid nanofluid flow model of PDEs is transformed into ODEs by using similarity conversion, which is then numerically solved in MATLAB using the bvp4c solver. The characteristics of hybrid nanofluid velocity, thermal distribution, friction drag, and heat transport rate are graphically depicted for various physical flow parameters. The outcomes reveal that the range of first and second solutions can be augmented by increasing nanoparticle volume percentage. Furthermore, the results suggest that increasing the suction parameter can improve the effective heat transfer performance of the hybrid nanofluid whereas thermal radiation and heat source/sink parameters have no effect on delaying the boundary layer separation.

The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth order of convergence. The type of convergence is also discussed, which is global under an appropriate choice of the initial matrix. Numerical experiments are reported based on input matrices of different sizes as well as various stopping termination levels with comparisons to methods of the same nature and same number of matrix–matrix multiplications. The simulation results confirm the efficiency of the proposed scheme in contrast to its competitors of the same nature.

Objective: This study aimed to find if certain places are more contaminated by SARS COV-2 than the others in an Emergency Department (ED) of a tertiary care hospital. Methods: This was a prospective cross-sectional study carried out at the tertiary care hospital of Dubai. The study was carried out over a course of 4 weeks. Total 50 swab samples were taken. Twenty five were collected from the "dirty" areas and twenty five from the "clean" areas. Patients who had a positive SARS-COV-2 polymerase chain reaction (PCR) test in both areas were included in the study. Results: From a total of 50 swabs collected, large number of swabs was collected from resuscitation and major treatment area (38% and 30%, respectively). Of total, positive SARS-COV-2 PCR was detected on 38% of swabs. Of which 44% were from dirty areas and 32% were from clean areas. Considering areas of ED positive SARS COV-2 PCR, it was detected majorly from zone 4 (50%) followed by major (40%) and minor treatment areas (33.3%), respectively. Conclusion: The detection of the virus in 32% of the samples taken from clean areas emphasizes on the importance of using personal protective equipment and hand hygiene measures even when working in areas where patients have been triaged without the presence of symptoms suggestive of a COVID-19 infection. [SJEMed 2023; 4(1.000): 031-035]

This work proposes a new scheme under the umbrella of iteration methods to compute the sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is given and then a new scheme is derived based on a multi-step Newton-type nonlinear equation solver. It is shown that the new method and its reciprocal converge globally with wider convergence radii in contrast to their competitors of the same order from the general Padé schemes. After investigation on the theoretical parts, numerical experiments based on complex matrices of various sizes are furnished to reveal the superiority of the proposed solver in terms of elapsed CPU time.

An analysis is carried out to examine the effects of chemical reactions on the flow of two-phase non-miscible liquids streaming through rotating parallel plates. The plates are isothermal and insulated electrically. The Couette flow is considered for the electrically conducting two phase viscous-Casson fluids under the impacts of inclined magnetic flux and applied electric field. The problem is also discussed under the influence of different orders of chemical reactions. The modelled equations elaborating the present situation under the implemented suppositions are transformed to ordinary differential equations. The numerical solution for the obtained equations is obtained with suitable matching conditions at the interface region using the shooting technique. The results are also validated by comparing them with the results of a well-known finite difference based numerical scheme known as the Keller-Box method. The numerical results for sundry parameters involved in the flow problem are presented through graphs and discussed in detail.

Key Clinical Message: Benign ancient retroperitoneal schwannomas (BARS) exhibit abdominal masses and flank pain to incidental findings at more advanced stages. Histopathological and immunohistochemical analysis is essential for confirmation of benign nature. Our patient was misdiagnosed as ureteric colic, highlighting the need to consider BARS in differential diagnosis to prevent complications like hydronephrosis. Ancient schwannomas are usually benign neoplasms that originate from Schwann cells of peripheral nerves. We present a novel case of a 24‐year‐old young male with left flank pain and nausea which was initially thought to be left ureteric colic. However, in‐depth imaging and biopsy revealed a retroperitoneal mass. The definitive diagnosis was narrowed down to Benign Retroperitoneal Ancient Schwannoma (BARS) via immunohistochemistry and histopathological analysis. This often marble‐shaped S100 protein‐positive tumor is an under‐recognized and potential cause of hydronephrosis if localized near the renal structures. In addition, the retroperitoneal location with infrarenal abdominal aortic adherence is another rare peculiarity in the present case that demands prompt diagnosis and surgical excision to avoid any cardiovascular sequelae such as hypotension and abdominal pain, as indicated by the natural history of growth of this benign tumor. Therefore, timely excision of this benign tumor prior to its further proliferation is paramount. We initially planned laparoscopic removal but adopted excision via laparotomy because of the proximity of the vital structures. The postoperative course of the patient was uneventful and subsequently the patient's presenting complaint of left abdominal flank pain greatly improved. The patient was advised to undergo follow‐up computed tomography scan of kidney ureter bladder and RFT evaluation 6 months postsurgery which indicated no evidence of recurrence or iatrogenic complications. The diagnosis and management of the present case share valuable experiences for similar future cases worldwide. [ABSTRACT FROM AUTHOR]

This paper reports the filamentation of hollow Gaussian beams of the first, second, third, and fourth orders during propagation in a cubic and quintic nonlinear medium. Due to spatial modulation instability, the hollow Gaussian beams split to form either co-centric circular filaments or ultrashort pulses. It is found that the properties of the nonlinear medium used for propagation have a strong influence on certain characteristics of the formed filaments, such as peak intensity and pulse width. This correlation between the system parameters of the medium and filament characteristics represents a method for calculating the system parameters of the medium. This investigation can be helpful in the development of a hollow Gaussian beam-based artificial intelligence system that can be used to measure the system parameters of the studied nonlinear medium.

The computation of the sign function of a matrix plays a crucial role in various mathematical applications. It provides a matrix-valued mapping that determines the sign of each eigenvalue of a nonsingular matrix. In this article, we present a novel iterative algorithm designed to efficiently calculate the sign of an invertible matrix, emphasizing the enlargement of attraction basins. The proposed solver exhibits convergence of order four, making it highly efficient for a wide range of matrices. Furthermore, the method demonstrates global convergence properties. We validate the theoretical outcomes through numerical experiments, which confirm the effectiveness and efficiency of our proposed algorithm.

Background: The outbreak of coronavirus 2019 (COVID-19) which emerged in December 2019 spread rapidly and created a public health emergency. Geospatial records of case data are needed in real time to monitor and anticipate the spread of infection. Methods: This study aimed to identify the emerging hotspots of COVID-19 using a geographic information system (GIS)-based approach. Data of laboratory-confirmed COVID-19 patients from March 15 to June 12, 2020, who visited the emergency department of a tertiary specialized academic hospital in Dubai were evaluated using ArcGIS Pro 2.5. Spatiotemporal analysis, including optimized hotspot analysis, was performed at the community level. Results: The cases were spatially concentrated mostly over the inner city of Dubai. Moreover, the optimized hotspot analysis showed statistically significant hotspots (p < 0.01) in the north of Dubai. Waxing and waning hotspots were also observed in the southern and central regions of Dubai. Finally, there were nonsustaining hotspots in communities with a very low population density. Conclusion: This study identified hotspots of COVID-19 using geospatial analysis. It is simple and can be easily reproduced to identify disease outbreaks. In the future, more attention is needed in creating a wider geodatabase and identifying hotspots with more intense transmission intensity.

Abstract Proteins are a vital component of cells that perform physiological functions to ensure smooth operations of bodily functions. Identification of a protein's function involves a detailed understanding of the structure of proteins. Stress proteins are essential mediators of several responses to cellular stress and are categorized based on their structural characteristics. These proteins are found to be conserved across many eukaryotic and prokaryotic linkages and demonstrate varied crucial functional activities inside a cell. The in-vivo, ex vivo, and in-vitro identification of stress proteins are a time-consuming and costly task. This study is aimed at the identification of stress protein sequences with the aid of mathematical modelling and machine learning methods to supplement the aforementioned wet lab methods. The model developed using Random Forest showed remarkable results with 91.1% accuracy while models based on neural network and support vector machine showed 87.7% and 47.0% accuracy, respectively. Based on evaluation results it was concluded that random-forest based classifier surpassed all other predictors and is suitable for use in practical applications for the identification of stress proteins. Live web server is available at http://biopred.org/stressprotiens , while the webserver code available is at https://github.com/abdullah5naveed/SRP_WebServer.git

In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the generalized multiquadric radial basis function (RBF). The time-fractional derivative is estimated by an L1-scheme but the spatial variable is discretized using fourth-order RBF-FD methodology. As a matter of fact, the PDE problem is transformed in the form of a linear set of algebraic equations. To support analytical discussions, numerical tests are furnished and reveal the efficacy of the presented solver.

The current research article explores the bio-convection magnetized Carreau-nanofluid flow utilizing activation energy and magnetic dipole. Magnetic nanomaterials have significant effect on the magnetized behavior of ferrofluids which leads to robust the changes in fluid viscosity and thermophysical characteristics. Darcy-Forchheimer flow model is also present. Thermal conductivity of nanofluid is dependent on the temperature. Brownian motion and thermophoresis aspects are also accounted. The PDEs are reduced to set of ODEs via appropriate functions. Numerical solutions are achieved with the help of the famous bvp4c solver a built-in function in MATLAB. Numerous flow parameters are graphically and numerically presented with physical significance. The proposed findings could be useful for applications of extrusion systems, organic compounds, improved energy generation and improved manufacturing techniques.

Abstract Epidemiological models have been playing a vital role in different areas of biological sciences for the analysis of various contagious diseases. Transmissibility of virulent diseases is being portrayed in the literature through different compartments such as susceptible, infected, recovered (SIR), susceptible, infected, recovered, susceptible (SIRS) or susceptible, exposed, infected, recovered (SEIR), etc. The novelty in this endeavor is the addition of compartments of latency and treatment with vaccination, so the system is designated as susceptible, vaccinated, exposed, latent, infected, treatment, and recovered (SVELITR). The contact of a susceptible individual to an infective individual firstly makes the individual exposed, latent, and then completely infection carrier. Innovatively, the assumption that exposed, latent, and infected individuals enter the treatment compartment at different rates after a time lag is also deliberated through the existence of time delay. The rate of change and constant solutions of each compartment are studied with incorporation of a special case of proportional fractional derivative (PFD). In addition, existence and uniqueness of the system are also comprehensively elaborated. Moreover, novel dynamic assessment of the system is carried out in context with the fractional order index. Succinctly, the manuscript accomplishes cyclic epidemiological behavior of the infectious disease due to the delay in treatment of the infected individuals.

Entropy is the measure of the amount of energy in any physical system that is not accessible for the useful work, which causes a decrease in a system’s thermodynamic efficiency. The idea of entropy generation analysis plays a vital role in characterizing the evolution of thermal processes and minimizing the impending loss of available mechanical power in thermo-fluid systems from an analytical perspective. It has a wide range of applications in biological, information, and engineering systems, such as transportation, telecommunication, and rate processes. The analysis of the entropy generation of axisymmetric magnetohydrodynamic hybrid nanofluid ( S i O 2 − M o S 2 ) /water flow induced by rotating and stretching cylinder in the presence of heat radiation, ohmic heating, and the magnetic field is focus of this study. Thermal energy transport of hybrid nanofluids is performed by applying the Maxwell model. Heat transport is carried out by using convective boundary condition. The dimensionless ordinary differential equations are acquired by similarity transformations. The numerical solution for these differential equations is obtained by the bvp4c program in MATLAB. A comparison between nanofluid and hybrid nanofluid is made for flow field, temperature, and entropy generation. Comparison of nanofluid flow with hybrid nanofluid flow exhibits a higher rate of heat transmission, while entropy generation exhibits the opposite behavior. It is observed that the flow and heat distribution increase as the solid volume fraction’s value grows. An increase in entropy is indicated by augmentation in the Brinkman number and temperature ratio parameter, but the Bejan number shows a declining trend. Furthermore, outcomes of the Nusselt number for hybrid nanofluid and nanofluid are calculated for various parameters. It is noticed that the Nusselt number is reduced for enlarging the magnetic field and Eckert number. The axial and azimuthal wall stress parameters are declined by augmenting the Reynolds number.

Abstract In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.

This work is concerned with the computational solution of the time-dependent 3D parabolic Heston–Cox–Ingersoll–Ross (HCIR) PDE, which is of practical importance in mathematical finance. The HCIR dynamic states that the model follows randomness for the underlying asset, the volatility and the rate of interest. Since the PDE formulation has degeneracy and non-smoothness at some area of its domain, we design a new numerical solver via semi-discretization and the radial basis function–finite difference (RBF-FD) scheme. Our scheme is built on graded meshes so as to employ the lowest possible number of discretized nodes. The stability of our solver is proven analytically. Computational testing is conducted to uphold the analytical findings in practice.

In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus. To avoid excessively increasing the number of discretization points, such as the standard finite difference or meshfree methods, and, at the same time, to increase the efficiency of the solver, we employ discretizations on spatially non-uniform meshes with an attention on the non-smoothness area of the underlying asset. Therefore, the PDE problem is transformed to a linear system of algebraic equations. We perform numerical simulations to observe and check the behavior of the presented scheme in contrast to the existing methods.

Abstract This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.

This article addresses the numerical approximation of third-grade nanoliquid flow over a stretchable rotating disk in the existence of nano-sized particles and gyrotactic motile microorganisms. The behavior of bioconvection is contemplated. The comportment of mixed convection, activation energy and Joule heating effects are also considered. Further the nano-characteristics for Brownian dispersion of fluid particles and thermophoresis aspect are also taken into account. Utilizing appropriate scaling group of transformation variables, the partial differential equations are converted into governing ordinary differential system. Then coupled ordinary differential equations are tackled numerically by using shooting technique via built-in function bvp4c solver with the help of computational software MATLAB. Graphical impact of miscellaneous arising sundry parameters on distribution, volumetric concentration of nano-particles, velocity field and rescaled density of motile micro-organisms are scrutinized and deliberated. The present model plays a crucial role in sectors of industry and engineering. This model is suitable for heating and cooling including engine cooling, microelectronics, biotechnology, bio-microsystems, cancer therapy, fertilizers and biofuel etc. Furthermore, the temperature distribution is enhanced for larger values of thermal radiation parameter.

This paper proposes a computational solver via the localized radial basis function finite difference (RBF-FD) scheme and the use of graded meshes for solving the time-dependent Bates partial integro-differential equation (PIDE) arising in computational finance. In order to avoid facing a large system of discretization systems, we employ graded meshes along both of the spatial variables, which results in constructing a set of ordinary differential equations (ODEs) of lower sizes. Moreover, an explicit time integrator is used because it can bypass the need to solve the large discretized linear systems in each time level. The stability of the numerical method is discussed in detail based on the eigenvalues of the system matrix. Finally, numerical tests revealed the accuracy and reliability of the presented solver.

The Heston–Hull–White three-dimensional time-dependent partial differential equation (PDE) is one of the important models in mathematical finance, at which not only the volatility is modeled based on a stochastic process but also the rate of interest is assumed to follow a stochastic dynamic. Hence, an efficient method is derived in this paper based on the methodology of the localized radial basis function generated finite difference (RBF-FD) scheme. The proposed solver uses the RBF-FD approximations on graded meshes along all three spatial variables and a high order time-stepping scheme. Stability is also studied in detail to show under what conditions the proposed method is stable. Computational simulations are given to support the theoretical discussions.

Increasing heat transfer is an important part of industrial, mechanical, electrical, thermal, and biological sciences. The aim of this study is to increase the thermal competency of a conventional fluid by using a ternary hybrid nanofluid. A magnetic field and thermal radiation are used to further improve the thermal conductivity of the base fluid. Irreversibility is analyzed under the influence of the embedded parameters. The basic equations for the ternary hybrid nanofluids are transformed from Partial Differential Equations (PDEs) to Ordinary Differential Equations (ODEs) using the similarity concept. The Marangoni convection idea is used in the mathematical model for the temperature difference between the two media: the surface and fluid. The achieved results are provided and discussed. The results show that ternary hybrid nanofluids are more suitable as heat-transmitted conductors than conventional fluids.

The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag–Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative methods with global convergence for finding special matrix functions. By employing such a methodology, we propose a new solver for the sign of an invertible square matrix. The presented method achieves the fourth rate of convergence by using as few matrix products as possible. Its attraction basin shows larger convergence radii, in contrast to its Padé-type methods of the same order. Computational tests are performed to check the efficacy of the proposed solver.

Solar thermal absorption has an important role in the solar power plant to store the energy and usually, the solar systems face the problem to store and control the energy at high temperatures. The research aims to study the hybrid nanofluids which is used as the solar energy absorber and tends to store the thermal energy. In the this study, the authors focus on response of the inclined plate solar collector when the base fluid of water is substituted by the Hybrid nanofluid containing MgO (Magnesium oxide), CuO (Copper Oxide) with MWCNTs (Multiple wall carbon nanotubes), and water is used as a base solvent. The inclined plate is embedded in the permeable medium in the existence of solar radiation. The solution to the problem has been tackled through analytical techniques. The essential physical features are observed for heat transfer, absorption, and omission rate of the solar radiations.

The three-dimensional flow of Water based Graphene Oxide (GO-W) and Ethylene Glycol based Graphene Oxide (GO-EG) nanofluids amongst the binary upright and parallel plates is considered. The unsteady movement of the nanofluid is associated with the porous medium and the uniform magnetic field is executed in the perpendicular direction of the flow field. The basic governing equations have been altered using the Von Karman transformation, including the natural convection in the downward direction. The solution for the modeled problem has been attained by means of optimal homotopy analysis method (OHAM). The influence of the physical parameters on the momentum boundary layer, pressure, and temperature fields is mainly focused. Moreover, the comparison of the GO-W and GO-EG nanofluids under the impact of physical constraints has been analyzed graphically and numerically. The imperative physical constraints of the drag force and heat transfer rate have been computed and discussed. The results have been validated using the error analysis and the obtained outcomes have been shown and discussed. The obtained results are compared with the numerical ND-Solve method. It is obtained that the increasing order of the iterations reduces the absolute error and the results go to the strong convergence. Moreover, the impact of the physical parameters is more precise in the GO-EG nanofluid due to its higher thermophysical properties.

In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock movement by using the GARCH model. Numerical simulations are given for a variety of stocks in equity markets to uphold the findings.

In the current article, a mathematical model is developed to visualize the flow of non-Newtonian magneto cross nanofluid with mass and heat transport rates having activation energy, motile microorganisms and bioconvection over the wedge. The phenomena of microorganisms is implemented to control the suspension of nanomaterials. The results of hydromagnetic are also integrated into the momentum expression. Nanofluid is developed by dispersing the nanosized particles in the regular fluid. Nanosized solid materials like carbides, ceramics, graphene, metal, alloyed CNTs etc. have been utilized for the preparation of nanofluid. Physically regular fluids have low thermal efficiency. Therefore, the nanosize particles can be utilized to enhance the thermal efficiency of the regular fluids. Nanofluids have many features in hybrid power engine, heat transfer and can be useful in cancer therapy and medicine. The constructed system is first simplified into nonlinear form by introducing similarity variables. Then obtained ordinary differential equations (ODEs) which are evaluated for numerical solution. Further, for numerical approximation, the popular bvp4c scheme built-in function in MATLAB is utilized. Reliable outcomes are achieved for the temperature, velocity, concentration and motile microorganism density profiles. Results for numerous essential flow parameters are shown via numerical outcomes and graphs. It is revealed that velocity upsurges with enhancement in mixed convection parameter while reduces for bioconvection Rayleigh and buoyancy ratio parameters. Furthermore, the volumetric concentration of nanoparticles boost up for growing estimations of activation energy parameter. The microorganisms field upsurges with larger microorganism slip parameters while reduces with the augmentation in magnitude of bioconvection Lewis number and Peclet number. The obtained numerical results are compared with the available data and found good agreement.

In this paper, we first derive a family of iterative schemes with fourth order. A weight function is used to maintain its optimality. Then, we transform it into methods with several self-accelerating parameters to reach the highest possible convergence rate 8. For this aim, we employ the property of the eigenvalues of the matrices and the technique with memory. Solving several nonlinear test equations shows that the proposed variants have a computational efficiency index of two (maximum amount possible) in practice.

This article examines magnetohydrodynamic three-dimensional (3D) squeezed flow by a rotating permeable channel subject to Dufour and Soret impacts. Impact of viscous dissipation is also considered. An applied magnetic field is considered subject to electrically conducting viscous fluid. The change from the non-linear partial differential framework to the non-linear ordinary differential framework is assumed into position by utilizing appropriate variables. Governing differential frameworks are computed numerically by shooting method. Numerical results have been achieved by considering numerous values of emerging flow parameters. Contributions of influential parameters on physical quantities are studied thoroughly. Surface drag coefficients and mass and heat transport rates are also processed and examined. Furthermore, the concentration and temperature distributions are reduced for larger values of Soret number. The prime interest of presented study is to model and examine the Dufour and Soret aspects in concentration and energy expressions. To our knowledge, no such analysis has been addressed in the literature yet.

This study examines Darcy-Forchheimer 3D nanoliquid flow caused by a rotating disk with heat generation/absorption. The impacts of Brownian motion and thermophoretic are considered. Velocity, concentration, and thermal slips at the surface of the rotating disk are considered. The change from the non-linear partial differential framework to the non-linear ordinary differential framework is accomplished by utilizing appropriate variables. A shooting technique is utilized to develop a numerical solution of the resulting framework. Graphs have been sketched to examine how the concentration and temperature fields are affected by several pertinent flow parameters. Skin friction and local Sherwood and Nusselt numbers are additionally plotted and analyzed. Furthermore, the concentration and temperature fields are enhanced for larger values of the thermophoresis parameter.

Nowadays, the problem of solar thermal absorption plays a vital role in energy storage in power plants, but within this phenomenon solar systems have a big challenge in storing and regulating energies at extreme temperatures. The solar energy absorber based on hybrid nanofluids tends to store thermal energy, and the hybrid nanofluids involve the stable scattering of different nano dimension particles in the conventional solvent at a suitable proportion to gain the desired thermophysical constraints. The authors focus on the behavior of the inclined plate absorber panel as the basic solution of water is replaced by a hybrid nanofluid, including Cu (Copper) and Al2O3 (Aluminum Oxide), and water is utilized as a base surfactant in the current investigation. The inclined panel is integrated into a porous surface with the presence of solar radiations, Joule heating, and heat absorption. The fundamental equations of the flow and energy model are addressed with the similarity transformations. The homotopy analysis method (HAM) via Mathematica software is used to explore the solution to this problem. Furthermore, the important physical characteristics of the rate of heat transfer, omission and absorption of solar radiation, and its impact on the solar plant are observed.

The goal of this article is to investigate a new solver in the form of an iterative method to solve X+A∗X−1A=I as an important nonlinear matrix equation (NME), where A,X,I are appropriate matrices. The minimal and maximal solutions of this NME are discussed as Hermitian positive definite (HPD) matrices. The convergence of the scheme is given. Several numerical tests are also provided to support the theoretical discussions.

Entropy generation plays a significant role in several complex processes, extending from cosmology to biology. The entropy generation minimization procedure can be applied for the optimization of mechanical systems including heat exchangers, elements of nuclear and thermal power plants, ventilation and air-conditioning systems. In order to present our analysis, entropy generation in a thin film flow of second grade nanofluid holding single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with a Cattaneo–Christov heat flux model is studied in this article. The flow is considered passing a linearly extending surface. A variable magnetic field with aligned angle ε is functioned along the extending sheet. With the aid of the homotopy analysis method (HAM), the fluid flow model is elucidated. The impressions of embedded factors on the flow are obtainable through figures and discussed in detail. It is observed that the velocity profile escalated with the increasing values of volume fraction of nanoparticles and second grade fluid parameter. The higher values of volume fraction of nanoparticles, second grade fluid parameter, non-linear heat source/sink, and thermal radiation parameter intensified the temperature profile. Surface drag force escalated with heightening values of nanoparticles volume fraction, unsteadiness, film thickness, magnetic, and second grade fluid parameters. Entropy generation increased with enhancing values of magnetic parameter, Brinkman number, and Reynolds number.

In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. Frozen Jacobian multistep iterative methods are computationally very efficient. They require only one inversion of the Jacobian in the form of LU-factorization. The LU factors can then be used repeatedly in the multistep part to solve other linear systems. The convergence order of the proposed iterative method is 5m-11, where m is the number of steps. The validity, accuracy, and efficiency of our proposed frozen Jacobian multistep iterative method is illustrated by solving fifteen IVPs and BVPs. It has been observed that, in all the test problems, with one exception in this paper, a single application of the proposed method is enough to obtain highly accurate numerical solutions. In addition, we present a comprehensive comparison of J-GL-C methods on a collection of test problems.