A sensitivity study on carbon nanotubes significance in Darcy-Forchheimer flow towards a rotating disk by response surface methodology

Magnetohydrodynamics Boundary Layer Flow Past a Wedge of Casson CuO-TiO2/EG Embedded in Non-Darcian Porous Media: Viscous Dissipation Effects

The movement physiognomies and heat transmission of viscous dissipative Casson hybrid nanoliquid (cupric oxide CuO titania TiO2/ethylene glycol EG) and nanoliquid (titania TiO2/ethylene glycol EG) MHD flow via a wedge saturated with non-Darcy porous medium and forced convection were the focus of this inquiry. The major partial differential equalities beside with the limit conditions were condensed to dimensionless forms by spending proper similarity transformation. The follow-on system of ODEs by the matching limit conditions was elucidated numerically by way of MATLAB, bvp4c solver. The research ramifications for basic TiO2/EG and hybrid CuO–TiO2/EG nanoliquids were presented and explained in detail. The greater upsides of the Casson parameter, magnetic parameter, first and second order porous resistance parameters, the velocity increases and the temperature profile decreases. Furthermore, the thermal field strengthens porosity and Eckert number. It was also found that the Nusselt number is an enhancing function of Casson parameter wheras, greater values of magnetic parameter and porosity parameter lessen the Nusselt number.

Response Surface Methodology (RSM) on the Hybrid Nanofluid Flow Subject to a Vertical and Permeable Wedge

The mixed convection flow with thermal characteristics of a water-based Cu-Al₂O₃ hybrid nanofluid towards a vertical and permeable wedge was numerically and statistically analyzed in this study. The governing model was constructed using physical and theoretical assumptions, which were then reduced to a set of ordinary differential equations (ODEs) using similarity transformation. The steady flow solutions were computed using the Matlab software bvp4c. All possible solutions were presented in the graphs of skin friction coefficient and thermal rate. The numerical results show that the flow and thermal progresses are developed by enhancing the controlling parameters (wedge parameter, volumetric concentration of nanoparticles, and suction parameter). Moreover, the response surface methodology (RSM) with analysis of variance (ANOVA) was employed for the statistical evaluation and conducted using the fit general linear model in the Minitab software. From the standpoint of statistical analysis, the wedge parameter and volumetric nanoparticle concentration have a considerable impact on all responses; however, the suction parameter effect is only substantial for a single response.

A sensitivity analysis of MHD nanofluid flow across an exponentially stretched surface with non-uniform heat flux by response surface methodology

The current study investigates the MHD flow of nanofluid across an elongating surface while taking into account non-uniform heat flux. For this, we have considered the flow of a boundary layer over a stretched sheet containing (water-based) Al₂O₃ nanoparticles. The convective boundary conditions for temperature have been invoked. The flow created by a surface that is exponentially expanding in the presence of a magnetic field and a non-uniform heat flux has been mathematically formulated by using laws of conservation. Transformed non-dimensional systems of governing equations have been analyzed numerically by using Adam’s Bashforth predictor corrector approach. The effects of emerging parameters on the fluid velocity and temperature profiles have been further described by plotting graphs. An experimental design and a sensitivity analysis based on Response Surface Methodology (RSM) are used to examine the effects of various physical factors and the dependence of the response factors of interest on the change of the input parameter. To establish the model dependencies of the output response variables, which include the skin friction coefficient and the local Nusselt number, on the independent input parameters, which include the magnetic field parameter, the nanoparticle volume fraction, and the heat transfer Biot number, RSM is used. On the basis of statistical measures such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q - Q$$\end{document}Q-Q residual plots, adjusted and hypothesis testing using p values, it is observed that both of our models for Skin Friction Coefficient (SFC) and the Local Nusselt Number (LNN) are best fitted. Further, it is concluded that the sensitivity of the SFC, as well as the LNN through heat transfer Biot number, is greater than that of nanoparticle volume fraction and magnetic field parameter. The SFC is sensitive to all combinations of the input parameters. At high levels of heat transfer Biot number, the LNN displays negative sensitivity via magnetic field parameters.

Statistical Modelling for the Darcy–Forchheimer Flow of Casson Cobalt Ferrite-Water/Ethylene Glycol Nanofluid under Nonlinear Radiation

Current research is focused on the utilization of a numerical solution of Casson cobalt ferrite nanofluid flow by taking two forms of base fluid. This investigation includes the gradual influence of nonlinear thermal radiation on the improvement of heat transfer related to the flow of nanofluids over a stretched rotating surface by the Darcy–Forchheimer law. The model constructed by a Casson nanoliquid in the boundary layer’s flow is studied for its symmetric behaviour, including cobalt ferrite nanomaterials. Two base liquids named as ethylene glycol and water are considered. The rate of heat transport is examined by considering Newtonian heating conditions. By utilizing similarity transformations, a partial differential system that governs the said model has been transformed into a highly nonlinear ordinary differential system, and numerical outcomes are obtained by implementing the RK4 via shooting methodologies. All obtained results, including local skin friction coefficients and local Nusselt number, are defined and discussed in the paper. The study’s findings ensure that the Casson cobalt ferrite nanofluid flowing towards a stretching plate has a unique solution: A variation of the solid volume fraction corresponds to the decrease in various values of the Casson nanofluid parameter for both type of nanofluid. Furthermore, a similar behaviour is noted for various values of the solid volume fraction, which corresponds to various values of the inertia coefficient parameter. Moreover, for the highest values of the solid volume fraction and all values of R1 and Ni taken into account, the rate of heat transfer upsurges. The data from the local skin friction coefficient (LSFC) and local Nusselt number (LNN) have been analysed using various statistical distributions, and it has been determined that both datasets generally fit the exponentiated Weibull distribution for various values of considered parameters. The findings would serve as a starting point for the manufacture of devices.

Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface

The thermal energy transfer characteristics during hybrid nanofluid migration are studied in the presence of a variable magnetic field, heat source, and radiation. The flow is governed by the conservation laws of mass, momentum, and energy, whereas it is modeled by the coupled set of nonlinear partial differential equations (PDEs). Suitable similarity transformations are employed to convert the developed set of PDEs to a nonlinear system of coupled ordinary differential equations (ODEs). The simplified system of ODEs is solved by using the well-established analytical procedure of homotopy analysis method (HAM). The effects of varying the strength of the physical parameters on the thermal energy transfer during hybrid nanofluid motion between two plates in which one of the plate is porous, rotating, as well as stretching are investigated through tables and two-dimensional graphs. The porosity is modeled through the Koo–Kleinstreuer model (KKL) correlation. The analysis reveals that the skin friction and Nusselt number augment with the increasing strength of the magnetic field and nanomaterials’ concentrations. The gradient in the fluid velocity has a dual dependence on the strength of the applied magnetic field and Grashof number and drops with the higher values of the unsteadiness parameter. The fluid velocity constricts with the enhancing magnetic field due to higher Lorentz forces, and it also drops with the increasing rotation rate. The enhancing buoyancy associated with higher Grashof number values augments the fluid velocity. The fluid’s temperature rises with the augmenting nanomaterial concentrations, Eckert number, nonsteadiness, heat source strength, and radiation parameter, while it drops with the higher Grashof number and Prandtl number. The applied technique of the HAM shows good convergence over a wide range of the convergent parameter. This work has potential applications in the development of efficient thermal energy transfer systems.

Topological Structure of the Solution Sets for Impulsive Fractional Neutral Differential Inclusions with Delay and Generated by a Non-Compact Demi Group

In this paper, we give an affirmative answer to a question about the sufficient conditions which ensure that the set of mild solutions for a fractional impulsive neutral differential inclusion with state-dependent delay, generated by a non-compact semi-group, are not empty compact and an Rδ-set. This means that the solution set may not be a singleton, but it has the same homology group as a one-point space from the point of view of algebraic topology. In fact, we demonstrate that the solution set is an intersection of a decreasing sequence of non-empty compact and contractible sets. Up to now, proving that the solution set for fractional impulsive neutral semilinear differential inclusions in the presence of impulses and delay and generated by a non-compact semigroup is an Rδ-set has not been considered in the literature. Since fractional differential equations have many applications in various fields such as physics and engineering, the aim of our work is important. Two illustrative examples are given to clarify the wide applicability of our results.

Analytical investigation of magnetized 2D hybrid nanofluid (GO + ZnO + blood) flow through a perforated capillary

The hydrothermal features of unsteady, incompressible, and laminar hybrid nanofluid motion through a porous capillary are analytically studied in the magnetic field presence. The hybrid nanofluid (GO + ZnO + Blood) is synthesized by blending nanomaterials of graphene oxide and zinc oxide with blood acting as the host fluid. The mathematical model of the flow comprises of a coupled nonlinear set of partial differential equations (PDEs) satisfying appropriate boundary conditions. These equations are reduced to ordinary differential equations (ODEs) by using similarity transformations and then solved with homotopy analysis method (HAM). The impacts of various pertinent physical parameters over the hybrid nanofluid state functions are examined by displaying 2 D graphs. It has been observed that the fluid velocity mitigates with the varying strength of M, A₀, N₀, and N₁. The enhancing buoyancy parameter ϵ augments the fluid velocity. The increasing Prandtl number causes to reduce, while the enhancing A₀, B, and N₂ augment the hybrid nanofluid temperature. The fluid concentration mitigates with the higher Schmidt number values and A₀, and augments with the increasing Soret number strength. The augmenting magnetic field strength causes to enhance the fluid friction, whereas the convective heat transfer increases with the Prandtl number rising values. The rising Sherwood number drops the mass transfer rate of the fluid. The achieved results are validated due to the agreement with the published results. The results of this computation will find applications in biomedicine, nanotechnology, and fluid dynamics.

Gyrotactic micro-organism flow of Maxwell nanofluid between two parallel plates

The present study explores incompressible, steady power law nanoliquid comprising gyrotactic microorganisms flow across parallel plates with energy transfer. In which only one plate is moving concerning another at a time. Nonlinear partial differential equations have been used to model the problem. Using Liao's transformation, the framework of PDEs is simplified to a system of Ordinary Differential Equations (ODEs). The problem is numerically solved using the parametric continuation method (PCM). The obtained results are compared to the boundary value solver (bvp4c) method for validity reasons. It has been observed that both the results are in best settlement with each other. The temperature, velocity, concentration and microorganism profile trend versus several physical constraints are presented graphically and briefly discussed. The velocity profile shows positive response versus the rising values of buoyancy convection parameters. While the velocity reduces with the increasing effect of magnetic field, because magnetic impact generates Lorentz force, which reduces the fluid velocity.

Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling

In current investigation, a novel implementation of intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural networks (ANN) with the Levenberg-Marquard algorithm is provided to interpret heat generation/absorption and radiation phenomenon in unsteady electrically conducting Williamson liquid flow along porous stretching surface. Heat phenomenon is investigated by taking convective boundary condition along with both velocity and thermal slip phenomena. The original nonlinear coupled PDEs representing the fluidic model are transformed to an analogous nonlinear ODEs system via incorporating appropriate transformations. A data set for proposed MLP-ANN is generated for various scenarios of fluidic model by variation of involved pertinent parameters via Galerkin weighted residual method (GWRM). In order to predict the (MLP) values, a multi-layer perceptron (MLP) artificial neural network (ANN) has been developed. There are 10 neurons in hidden layer of feed forward (FF) back propagation (BP) network model. The predictive performance of ANN model has been analyzed by comparing the results obtained from the ANN model using Levenberg-Marquard algorithm as the training algorithm with the target values. When the obtained Mean Square Error (MSE), Coefficient of Determination (R) and error rate values have been analyzed, it has been concluded that the ANN model can predict SFC and NN values with high accuracy. According to the findings of current analysis, ANN approach is accurate, effective and conveniently applicable for simulating the slip flow of Williamson fluid towards the stretching plate with heat generation/absorption. The obtained results showed that ANNs are an ideal tool that can be used to predict Skin Friction Coefficients and Nusselt Number values.

Statistical modeling for bioconvective tangent hyperbolic nanofluid towards stretching surface with zero mass flux condition

This article presents the implementation of a numerical solution of bioconvective nanofluid flow. The boundary layer flow (BLF) towards a vertical exponentially stretching plate with combination of heat and mass transfer rate in tangent hyperbolic nanofluid containing microorganisms. We have introduced zero mass flux condition to achieve physically realistic outcomes. Analysis is conducted with magnetic field phenomenon. By using similarity variables, the partial differential equation which governs the said model was converted into a nonlinear ordinary differential equation, and numerical results are achieved by applying the shooting technique. The paper describes and addresses all numerical outcomes, such as for the Skin friction coefficients (SFC), local density of motile microorganisams (LDMM) and the local number Nusselt (LNN). Furthermore, the effects of the buoyancy force number, bioconvection Lewis parameter, bioconvection Rayleigh number, bioconvection Pecelt parameter, thermophoresis and Brownian motion are discussed. The outcomes of the study ensure that the stretched surface has a unique solution: as Nr (Lb) and Rb (Pe) increase, the drag force (mass transfer rate) increases respectively. Furthermore, for least values of Nb and all the values of Nt under consideration the rate of heat transfer upsurges. The data of SFC, LNN, and LDMM have been tested utilizing various statistical models, and it is noted that data sets for SFC and LDMM fit the Weibull model for different values of Nr and Lb respectively. On the other hand, Frechet distribution fits well for LNN data set for various values of Nt.

Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications.