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The main objective of the present investigation is to examine the couple stress fluid flow occurring as a result of rotation of a disk. On implementing a suitable transformation, the governing system of partial differential equations (PDEs) is converted into nonlinear differential equations of a single independent variable. These equations are solved analytically by virtue of the Homotopy Analysis Method (HAM) which gives solutions in the form of a series. The solution of most of the governing problems is determined in terms of the absolute exponential and decaying functions by means of this powerful technique. To support analytic results, some graphs are plotted for determining the convergence of the solution. Also the graphical interpretation of velocity profiles corresponding to the effects of pertinent parameters are shown and discussed in detail. The numerical results are calculated for evaluation of the influence of fluid parameter. It can also be anticipated that the radial and axial velocity components show decreasing behavior due to rise in the values of couple stress parameter which conflict the behavior of the tangential component of velocity.

Purpose - The purpose of this paper is to investigate the approximate solution of the couple stress fluid equations in a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls.Design methodology approach - Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real-life nonlinear problems. The governing partial differential equations are transformed using a transformation into an ordinary differential equation that is solved by homotopy analysis method (HAM) and shooting technique.Findings - To assess the accuracy of the solutions, the comparison of the obtained results reveals that both methods are tremendously effective. Analytical and numerical solutions comparison indicates an excellent agreement and this comparison is also presented. Graphs are portrayed for the effects of some values of parameters.Practical implications - Expansion or contraction problems occur naturally in the transport of biological fluids, the air circulation in the respiratory system, expanding or contracting jets and the synchronous pulsating of porous diaphragms. This work provides a very useful source of information for researchers on this subject.Originality value - In the present study, the flow of couple stress fluids in expanding and contracting scenarios is investigated.

This paper provides analytical solution of the non-aligned stagnation point flow of second grade fluid over a porous rotating disk in the presence of a magnetic field and suction/injection at the disk surface. The mathematical formulation of the fluid model is obtained in terms of partial differential equations (PDEs). The PDEs governing the motion are transformed into a system of ordinary differential equations (ODEs) by means of a similarity transformation and these corresponding nonlinear ODEs are solved by employing the homotopy analysis method (HAM) and the convergence analysis of the presented method is also performed graphically. An inclusion of the influences of various admissible parameters has been shown numerically and graphically on the flow field. Furthermore, comparison is made and it concedes that the obtained results are found to be in good agreement with results existing in literature.

The flow and heat transfer analysis in the conventional nanofluid A l 2 O 3 − H 2 O and hybrid nanofluid C u − A l 2 O 3 − H 2 O was carried out in the present study. The present work also focused on the comparative analysis of entropy generation in conventional and hybrid nanofluid flow. The flows of both types of nanofluid were assumed to be over a thin needle in the presence of thermal dissipation. The temperature at the surface of the thin needle and the fluid in the free stream region were supposed to be constant. Modified Maxwell Garnet (MMG) and the Brinkman model were utilized for effective thermal conductivity and dynamic viscosity. The numerical solutions of the self-similar equations were obtained by using the Runge-Kutta Fehlberg scheme (RKFS). The Matlab in-built solver bvp4c was also used to solve the nonlinear dimensionless system of differential equations. The present numerical results were compared to the existing limiting outcomes in the literature and were found to be in excellent agreement. The analysis demonstrated that the rate of entropy generation reduced with the decreasing velocity of the thin needle as compared to the free stream velocity. The hybrid nanofluid flow with less velocity was compared to the regular nanofluid under the same circumstances. Furthermore, the enhancement in the temperature profile of the hybrid nanofluid was high as compared to the regular nanofluid. The influences of relevant physical parameters on flow, temperature distribution, and entropy generation are depicted graphically and discussed herein.

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail.

This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease’s spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease.

Infectious diseases like COVID-19 continue to pose critical challenges globally, underscoring the need for effective control strategies that go beyond traditional vaccinations and treatments. This study introduces an advanced SEI1I2I3QCR model, uniquely incorporating fractional-order delay differential equations to account for latency periods and dynamic transmission patterns of COVID-19, improving accuracy in capturing disease progression and peak oscillations. Stability analyses of the model reveal the critical role of delay and fractional order parameters in managing disease dynamics. Additionally, we applied optimal control theory to simulate non-pharmaceutical interventions, such as quarantine and awareness campaigns, demonstrating a notable reduction in infection rates. Numerical simulations align the model closely with real-world COVID-19 data from China, validating its utility in guiding pandemic response strategies. Our findings emphasize the significance of integrating time-delay factors and fractional calculus in epidemic modeling, offering a novel framework for pandemic management through targeted, cost-effective control measures.

Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the nth order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.

In the study, intelligent computing technique is developed for solving the nonlinear system for wire coating analysis with the bath of Oldroyd 8-constant fluid having pressure gradient using feedforward artificial neural networks (ANNs), evolutionary computing, active-set algorithm (ASA) and their hybrid. Original partial differential equations of wire coating process are converted to nonlinear ordinary differential equation (NL-ODEs) in dimensionless form using similarity transformation. Strength of ANNs is exploited to develop mathematical model of the transformed equations by defining an unsupervised error. Training of design variables of the network is carried out globally using evolutionary computing techniques based on genetic algorithms (GAs) hybrid with ASA for rapid local convergence. Design scheme is applied to analyze the dynamics of the problem for number of variants based on dilatant constant, the pseudoplastic constant, the pressure gradient, shear stress under the effect of viscosity parameter and varying the coating thickness of the polymer. Results of the proposed method are compared with standard numerical solver for NL-ODEs based of Adams method to establish its correctness. Reliability of the method is further validated through the results of statistics based on different performance measures for accuracy and computational complexity.

In this study, new intelligent computing methodologies have been developed for highly nonlinear singular Flierl–Petviashivili (FP) problem having boundary condition at infinity by exploiting three different neural network models integrated with active-set algorithm (ASA). A modification in the modeling is introduced to cater the singularity, avoid divergence in results for unbounded inputs and capable of dealing with strong nonlinearity. Three models have been constructed in an unsupervised manner for solving the FP equation using log-sigmoid, radial basis and tan-sigmoid transfer functions in the hidden layers of the network. The training of adaptive adjustable variables of each model is carried out with a constrained optimization technique based on ASA. The proposed models have been evaluated on three variants of the two FP equations. The designed models have been examined with respect to precision, stability and complexity through statistics.