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The ability of nanofluids to improve heat transmission in thermal systems is well established. This work investigates the three-dimensional theoretical behavior of Darcy-Forchheimer nanofluids in tilted magnetohydrodynamics. In this study, the Soret effect, micro-motile organisms, thermophoresis, and heat radiation are also considered. The finite element method is used to solve the challenging mathematical model. Using graphs and tables, patterns may be seen in the velocity profiles, temperature distributions, concentrations of micro- and nano-motile organisms, and nanoparticle concentrations. The governing equations for mass, concentration, momentum, and motile microbes are derived using partial derivatives. These equations are then transformed into dimensionless ordinary differential equations utilizing appropriate similarity transformations. Permeability and viscosity have an impact on the properties of fluid flow. According to the results, improved thermophoresis and Brownian motion parameters raise the temperature profiles. In keeping with other studies, more inclined magnetohydrodynamics also accelerate heat transfer rates. The mass transfer rate at Fr=0.8 is 32.67% and 33.99% for Fr=1.4. Thus, mass transfer increased 1.32%. The novelties of the current work are: the Buongiorno nanofluid model is utilized for 3D geometry, inclined MHD and motile microorganisms are considered for rotating nanofluid flow, effects of slip and non-slip boundary conditions are compared, and the finite element technique is used to solve the developed problem.

Abstract This study aims to explore the precise resolution of the nonlinear Benjamin Bona Mahony Burgers (BBMB) equation, which finds application in a variety of nonlinear scientific disciplines including fluid dynamics, shock generation, wave transmission, and soliton theory. Within this paper, we employ two versatile methodologies, specifically the extended $$\exp (-\Psi (\chi ))$$ exp ( - Ψ ( χ ) ) expansion technique and the novel Kudryashov method, to identify the exact soliton solutions of the nonlinear BBMB equation. The solutions we discovered involve trigonometric functions, hyperbolic functions, and rational functions. The uniqueness of this research lies in uncovering the bright soliton, kink wave solution, and periodic wave solution, and conducting stability analysis. Furthermore, the solutions’ graphical characteristics were explored through the utilization of the mathematical software Maple 2022 ( https://maplesoft.com/downloads/selectplatform.aspx?hash=61ab59890f2313b2241fde3423fd975e ). The system’s physical interpretation is defined through various types of graphs, including contour graphs, 3D-surface graphs, and line graphs, which use appropriate parameter values. These recommended techniques hold significant importance and are applicable in diverse nonlinear evolutionary equations found in the field of nonlinear sciences for illustrating nonlinear physical models.

Abstract Energy loss during the transportation of energy is the main concern of researchers and industrialists. The primary cause of heat exchange gadget inefficiency during transportation was applied to traditional fluids with weak heat transfer characteristics. Instead, thermal devices worked much better when the fluids were changed to nanofluids that had good thermal transfer properties. A diverse range of nanoparticles were implemented on account of their elevated thermal conductivity. This research addresses the significance of MHD Maxwell nanofluid for heat transfer flow. The flow model comprised continuity, momentum, energy transport, and concentration equations in the form of PDEs. The developed model was converted into ODEs by using workable similarities. Numerical simulations in the MATLAB environment were employed to find the outcomes of velocity, thermal transportation, and concentration profiles. The effects of many parameters, such as Hartman, Deborah, buoyancy, the intensity of an external heat source, chemical reactions, and many others, were also evaluated. The presence of nanoparticles enhances temperature conduction. Also, the findings are compared with previously published research. In addition, the Nusselt number and skin friction increase as the variables associated with the Hartman number and buoyancy parameter grow. The respective transfer rates of heat are 28.26 $$\%$$ % and 38.19 $$\%$$ % respectively. As a result, the rate of heat transmission increased by 14.23 $$\%$$ % . The velocity profiles enhanced while temperature profiles declined for higher values of the Maxwell fluid parameter. As the external heat source increases, the temperature profile rises. Conversely, buoyancy parameters increase as it descends. This type of problem is applicable in many fields such as heat exchangers, cooling of electronic devices, and automotive cooling systems.

In this paper, we study the effects of activation energy and solar radiation on expanding solar sheets, as well as non-Newtonian nanofluid dynamics, which are important in these applications and are driving efforts to find solutions to the world’s energy problems. We provide numerical solutions to physical flow problems by solving partial differential equations. We utilise the MATLAB-integrated bvp4c methodology after applying similarities to turn these PDEs model into ODEs. By investigating dimensionless momentum, concentration, and thermal profiles under different conditions, our research delves into the physical relevance of nanofluids. Important flow field components have also been numerically and tabulatively studied and displayed graphically. The rates at which heat is transferred is 29.06% and 37.99%, respectively. The rate of heat transport rose by 13.93% as a result. At greater values for the Maxwell fluid parameter, the velocity profiles improved while the temperature profiles decreased. This paper contributes significant new information to the ongoing discussion in this area, which is in line with earlier findings.

Abstract The use of renewable energy sources is leading the charge to solve the world’s energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are $$25.87\%$$ 25.87 % , $$33.61\%$$ 33.61 % and $$40.52\%$$ 40.52 % at $$Rd =0.5, Rd=1.0$$ R d = 0.5 , R d = 1.0 , and $$Rd=1.5$$ R d = 1.5 , respectively. The heat transfer rate is increased by $$6.91\%$$ 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation.

Abstract In this paper, we study linear and nonlinear mixed convection, activation energy, and heat radiation effects caused by nanoparticles. This study aims to improve the understanding of how nanofluids behave in the presence of rotating disks and develop more efficient and effective cooling technologies. The flow problem consisted of partial differential equations (PDE). It is challenging to calculate these equations as a result of these nonlinear PDEs. Consequently, we use appropriate similarities to transform them into ordinary differential equations (ODEs). The bvp4c Matlab built-in technique is then used to resolve these ODEs. The velocities, temperature, and concentration outcomes with the various factors are examined graphically. Additionally, tables are employed to analyze the skin friction and Nusselt number values. It is analyzed that increasing the linear and linear mixed convection parameters enhances the velocity profiles of nanofluid. Enhancements in heat are analyzed by increasing nonlinear thermal radiation and enhancement in concentration is examined by increasing activation energy. Furthermore, as the variables for thermophoresis and Brownian motion are increased, the Nusselt number falls. The heat transfer rate is 27.16% for $$Rd=0.6$$ R d = 0.6 and 39.28% for $$Rd=1.4$$ R d = 1.4 . Thus, the heat transfer rate is enhanced 12.12%. This study’s practical applications include improving the behavior of fluids and the transfer of heat in rotating frameworks, which may affect energy systems, heat exchangers, and cooling advances in technology.

Abstract Nanofluids are implementable in a variety of applications, such as heat exchangers, the healthcare sector, the cooling of various devices, hybrid-powered machines, microelectronics, power plants, chemical processes, astronomical technology, cancer treatment, etc. Nanofluids also have enhanced heat transmission and thermal efficiency. The heat radiation of nanoparticles and the natural-convective flow of electrically conducting nanofluids over the rotating disk using Darcy Forchheimer’s porous media, thermal radiation is investigated in this paper. The nanoparticles titanium dioxide and single-walled carbon nanotubes are taken into account with base fluid water. The main goal of this investigation is to enhance heat transfer in nanofluids. The mathematical solution for the model has been obtained through the utilization of cylindrical coordinates. The flow model, which forms the basis of the investigation, is constructed around partial differential equations (PDEs). To address the inherent nonlinearity of these PDEs, physical similarities are employed to transform them into ordinary differential equations (ODEs). Subsequently, the fourth-order Runge–Kutta technique is employed via Matlab to solve these ODEs. The graphical examination of the velocities and temperature with various parameters is an exquisite display of scientific artistry. The magnetic field component is anticipated to exhibit an inverse correlation with velocities, while the temperature profile is expected to surge with the rise of the nonlinear mixed convection parameter. Additionally, the skin friction and Nusselt number are meticulously computed and presented in a tabular format, adding a touch of elegance to the already breathtaking analysis. By boosting the radiation parameter, the Nusselt value declined. Moreover, it is observed that the nanofluids having a laminar nanoparticle shape have a greater heat transfer rate.

Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution systems in the field of mathematical physics. In the present research, we employ the modified sub-equation approach, a very effective and strong technique, to ensure the solutions for the Klein–Gordon featuring cubic nonlinearity and Zakharov Kuznetsov–Benjamin Bona Mahony equations. Several restriction requirements that ensure the existence of these solutions are emphasized. By employing a linearization technique, we ascertain the stability gain. This methodology acquires original precise solutions of soliton nature. Furthermore, the nonlinear wave structures of both equations are illustrated through the consideration of several three-dimensional and two-dimensional plots. These plots are generated by selecting appropriate values for the parameters. It is expected that these innovative solutions would facilitate an in-depth understanding of the evolution and fluidity of these models. The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions.

The activation energy model is used in this work to examine how hybrid nanoparticles affect the flow across a rotating disk. Here, we considered nanoparticles of silver (Ag) and titanium dioxide (TiO2) dissolved in water, a base liquid. These nanoparticles have real applications such as photography, photocatalysis, water purification, and solar energy conversion. The current study investigates the combined effects of a changing magnetic field, Darcy Forchheimer, porosity, thermal radiation, Brownian motion, and thermophoresis on hybrid nanofluid flow across a rotating disk. By applying similarity transformations, the partial differential equations system of the current scheme is converted into an ordinary differential equations system, after which it is calculated with MATLAB using the bvp4c scheme. Graphs are used to assess the investigation of mass and heat transport. Also, the change in concentration, temperature, and velocity profiles for various non-dimensional factors are discussed briefly using corresponding graphs. It has been noted that the velocity gradient of mono and hybrid nanofluids is reduced as the magnetic parameter inputs increase. The velocity profiles decline as the input of the Darcy-Forchheimer parameter increases. The outcome demonstrates that temperature and concentration increase as the thermophoresis parameter rises. The concentration profile is enhanced as an activation energy parameter increases. Moreover, the average Nusselt number is 37.73 % at M=0.8, and when M=2.2, the value of the average number decreased by 29.43 %. The concentration of silver (Ag) and titanium dioxide (TiO2) is (0−6)%.

This work covers the theoretical and computational examination of the Ellis hybrid nanofluid flow model with magnetic, Darcy-Forchheimer, and non-linear thermal radiation effects across the stretching cylinder. The convective slip boundary condition is imposed on the surface of the cylinder. Hybrid nanoparticles (AA7072 and AA7075) are scattered in base fluid (water) to create a hybrid nanofluid. The phenomenon of fluid flow has been analytically developed for energy and fluid velocity as a non-linear partial differential equation (PDE)-based system. Through appropriate similarity replacements, the design of PDEs is further streamlined to the set of ordinary differential equations (ODEs). Utilizing a built-in MATLAB (R2020b) algorithm called bvp4c, numerical solutions are found for the obtained dimensionless equations. Graphical discussions are used to illustrate the outcomes of velocity and temperature profiles. The velocity profile of mono and hybrid nanofluids declined for higher inputs of Darcy–Forchheimer and magnetic parameters. Additionally, it has been observed that the energy contour is improved caused of thermal radiation and thermal Biot number. Moreover, our results are consistent with the existing literature.

This study aims to determine the heat transfer properties of a magnetohydrodynamic Prandtl hybrid nanofluid over a stretched surface in the presence of bioconvection and chemical reaction effects. This article investigates the bio-convection, inclined magnetohydrodynamic, thermal linear radiations, and chemical reaction of hybrid nanofluid across stretching sheets. Also, the results are compared with the nanofluid flow. Moreover, the non-Newtonian fluid named Prandtl fluid is considered. Microfluidics, industry, transportation, the military, and medicine are just a few of the real-world applications of hybrid nanofluids. Due to the nonlinear and convoluted nature of the governing equations for the problem, similarity transformations are used to develop a simplified mathematical model with all differential equations being ordinary and asymmetric. The reduced mathematical model is computationally analyzed using the MATLAB software package’s boundary value problem solver, Runge-Kutta-fourth-fifth Fehlberg’s order method. When compared to previously published studies, it is observed that the acquired results exhibited a high degree of symmetry and accuracy. The velocity profiles of basic nanofluid and hybrid nanofluid are increased by increasing the Prandtl parameters’ values, which is consistent with prior observations. Additionally, the concentration and temperature of simple and hybrid nanofluids increase with the magnetic parameter values.

Switched reluctance motor (SRM) is an energy efficient machine, which receives electrical energy from the power source and returns part of the stored magnetic energy back to the supply, during each cycle of the machine operation. Characteristically, the SRM possesses nonlinear characteristics due to dual saliency and magnetic saturation. The exertion is realized in developing a mathematical model of the machine in presence of huge input data tables, famously, known as static characteristics. These data tables are required for mathematical modeling of the machine in a single pulse, steady state and transient performances separately. This paper presents a simple and flexible mathematical model of a switched reluctance machine in MATLAB/Simulink environment. In Simulink, based on graphical coding environment, the proposed model uses fewer data tables and less simulation time. Furthermore, with less addition to the same proposed model, another operating mode of the machine is possible, under the same operating conditions. A similar model in MATLAB, based on test code environment is also proposed, using the same operating conditions as in the Simulink based model to see the difference. The obtained results are validated by comparing the results of both the models, and with the experimentally obtained results, under single pulse, steady-state, and dynamic modes of the machine operation. The proposed model can handle the measured or computed data of the flux linkage and static torque, respectively.

Performance evaluation based on transient analysis has significant importance to those systems which never reached at equilibrium. In this paper, we develop and analyze the system through controlled arrival rate using internal limits. The system is modeled with Markovian and phase-type distributions for various internal limits and queue size. The transient analysis is carried out for the systems in vector domain through matrix geometric method and Runge-kutta procedure. The comparisons of results of transient analysis for Markovian and phase-type controlled arrival rate systems are also done.

In this paper the major findings of a formal experiment about onscreen text line lengths are presented. The experiment examined the effects of four different line lengths on the reading speed and the reading efficiency. Efficiency is defined as a combination of reading speed and accuracy. Sixteen people between the age of 24 and 36 participated at the experiment. The subjects had to read four different texts with an average line length around 2000 characters. The texts contained substitution words, which had to be detected by the subjects to measure reading accuracy. Besides objective measures like reading speed and accuracy, the subjects were asked to subjectively vote on their reading experience. The results from our objective measures show strong similarities to those of the work done previously by different researchers. The absolute reading speed grows when the line length grows from CPL (Characters Per Line) 30-120. The measured reading efficiency, however, doesn\\\'t grow steadily, although a growing trend can be seen. This is due to the fact, that the test persons found in average more substitution words from the 60 CPL text than they did from the 30 and 90 CPL texts. The reading speed seems to increase while the line length increases but the overall comprehension seems to peak at medium line lengths. As in the previous studies, our test persons also prefer the medium (60 and 90 CPL) line lengths, although they perform better when reading longer lines. In the overall subjective opinion 13 out of 16 test persons selected the 60 or 90 CPL line length as their favorite. The literature doesn\\\'t truly provide a scientific explanation for the difference between the objective performance and the subjective preference. A natural hypothesis would be that the line length that is the fastest to read would also feel most comfortable to the readers but in the light of this and the earlier research it seems like this is not the case.

Flow time analysis is a powerful concept to analyze the flow time of any arriving customer in any system at any instant. A load management mechanism can be employed very effectively in any queueing system by utilizing a system which provides probability of dual service rate. In this paper, we develop and demonstrate the flow and service processes transition diagram to determine the flow time of a customer in a load management late arrival state dependent finite discrete time queueing system with dual service rate where customers are hypogeometrically distributed. We compute the probability mass function of each starting state and total probability mass function. The obtained analytical results are validated with simulation results for varying values of arrival and service probabilities.

Various analytical methods have been proposed for the transient analysis of a queueing system in the scalar domain. In this paper, a vector domain based transient analysis is proposed for the hysteresis queueing system with internal thresholds for the efficient and numerically stable analysis. In this system arrival rate of customer is controlled through the internal thresholds and the system is analyzed as a quasi-birth and death process through matrix geometric method with the combination of vector form Runge-Kutta numerical procedure which utilizes the special matrices. An arrival and service process of the system follows a Markovian distribution. We analyze the mean number of customers in the system when the system is in transient state against varying time for a Markovian distribution. The results show that the effect of oscillation/hysteresis depends on the difference between the two internal threshold values.

WSNs (Wireless Sensor Networks) are generally deployed for long-lived missions. However, they rely on finite energy resources which lead to network partitioning. Network partitioning limits the dependability of WSN by making relevant spatial regions disconnected thus requiring the maintenance of the network. The network maintenance necessitates early warning and consequently forecasting of the network partitioning such that some early action can be taken to mitigate the problem. There exist approaches allowing for detection of network partitioning but none for its forecasting. We present an efficient approach for a proactive network ParFor (Partition Forecasting) based on energy maps. ParFor implements spatial and temporal suppression mechanisms such that from energy weak regions only a few nodes report short alarms to the sink. Using these alarms the forecasting is done centrally at the sink. Using simulations we highlight the efficiency and accuracy of ParFor.

Assorted analytical methods have been proposed for evaluating the performance of a slotted ring network. This paper proposes MGM (Matrix Geometric Method) to analyze the station buffer of a slotted ring for DT (Discrete-Time) queueing. The slotted ring is analyzed for infinite station buffer as a late arrival DT system. Utilizing the characteristics of 2-D Markov chain, various performance measures are validated with their corresponding results such as, throughput and MPAD (Mean Packet Access Delay) as well as the packet rejection probability for finite station buffer. The presented results prove efficacy of the method.

The texture descriptors derived from 1-D DFT (Discrete Fourier Transform) of the pixel values of a local neighbourhood have been shown to perform better than the methods based on wavelets for image retrieval and recognition. These DFT-based texture descriptors were extracted from rectangular or circular neighbourhoods. This paper compares the texture descriptors extracted from rectangular and the circular neighbourhoods previously proposed in the literature. A database of images is constructed from Brodatz album and the texture descriptors extracted from the two types of neighbourhoods are compared for texture retrieval. This paper shows that extracting DFT-based features from circular neighbourhood is almost thrice as expensive as extracting the same from the rectangular neighbourhood. The results of image retrieval on a large image database show that the descriptor extracted from rectangular neighbourhoods performs better than the same extracted from the circular neighbourhoods.