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This study investigates the flow of Jeffrey nanofluid through the gap between a disk and a cone, incorporating the influences of thermophoresis and Brownian motion within the flow system. Suitable variables have used to convert the modeled equations to dimension-free notations. This set of dimensionless equations has then solved by using Levenberg Marquardt Scheme through Neural Network Algorithm (LMS-NNA). In this study, it has been observed that the absolute error (AE) between the reference and target data consistently falls in the range 10-4 to 10-5 demonstrating the exceptional accuracy performance of LMS-NNA. In all four scenarios it has noticed that transverse velocity distribution has declined with augmentation in magnetic and Jeffery fluid factors by keeping all the other parameters as fixed. It is evident that the optimal validation performance 2.8227×10-9 has been achieved at epoch 1000 for the transverse velocity when cone and disk gyrating in opposite directions.

This study examines the generation of irreversibility and the behavior of stagnation point hybrid nanofluid flow on a Riga plate. The effects of nonlinear thermally convective and solar radiation are incorporated in the modeled equations. The nanoparticles of (Cu) and (Al2O3) are mixed with Glycol (C3H8O2) to hybridized it. The leading equations have been changed to dimension-free form by using the set of appropriate variables and then have been evaluated by Artificial Neural Network (ANN) approach. It is revealed in this work that, the velocity panels are amplified with expansion in Grashof number and electromagnetic factor while declined with escalation in magnet/electrode factor and nanoparticles concentration. Upsurge, in Eckert number for both the scenarios (Ec < 0) and (Ec > 0), the radiation factor and nanoparticles concentration cause augmentation in thermal characteristics. Radiation factor has positive impacts on Bejan number and generation of Entropy. Moreover, Bejan number is retarded while entropy is augmented with growth in Brinkman number. It is also established in this work that the principle of entropy generation for hybrid nanoparticles supports the efficient delivery of drug in cancer treatment.

Abstract Low-carbon steel (AISI 1010) is the predominant material used in industrial food processing equipment. Such equipment is vulnerable to the corrosive environment produced by various production stages. Different processes, such as sulphonation and carbonation, are used in the processing of sugar in the sugar industry, creating a corrosive atmosphere. The corrosion behavior of low carbon steel (AISI 1010) is strongly influenced by grain size variations, which in turn affect the microstructural mechanical properties of the material. The mechanical behavior and performance of metallic materials, including their corrosion resistance, is determined by grain size which is an important parameter for this phenomena. The impact of low-carbon steel (AISI 1010) microstructure on corrosion behavior is discussed in this work. Heat treatment produces two different types of microstructure from the same material, which are then analyzed. Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) have both been used to study characteristics including morphology and content. By supplying an appropriate corrosive medium, the corrosion performance of several microstructures of low-carbon steel (AISI 1010) was assessed, and corrosion rates were calculated using weight-loss and electrochemical techniques. Results show that the creation of a protective coating with a higher charge transfer resistance is caused by the adsorption process. The variety in phases and grain sizes may contribute to the corrosion stability of different microstructures, and as a result, the corrosion rate lowers as average grain sizes are reduced. Employing the galvanic effect, pearlite increases the rate of ferrite corrosion. The study's findings support the notion that quenching low-carbon steel (AISI 1010) results in a finer grain structure and greater corrosion resistance.

The present work investigates the impacts of the Lorentz forces, porosity factor, viscous dissipation and radiation in thermo-Marangoni convective flow of a nanofluids (comprising two distinct kinds of carbon nanotubes (CNTs)), in water (H2O). Heat transportation developed by Marangoni forces happens regularly in microgravity situations, heat pipes, and in crystal growth. Therefore, Marangoni convection is considered in the flow model. A nonlinear system is constructed utilizing these assumptions which further converted to ordinary differential equations (ODEs) by accurate similarity transformations. The homotopic scheme is utilized to compute the exact solution for the proposed system. The study reveals that higher estimations of Hartmann number and Marangoni parameter speed up the fluid velocity while the opposite behavior is noted for porosity factor. Further, the rate of heat transfer shows upward trend for the Hartmann number, Marangoni parameter, nanoparticle solid volume fraction, radiation parameter whereas a downward trend is followed by the Brinkman number and porosity factor. It is fascinating to take observe that contemporary analytical outcomes validate the superb convergence with previous investigation.

Copper (Cu) nanoparticles (NPs) and polyvinyl alcohol (PVA) are utilized to enhance heat transfer (HT) which is used in the efficiency of solar energy systems. Copper nanoparticles have excellent thermal conductivity (TC) properties that enable them to conduct heat efficiently. In this arrangement, the gap between the two cylindrical channels is settled for the hybrid nanofluids (HNFs) flow in an inclined position that is favourable to sunlight. The nanomaterials consist of a mixture of PVA and Cu nanoparticles (NPs), to execute HNFs. Solar radiation is present on the hot side of the system. The porous gap between the two channels is considered variable which plays a crucial role in enhancing heat transfer and energy conversion. The varying permeability of the gap is adjusted to control the flow resistance and improve the stability of the system. It is observed that higher porosity allows for better convective heat transfer and reduced pressure drop. The transformed equations are solved through an artificial neural network (ANN) while the control volume finite element method (CVFEM) is also used to handle the governing equations. The Cu and PVA (HNF) improves solar radiation absorption and protects components, ultimately increasing the performance and efficiency of the systems.

ABSTRACTIn this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem’s consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system’s numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified.

In a recent study, researchers investigated the flow behavior of Casson Hybrid nanofluids (HNFs) combination of single and multi-walled carbon nanotubes (SWCNTs), (MWCNTs) on a Riga plate for drug delivery applications. The study found that the Casson HNFs exhibited non-Newtonian behavior on the Riga plate, with the presence of nanoparticles causing an increase in viscosity and shear-thinning behavior. This rheological behavior is favorable for drug delivery applications as it improves the stability and dispersion of drug particles in the fluid. The similarity equations of the flow problem are easily tackled with the homotopy analysis method (HAM) built on fundamental homotopy mapping. In high-speed flows, Riga actuators are expected to achieve the requirements, since HNF is enhanced by modified Hartmann numbers. As the Eckert number, heat generation/absorption parameter, and thermal relaxation time parameter decrease the temperature, thermal transport increases. Furthermore, with the increments in paramount parameters, the skin friction coefficient and heat transfer rate are remarkably meliorated under higher modified Hartmann number. Furthermore, the study also found that the Casson Hybrid nanofluids showed enhanced heat transfer properties on the Riga plate, which is beneficial for localized drug delivery applications that require precise temperature control.

Abstract This study explores the impacts of heat transportation on hybrid (Ag + MgO) nanofluid flow in a porous cavity using artificial neural networks (Bayesian regularization approach (BRT-ANN) neural networks technique). The cavity considered in this analysis is a semicircular shape with a heated and a cooled wall. The dynamics of flow and energy transmission in the cavity are influenced by various features such as the effect of magnetize field, porosity and volume fraction of nanoparticles. To explore the outcomes of these features on hybrid nanofluid thermal and flow transport, a BRT-ANN model is developed. The ANN model is trained using a dataset generated through numerical scheme. The trained ANN model is then used to predict the heat and flow transport characteristics for various input parameters. The accuracy of the ANN simulation is confirmed through comparison of the predicted results with the results obtained through numerical simulations. By maintaining the corrugated wall uniformly heated, we inspected the levels of isotherms, streamlines and heat transfer distribution. A graphical illustration highlights the characteristics of the Hartmann and Rayleigh numbers, permeability component in porous material, drag force and rate of energy transport. According to the percentage analysis, nanofluids (Ag + MgO/H2O) are prominent to enhance the thermal distribution of traditional fluids. The study demonstrates the potential of ANNs in predicting the impacts of various factors on hybrid nanofluid flow and heat transport, which can be useful in designing and optimizing heat transfer systems.

This article focuses on discrete survival data analysis, employing a doubly Type-I censoring scheme (DT1SC) under a Bayesian framework for parameters estimation in a 3-component mixture geometric (3-CMG) distribution. The non-informative (uniform) prior is utilized under squared error, DeGroot, and precautionary loss functions. The time is considered as discrete in this paper, presenting a departure from continuous approaches in survival analysis. The methodology is tailored to address challenges that traditional survival analysis encounters when faced with limited or missing information. The proposed method effectively handles the complexities arising from incomplete or missing data, providing a robust mechanism for accurate parameter estimation. Through extensive simulations and application to real-world datasets, our approach demonstrates its effectiveness in managing uncertainties, particularly in scenarios involving sparse or missing data. This work represents a noteworthy contribution to methodological advancements in survival analysis, offering a valuable tool for researchers and practitioners navigating intricate dynamics within the 3-CMG under DT1CS with time being considered as discrete.

In the present analysis, the stagnation point flow model is employed to evaluate the energy transient across the nanofluid using the comparative analysis. The consequences of slip surface are engaged to the momentum equation, to assess the lubrication. Hybride nanofluid has been synthesized by the dispersion of silver (Ag) and Titanium oxide (TiO2), in two different solvents (H2O and C2H6O2), having a great deal of interest in the field of advancement and innovation. The flow mechanism is formulated in the form of a nonlinear set of PDEs with an additional impact of a magnetic field, thermal radiation, and natural convection.As a principal contribution, a specific type of thermophysical model based on thermal conductivity and viscosity is used in the present study with slip boundary conditions. The modeled system of equations is processed by the Numerical Runge Kutta (RK-4) procedure. The accuracy of the observation is checked using the control volume finite element method (CVFEM). The influence of Cf and Nu is estimated according to the characteristics of the flow rate. Drag force and heat transmission velocity are displayed for optimization with the modeled parameters. The results are authenticated by prior studies and a decent level of coherence is demonstrated.

Abstract Advanced techniques are used to enhance the efficiency of the energy assets and maximize the appliance efficiency of the main resources. In this view, in this study, the focus is paid to the solar collector to cover thermal radiation through optimization and enhance the performance of the solar panel. Hybrid nanofluids (HNFs) consist of a base liquid glycol (C3H8O2) in which nanoparticles of copper (Cu) and aluminum oxide (Al2O3) are doped as fillers. The flow of the stagnation point is considered in the presence of the Riga plate. The state of the solar thermal system is termed viva stagnation to control the additional heating through the flow variation in the collector loop. The inclusion of entropy generation and Bejan number formation are primarily conceived under the influence of physical parameters for energy optimization. The computational analysis is carried out utilizing the control volume finite element method (CVFEM), and Runge–Kutta 4 (RK-4) methods. (FEATool Multiphysics) software has been used to find the solution through (CVFEM). The results are further validated through a machine learning neural networking procedure, wherein the heat transfer rate is greatly upgraded with a variation of the nanoparticle's volume fraction. We expect this improvement to progress the stability of heat transfer in the solar power system.

Abstract The flow at a time-independent separable stagnation point on a Riga plate under thermal radiation and electro-magnetohydrodynamic settings is examined in this research. Two distinct base fluids-H2O and C2H6O2 and TiO2 nanostructures develop the nanocomposites. The flow problem incorporates the equations of motion and energy along with a unique model for viscosity and thermal conductivity. Similarity components are then used to reduce these model problem calculations. The Runge Kutta (RK-4) function yields the simulation result, which is displayed in graphical and tabular form. For both involved base fluid theories, the nanofluids flow and thermal profiles relating to the relevant aspects are computed and analyzed. According to the findings of this research, the C2H6O2 model heat exchange rate is significantly higher than the H2O model. As the volume percentage of nanoparticles rises, the velocity field degrades while the temperature distribution improves. Moreover, for greater acceleration parameters, TiO2/ C2H6O2has the highest thermal coefficient whereas TiO2/ H2O has the highest skin friction coefficient. The key observation is that C2H6O2 base nanofluid has a little higher performance than H2O nanofluid.

Abstract This study looks at the natural convections of Cu + Al2O3/H2O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties.

The potential of hybrid nanofluid (HNF) to maximize heat transportation has captured the attention of many researchers, inspiring them to further investigate the performance of the common base fluid. Conventional flow in Cu-Al 2 O 3 /H 2 O hybrid nanofluid (HNF) toward a high permeability horizontal flat plate incorporated in Darcy porous medium has been explored in this research to determine how Cu-Al 2 O 3 /H 2 O hybrid fluid will respond thermodynamically when physical factors like suction/injection and slip boundary conditions are present. In addition, the effects of radiation, dissipations, energy engagement, and inclined magnetized field associated with the fluid flow were studied. The governing system is transformed by similarity transformations to a solvable ordinary differential equation by employing HAM (Homotopy Analysis Method) scheme. The main results show that Cu-Al 2 O 3 /H 2 O has high thermal conductivity compared to Cu/H 2 O. As a result, hybrid fluids are essential for the development of thermal phenomena.

Abstract In the pump of different machines, the vacuum pump oil (VPO) is used as a lubricant. The heat rate transport mechanism is a significant requirement for all industries and engineering. The applications of VPO in discrete fields of industries and engineering fields are uranium enrichment, electron microscopy, radio pharmacy, ophthalmic coating, radiosurgery, production of most types of electric lamps, mass spectrometers, freeze-drying, and, etc. Therefore, in the present study, the nanoparticles are mixed up into the VPO base liquid for the augmentation of energy transportation. Further, the MHD flow of a couple stress nanoliquid with the applications of Hall current toward the rotating disk is discussed. The Darcy-Forchheimer along with porous medium is examined. The prevalence of viscous dissipation, thermal radiation, and Joule heating impacts are also considered. With the aid of Cattaneo-Christov heat-mass flux theory, the mechanism for energy and mass transport is deliberated. The idea of the motile gyrotactic microorganisms is incorporated. The existing problem is expressed as higher-order PDEs, which are then transformed into higher-order ODEs by employing the appropriate similarity transformations. For the analytical simulation of the modeled system of equations, the HAM scheme is utilized. The behavior of the flow profiles of the nanoliquid against various flow parameters has discoursed through the graphs. The outcomes from this analysis determined that the increment in a couple-stress liquid parameter reduced the fluid velocity. It is obtained that, the expansion in thermal and solutal relaxation time parameters decayed the nanofluid temperature and concentration. Further, it is examined that a higher magnetic field amplified the skin friction coefficients of the nanoliquid. Heat transport is increased through the rising of the radiation parameter.

The study of well-known Darcian fluidic streams and hybrid nanofluids is an essential need of nowadays researchers in regard to their exceptional heat transfer rates and implementations. The significance of hybrid nanofluids in controlling heat transmission cannot be overemphasized. Therefore, this article scrutinizes the Darcy Forchheimer flow of hybrid nanofluid toward a flexible tube. The flow rates near the surface of the cylinder are investigated by applying the Darcy-Forchheimer theory while examining the heat transfer rate, nonlinear convection expressions are used. The analysis also considers thermal radiation and chemical reactions. One of sophisticated numerical approach Runge–Kutta method (RK4) is selected for the proposed problem’s solution. The main novelty of present research is to examine the characteristics of hybrid nanofluids in the context of heat transfer over an extending cylinder for the purposes of enhancement regarding thermal transference and inertial impacts. Results shows that hybrid-based nanofluid provides upsurges in solid volume fraction of nanoparticles accompanied by an enhancement in the heat transfer rate by 4.32%, 5.8%, and 14.46% individually. The outcomes witnessed that hybrid based proposed nanofluids increased thermal transportation processes more effectively than other nanofluids.

The current investigation employs a numerical simulation to demonstrate the impact of hall current on unsteady free convective flow caused by hybrid-nanofluid over a revolving sphere approaching the stagnation point. The prominent characteristics of Lorentz force as a result of magnetic field coupling with hybrid nanofluid is also explored. The process of energy and mass transmission is inspected with nonlinear thermal radiations, non-uniform energy supply, dissipation and nonlinear chemical reaction. In current flow model, a unique class of nanofluid known as the hybrid nanofluid is being used, which contain GO (graphene oxide) and MoS2 (molybdenum disulfide) with water. The angular speed of both the sphere and free stream changes frequently with time. Employing adequate dimensionless variables, the partial-differential patterns strongly non-linear that represent the situational analysis are morphed into non-linear ordinary differential patterns. The analytical outcomes of ordinary differential pattern have been developed via OHAM technique. Utilizing tables and graphs, various aspects of such controllable physical characteristics have been highlighted and explored in depth. For varying values of M,φ,δ,Sc and Kn,the variations in Cfx, Cfz,Nu and Sh in MoS2-GO/H2O are the greatest as contrasted to MoS2/H2O. The results are also compared to those reported existing literature and they are noticed to be in very close agreement.

The subject of discussion in this analysis is the time independent flow of electrically conducting nanofluid with entropy generation over a radially flexible disk. Considerations for magnetic fields, nonuniform heat generation, Darcy-Forchheimer porous space, dissipation, Ohmic heating and chemical reactions with activation energy are incorporated into the flow distribution. For a number of engineering and biomedical objectives, a mathematical model is introduced with the goal of accelerating the rate of energy transmission and improving the performance and efficiency of heat energy transportation. Titanium dioxide nanomaterial is consisting of two base fluid, water and ethylene glycol (EG), to synthesize the nanofluid (water/TiO2 and ethylene EG/TiO2). Additionally, the second thermodynamic law has been used to model entropy generation. This model takes into account the irreversibility of heat, fluid friction and joule dissipation processes. The problem has been modeled as a set of partial differential equations. That are streamlined into a system of ODEs by using similarity substitutions. The retrieved differential equations are then assessed utilizing computational approach HAM. For consistency and validity, the results are examined using numerical methodology (shooting method). Also, investigations are conducted into the effects of the radiation, magnetic factors, Brinkman number, volume fraction of nanoparticles on the entropy and Bejan number. Moreover, visually and computationally, the impacts of design variables on the movement, temperature and concentration profile, drag force, heat and mass flux rate are explored. The findings exhibit great comparability when examined to those of the articles that were previously published. The planned analysis demonstrates the significance of this nanofluids in industrial, pharmaceutical, chemical and nuclear plants as well as solar and other technologies.

Abstract The energy transmission through micropolar fluid have a broad range implementation in the field of electronics, textiles, spacecraft, power generation and nuclear power plants. Thermal radiation's influence on an incompressible thermo-convective flow of micropolar fluid across a permeable extensible sheet with energy and mass transition is reported in the present study. The governing equations consist of Navier–Stokes equation, micro rotation, temperature and concentration equations have been modeled in the form of the system of Partial Differential Equations. The system of basic equations is reduced into a nonlinear system of coupled ODE's by using a similarity framework. The numerical solution of the problem has been obtained via PCM (Parametric Continuation Method). The findings are compared to a MATLAB built-in package called bvp4c to ensure that the scheme is valid. It has been perceived that both the results are in best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, energy and mass profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise in micro-rotation profile.

The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors.

Nonlinear thermal transport of non-Newtonian polymer flows is an increasingly important area in materials engineering. Motivated by new developments in this area which entail more refined and more mathematical frameworks, the present analysis investigates the boundary-layer approximation and heat transfer persuaded by a symmetrical cylindrical surface positioned horizontally. To simulate thermal relaxation impacts, the bioconvection Cross nanofluid flow Buongiorno model is deployed. The study examines the magnetic field effect applied to the nanofluid using the heat generated, as well as the melting phenomenon. The nonlinear effect of thermosolutal buoyant forces is incorporated into the proposed model. The novel mathematical equations include thermophoresis and Brownian diffusion effects. Via robust transformation techniques, the primitive resulting partial equations for momentum, energy, concentration, and motile living microorganisms are rendered into nonlinear ordinary equations with convective boundary postulates. An explicit and efficient numerical solver procedure in the Mathematica 11.0 programming platform is developed to engage the nonlinear equations. The effects of multiple governing parameters on dimensionless fluid profiles is examined using plotted visuals and tables. Finally, outcomes related to the surface drag force, heat, and mass transfer coefficients for different influential parameters are presented using 3D visuals.

Abstract Fractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano liquid consisting of TiO2 and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO2 nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one.

Abstract The current study provides a detailed analysis of steady two-dimensional incompressible and electrically conducting magnetohydrodynamic flow of a couple stress hybrid nanofluid under the influence of Darcy–Forchheimer, viscous dissipation, joule heating, heat generation, chemical reaction, and variable viscosity. The system of partial differential equations of the current model (equation of motion, energy, and concentration) is converted into a system of ordinary differential equations by adopting the suitable similarity practice. Analytically, homotopy analysis method (HAM) is employed to solve the obtained set of equations. The impact of permeability, couple-stress and magnetic parameters on axial velocity, mean critical reflux condition and mean velocity on the channel walls are discussed in details. Computational effects show that the axial mean velocity at the boundary has an inverse relation with couple stress parameter while the permeability parameter has a direct relation with the magnetic parameter and vice versa. The enhancement in the temperature distribution evaluates the pH values and electric conductivity. Therefore, the $$SWCNTs\,\,{\text{and}}\,\,MWCNTs$$ S W C N T s and M W C N T s hybrid nanofluids are used in this study for medication purpose.

The study of fluid dynamics due to the stretching surface is one of the most eminent topics due to its potential industrial applications viz. drawing wire and plastic films, metal and polymer extrusion, fiber and glass production. In the present article, the author is going to study the effects of hybrid nanofluids flow on an inclined plate including CuO (Copper Oxide), and Cu (Copper). The Casson fluid with a couple-stress term has been used in the flow analysis. The surface of the plate is considered slippery. The convection has been taken nonlinear with thermal radiation. The governing equation of the flow of hybrid nanofluids with energy equation has been transformed into highly nonlinear ODEs through similarity transformation. The proposed model has been solved through a numerical RK-4 method. Significant variables of the physical process such as solar radiation, nonlinear convection parameters, heat transfer rates, and their effect on the solar power plant have been noticed.

Due to their accelerated rate of heat transfer, nanofluids are of immense interest. This work analyzes an innovative concept of hybrid nanoemulsion with an optimized design under the chemical radiative flow and its thermophysical properties. We are able to achieve great aspects of the flow with the assistance of the sheet’s permeable texture and inclined surface. Furthermore, the effects of thermal conductivity mix convection, chemical reaction, and thermal radiations on velocity, temperature, and concentration fields are also investigated. After converting the fundamental equations to ordinary differential equations with the use of similarity transportation, the problem is then solved analytically with the HAM technique. To investigate key attributes and parameters, a hybrid nanofluid with Ag and Al2O3 nanoparticles as well as Al2O3 for conventional nanofluids with the base solvent water is taken. To illustrate the effects of chemical radiative and mix convection on the thin-film flow, numerous graphs, charts, and tables are shown. Calculations and reviews are performed for reduced friction coefficient, heat, and mass transportation. According to this study, hybrid nanofluids have a higher heat-transfer rate than nanofluids when exposed to thermal radiation and at the appropriate surface angle of inclination. Due to ϕAl2O3, ϕAg,S, Rd, the temperature increases, but velocity has the opposite effect. This investigation’s innovative findings will promote the study of condensed nanostructures and nanomaterials.

Abstract To enhance the surface properties of solids the mechanism of thin films is frequently used. Penetration, degradation, stiffness, illumination, diffusion, absorption, and electric performance are all characteristics of a bulk substance medium that a thin film can improve. In nanotechnology, thin film processing can be extremely useful. Therefore, the time-dependent nonlinearly convective stream of thin film nanoliquid over an inclined stretchable sheet with magnetic effect is investigated in current work. The features of mass and heat transport processes are explained using important factors like thermophoresis and Brownian movement. Nonlinear partial differential equations are obtained to model the time-dependent liquid film flow over an inclined surface, which are then turned into couple ordinary differential equations utilizing appropriate alterations. The results of the computation of the model problem are collected using an analytical approach Homotopy Analysis Method and presented the final finding numerically and graphically. During the flow assessment, the impact of individual flow factors such as magnetic, Brownian, and thermophoresis parameters on regular profiles (temperature, velocity, and concentration) are analyzed and found to be quite remarkable. Furthermore, the consequence of M and Nt factors on the velocity, concentration and thermal distribution leads to diminishing conduct. On the other hand, the thermal profile of the liquid film rises in response to the thermophoresis factor. The % wise variation in the skin friction, Nusselt number and Sherwood number versus physical parameters has been obtained and discussed.

Abstract This investigation describes the hydromagnetic flow of gravity-driven couple stress hybrid nanofluid past a heated plate. The carbon nanotubes (CNTs) are used to characterize the hybrid nanofluid. The heated plate is placed vertically with an application of homogenous-heterogeneous reactions to the assumed flow system. The homogeneous reaction governs by isothermal cubic autocatalytic kinetics while the heterogeneous reaction governs by the first order kinetics. For current study the couple stress hybrid nanofluid is presumed to be conducted electrically with impact of non-uniform magnetic effects. An appropriate set of dimensionless quantities has employed to governing equations and then has solved by homotopy analysis method. The influence of emerging parameters encountered in this work has discussed in detail with the help of graphs. In this study it has examined that, flow of fluid reduces with upsurge in magnetic parameter and volumetric concentrations, whereas thermal and concentration characteristics augment with increase in volumetric concentrations. Moreover, growth in Prandtl number leads to a reduction in thermal characteristics and growth in Schmidt number result a reduction in concentration profile. The impact of various emerging parameters has also studied numerically upon physical quantities. It has established that, with augmentation in values of buoyancy parameter there is a growth in the values of skin friction. A comparison has also carried out between current and established results with a fine agreement in both results.

Abstract In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

Abstract This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid $$f^{\prime}\left( \xi \right),g\left( \xi \right)$$ f ′ ξ , g ξ are decayed for high values of $$\phi_{1} ,\phi_{2} ,\,Fr$$ ϕ 1 , ϕ 2 , F r and $$k_{1}$$ k 1 factors.

This paper explores the numerical optimization of heat and mass transfer in the buoyancy-driven Al2O3-water nanofluid flow containing electrified Al2O3-nanoparticles adjacent to a symmetrically-vertical plane wall. The proposed model becomes a set of nonlinear problems through similarity transformations. The nonlinear problem is solved using the bvp4c method. The results of the proposed model concerning heat and mass transfer with nanoparticle electrification and buoyancy parameters are depicted in the Figures and Tables. It was revealed that the electrification of nanoparticles enhances the heat and mass transfer capabilities of the Al2O3 water nanoliquid. As a result, the electrification of nanoparticles could be an important mechanism to improve the transmission of heat and mass in the flow of Al2O3-water nanofluids. Furthermore, the numerical solutions of the nanofluid model of heat/mass transfer using the deep neural network (DNN) along with the procedure of Bayesian regularization scheme (BRS), DNN-BRS, was carried out. The DNN process is provided by taking eight and ten neurons in the first and second hidden layers along with the log-sigmoid function.

The goal of this research is to examine how a magnetic field affects the unsteady flow of a hybrid nanofluid over a spinning disk that is inclined and stretched while the flow is surrounded by a non-Darcy porous medium. Furthermore, for heat transmission mechanisms, Joule heating and viscous dissipation are considered. The current article is made more realistic by imposing thermal radiation to enhance the heat transmission system under the effects of convection. Moreover, thermal and velocity slip conditions have also been incorporated into the current study. The equations that administer the flow problem along with constraints at the boundaries are converted to dimension-free form by employing a set of appropriate similarity transformations, which are then solved by the numerical technique Runge-Kutta method of order four (RK-4). The new and advanced trend for the convergence of the obtained results is validated through a neural networking approach. The temperature of hybrid nanofluid is augmented by an increase in the porosity parameter, the unsteadiness factor, the Eckert number, the magnetic field, and the Forchheimmer number, while for the values of the radiation factor, the thermal heat is decreasing near the disk and increasing away from the disk. The precision of the obtained results has been ensured by comparing them with established results, with good agreement among these results.

Abstract The current study focuses on the laminar flow of copper and copper oxide ( $${\text{Cu/blood}}$$ Cu/blood and $${\text{Cu}} + {\text{CuO/blood}}$$ Cu + CuO/blood ) hybrid nanoliquid, considering blood as a carrier fluid in a rectangular domain between two permeable channels. This study may manipulate for the purpose such as the drug delivery process, flow dynamic mechanism of the micro-circulatory system. In the proposed model, MHD and heat source/sink on the flow pattern have been studied. Furthermore, the sides of each channel are permeable, allowing the nanoliquid to escape, filter, squeezing and dilating with a fixed velocity. Appropriate transformations are incorporated to convert the governing partial differential equations and the boundary conditions suitable for computation. The elegant homotopy analysis method (HAM) is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The features of flow characteristics such as velocity, and temperature profiles in response to the variations of the emerging parameters are simulated and examined with a physical explanation. The magnetic field plays a vital role in the blood flow and therefore the existing literature has been extending with the addition of magnetic field. Among the many outputs of the study, it is found that the pressure distribution decline with the accumulated values of the magnetic parameter at the center of the flow regime. The augmentation in the temperature distribution estimates the pH values and electric conductivity. Therefore, the $${\text{Cu}}\,\,{\text{and}}\,\,{\text{CuO}}$$ Cu and CuO hybrid nanofluids are used in this study for medication purposes. The magnetic field has an important role in the blood flow and therefore the extending study has been extending using the magnetic field. The heat emission/absorption term is added to the energy equation to maintain the homogeneous temperature for the blood flow. We expect that this work will provide efficient outputs for medical purposes such as drug delivery.

Abstract In this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative characteristics and aims of this work are to note that the transportation heat couple stress model involves EMHD, viscous dissipation, Joule heating, and heat absorption, and omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in pure human blood. This mathematical model is an appropriate model for biological advantages including testing of human blood for drug deliveries to various parts of the human body. Particularly, the Prandtl number used for the blood is 21 and very large as compared to the other base fluids. Necessary modifications are used to translate the defining partial differential equations and boundary conditions into a layout that can be computed. To obtain mathematical approximations for the resulting scheme of nonlinear differential equations, the innovative homotopy analysis method (HAM) is used. The explanation for velocity, energy, and entropy are exposed and the flow against various influential factors ( $$E,\;M,\;k,\;Q,\;S\;{\text{and}}\;Ec$$ E , M , k , Q , S and E c ) is discussed graphically. The numerical values are calculated and summarized for dimensionless $$C_{{fx}} \;{\text{and}}\;Nu_{x} .$$ C fx and N u x . In addition, the current study is compared for various values of $$\Pr$$ Pr to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the $$M$$ M and $$E$$ E factors retard the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors. 11.95% enhancement in the heat transfer rate has been attained using the hybrid nanofluids.

Abstract In the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

Abstract In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper $$\left( {Cu} \right)$$ Cu and Alumina $$\left( {Al_{2} O_{3} } \right)$$ A l 2 O 3 are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

Abstract In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, $${\text{TiO}}_{2} \,\,{\text{and}}\,\,{\text{Ag}}$$ TiO 2 and Ag as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both $${\text{TiO}}_{2} + {\text{Ag}} + Blood$$ TiO 2 + Ag + B l o o d and $${\text{TiO}}_{2} + Blood$$ TiO 2 + B l o o d . One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.

Nanofluids play a prominent role in the development of various electronic structures and technological devices. Herein, we devise new and efficient techniques for overcoming the problems faced by the base fluids. This article describes water-based carbon nanotubes, including two major types of single-wall carbon nanotubes (SWCNT) and multi-wall carbon nanotubes (MWCNT). A mathematical model is considered for unsteady three-dimensional CNTs nanofluids flow with a uniform magnetic field between two revolving disks. The basic equations of the modeled flow problem are solved by the BVPh 2.0 package which is implemented using the Optimal Homotopy Analysis Method (OHAM). It has been observed that by stretching the top disk while keeping the lower disk stationary, the rotation aspect is reduced, whilst radial velocity near the top disk significantly increases. Moreover, The higher the values of unsteadiness parameter, the more accurate the temperature profile.

Abstract The magnetohydrodynamic hybrid second-grade nanofluid flow towards a stretching/shrinking sheet with thermal radiation is inspected in current work. Main concern of current investigation is to consider hybrid $$Al_{2} O_{3} - Cu$$ A l 2 O 3 - C u nanofluid which is perceived by hanging two dissimilar kinds of nanoparticles known as alumina and copper within the base fluid. The fluid motion is produced by non-linear stretching/shrinking sheet. The modeled equations which comprise of energy, motion and continuity equations are changed into dimensionless form using group of similar variables. To determine the solution of transformed problem, the Homotopy Analysis technique is used. The findings of this work revealed that the magnetic parameter improves the heat transfer rate. This work also ensures that there are non-unique solutions of modeled problem for shrinking case and a unique solution for stretching case. Higher values of $${\text{Re}}_{x}$$ Re x results in declining of flow field. Rise in $$M$$ M agrees to a decline in velocity distributions. Higher values of second order fluid parameter reduces the viscosity of fluid and accordingly velocity increases. Velocity profile is also a decreasing function of volume friction.

Abstract The thermal management of the flow of the hybrid nanofluid within the conical gap between a cone and a disk is analyzed. Four different cases of flow are examined, including (1) stationary cone rotating disk (2) rotating cone stationary disk (3) rotating cone and disk in the same direction and (4) rotating cone and disk in the opposite directions. The magnetic field of strength $$B_{0}$$ B 0 is added to the modeled problem that is applied along the z-direction. This work actually explores the role of the heat transfer, which performs in a plate-cone viscometer. A special type of hybrid nanoliquid containing copper Cu and magnetic ferrite Fe 3 O 4 nanoparticles are considered. The similarity transformations have been used to alter the modeled from partial differential equations (PDEs) to the ordinary differential equations (ODEs). The modeled problem is analytically treated with the Homotopy analysis method HAM and the numerical ND-solve method has been used for the comparison. The numerical outputs for the temperature gradient are tabulated against physical pertinent variables. In particular, it is concluded that increment in volume fraction of both nanoparticles $$\left( {\phi_{{Fe_{3} O_{4} }} ,\phi_{Cu} } \right)$$ ϕ F e 3 O 4 , ϕ Cu effectively enhanced the thermal transmission rate and velocity of base fluid. The desired cooling of disk-cone instruments can be gained for a rotating disk with a fixed cone, while the surface temperature remains constant.

This study aims to show the role of the stagnation point flow in solar optimization in the presence of a Riga plate. This requirement is conceivable in the case of solar energy management with a suitable solar collector covering and visual thermal optimization. Solar energy radiation and thermal convection of glycol (C3H8O2)-based aluminum oxide (Al2O3) and copper (Cu) nanoparticles were used for a solar collector, and were studied in terms of the stagnation point flow theoretically. Stagnation refers to the state of a solar thermal system in which the flux varies in the collection loop to control the extra heating. The CVFEM code was used to analyze the flow in the case of represented stagnation using the FEA-Tools multiple physics software that manages partial derivative equations (PDEs). The streamlined patterns and energy contours for different cases were studied in detail. The transformation equations were treated with the numerical method (RK-4 technique) and showed strong agreement of the physical results corresponding to the initial conditions and boundaries. The results showed that hybrid nanofluids have the advanced capability to enhance the thermal performance of the base solvent and provide uniform distribution to the solar panel. The solar optimization and uniform thermal expansion results are displayed graphically.

This study explored the Darcy Forchheimer flow of Casson hybrid nanofluid (NF) via a persistently stretching curved surface. The Darcy-Forchheimer contribution articulates viscous fluid flow in permeable media. Hybrid nanofluids are made from carbon nanotubes (CNTs) having a cylindrical shape and iron ferrite nanoparticulate. The main equations are reorganized into non-dimensional ODEs via similarity replacement. To accomplish the analytic simulation of modeled equations, the “Homotopy analysis approach” is performed. The effects of flow factors on velocity and energy profiles have been tabulated and discussed. It has been noticed that the integration of iron ferrite and CNT nanoparticulate in the base fluid to control the coolant level in industrial apparatus is quite useful. The energy field ascension effect is helpful for industrial uses since the energy fields exhibit favorable behavior against rising values of both type of nanomaterials. The Casson constraint’s rising values decline the hybrid NF motion.

Investigations are performed for further observations of heat and mass transfer in magneto-hydrodynamic mixed-convectional nano-fluid flow with the assumption of variable viscosity and thermal-conductivity over an unsteady stretching sheet. Base fluid is Carboxy-methyl cellulose (CMC) water as a carrier fluid with different nano-particles such as Ti O 2 (Titanium), Ag (Silver), A l 2 O 3 (Aluminum), and Cu (Copper). Flow contains different physical parameters, such as heat source, chemical reaction effect, Schmidt number, and radiation absorptions effects are observed to be significant in the presences of magnetic field. Obtained equations are solved by numerically BVP4C-package (shooting method) and analytically by BVPh2.0-package (Homotopy Analysis Method “HAM”). Interested physical quantities are, viscosity-parameter ( A ), Thermal-conductivity parameter ( N ),Thermocapillary-number ( M ), Hartmann-number (Ma), Prandtl-number (Pr), 4-nano-particles ( ϕ ), temperature Grashof number ( G r t ), and mass Grashof number ( G r c ) are the focus to the velocity, temperature, and solute concentration profiles. It is concluded that, Solute concentration of ( A l 2 O 3 )-water has higher than the other 3-nano-fluids. Mass flux, heat flux, and Skin friction of fluids are direct functions of magnetic force, while inverse function of temperature. Magnetic force also decreased the speed of fluids and hence mass flux reduced which implies that, the temperature reduces. G r t has also inverse relation with mass flux, heat flux, and skin friction, while direct relation with the speed of fluids. Similarly, G r c has inverse relation with − Φ ′ ( 0 ) , − θ ′ ( 0 ) , and − f ″ ( 0 ) , but direct relation with θ ( 1 ) . Different results are shown in graphical and tabular form.

In the present analysis, the thin film flow of Carreau fluid under the consequences of uniform magnetic field over an extending substrate has been addressed. Marangoni convection and couple stress has been also considered to find the fine point of the flow. The intention behind this work is to enhance the energy and mass transmission rate over a stretching sheet. The phenomena have been modeled in the form of system of PDEs, which are reduced to dimensionless system of ODEs through the similarity approach. The results are obtained via analytical framework homotopy analysis method (HAM). The behavior of velocity, energy and mass transmission profile has been disclosed through Figures and Tables. It has been perceived that the fluid velocity declines with the improvement of magnetic field, Marangoni parameter, unsteadiness term, thin film parameter, Weissenberg number We2and couple stress parameter K. The thermal energy transmission rate enhances with the consequences of thermophoresis term and Brownian motion factor, while reduces with the effect of Prandtl number.

The recent study concentrates on the liquid film flow considering Oldroyd-B fluid past a rotating disc in three-dimensional space. The flow pattern has been modeled under the effects of heat absorption/omission and radiation terminologies. The activation energy, bio-convectional, and gyrotactic microorganism phenomena are also included in this study. The Von Karman alterations have been used to alter the basic equations into the set of nonlinear differential equations. The elegant homotopy analysis method (HAM) has been used to obtain the solution of the system of nonlinear differential equations. The influence of the emerging parameters is scrutinized with physical descriptions against the flow pattern, temperature distribution, concentration profile, and gyrotactic microorganism. The detailed outcomes in the heat transfer rate, mass transfer, and motile organism due to the variation of physical parameters have also been shown through bar charts and discussed. It is found that the velocity field decline with the augmentation of magnetic parameter, film thickness parameter, time retardation, and relaxation parameters. The heat transfer enhances with the augmentation of radiation and heat absorption/omission parameters while declining with the Prandtl number. The greater magnitude of the Schmidt number declines the concentration profile.

The study of fluid flow around a stretching cylinder has great importance, due to its broad range of applications in engineering and industries. In this article, unsteady incompressible Maxwell nanofluid flow around a stretching cylinder escorted by unfluctuating suction/injection impact has been scrutinized. The Maxwell nanofluid nature is described through Buongiorno's model. The dimensionless system of ODEs is diminished from the system of modeled equations, through a proper similarity transformation. The obtained system of ordinary differential equations is further numerically computed with PCM (Parametric continuation method). For the validity of the results, the outcomes are compared with Matlab package boundary value solver (bvp4c). The physical entities influence on velocity, energy, concentration, and magnetic strength profiles are sketched and discussed. It has been perceived that the momentum of mass transmission is significantly increases with the effects of thermophoresis parameter, while the velocities in angular and radial directions are reducing with enlarging of viscosity parameter. The influences of thermal radiation Rd and Brownian motion are particularly more valuable to enhance the temperature of the fluid. Furthermore, by applying the magnetic field a resistive force is formed, which reduced the velocities and boosted the temperature of the fluid.

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.

A modern development in the field of fluid dynamics emphasizes on nanofluids which maintain remarkable thermal conductivity properties and intensify the transport features of heat in fluids. The present communication provides an innovative idea of MHD (magneto-hydrodynamics) unsteady, incompressible nanoliquid flow due to the stretching rotating disk with the effect of Joule heating and dissipation. The engine oil is used as a carrier fluid for an immersed rotating disk. A special type of nanoliquid, which consists of cylindrical shape nano materials CNTs (Carbon Nanotubes), is being taken into an account. The CNTs are assembled of both single and multi-walled carbon nanotubes. Some other factors such as the effect of joule heating and viscus dispassion are also used in this investigation. The foremost set of PDEs (Partial Differential Equations) of our model is reformed to the dimensionless form via invoking suitable variables. The resultant set of equations is sketched out through RK-4 method. Furthermore, the velocity profile and energy distribution versus dimensionless flow factors have been sketched and discussed. Also, the outcomes of important engineering curiosity like Nusselt number and skin friction are depicted and interpreted by taking various model factors. Radial and transverse velocity fields, declines via M (magnetic factor), while the temperature field enhances. Furthermore, the larger estimation of ϕ and ω leads to enhance the velocity field while higher estimation of S reducing the velocity and temperature fields. The current work has an extensive verity use such as nano-mechanics and electro-magnetic micro pumps.

The study of nanofluid dynamics considering the bioconvection effects has significant applications, because nanofluid has remarkable capabilities for thermal transportation in comparison with pure fluids in various industrial and engineering applications. Keeping in view, such incredible characteristics the main objective of this work is to examine the influence of bioconvective micropolar nanofluid flow over a thin moving needle comprising of gyrotactic microorganism. The flow is also exposed to Arrhenius activation energy, binary chemical reaction and viscous dissipation. The governing equations are transformed to a dimensionless form by making use of a set of suitable variables and solved afterwards by employing homotopy analysis method (HAM). As main outcomes it is established in this work that, flow profiles decline with growing values of buoyancy ratio parameter, material parameter, volume fraction and bioconvection Rayleigh number. Thermal profile grows up with higher values of volumetric fraction, Brownian motion, Eckert number and thermophoretic parameter. Concentration profiles decline with growing values of thermosphoretic parameter, Brownian motion, Lewis number, chemical reaction parameter and grow up for increasing values of activation energy parameter. Moreover, a fine agreement between current results and the results available in literature has also established in current work.

The melting procedure with a direct contact of phase change material is taken into account to consider the porous medium in the presence of a uniform and transverse magnetic field. A permeable rotating disk is taken as a heater in the melting progression of solid phase change material. The three-dimensional melting layer takes place due to the accruing of the temperature difference among the porous disk and solid material. Movement is subject to the effect of pressure loading (counting the weight of solid), direct relation with solid and rotation due to centrifugal force. The removal of melting is controlled due to the joint exertions of the porous media, wall permeability and resistive force generated due to the applied magnetic field. The motion of the melting layer is assumed unsteady and governed the nonlinear similarity equations. Furthermore, magnetic field, porosity, external load and wall suction enhance melting and heat transfer rates at the thin melts film thickness. The melting rate, momentum and thermal boundary layers are estimated under the impact of Stefan number, magnetic field, porosity parameter and unsteadiness parameter. The Eckert number enhances the thermal boundary layer, and consequently the larger amount of melting received. The governing PDEs is highly nonlinear; thus for the solution we use analytical method of HAM and BVPh 2.0 package. The important outputs of the thickness of the thin layer during melting process in the presence and absence of wall suction are mainly focused.

The impact of the Marangoni convection over the thin film flow on an expanding cylinder has been examined in this study. The diverse effect of the embedded constraints has been detected during the liquid film flow. It has been examined that the behavior of the physical parameters altered after the small intervals and diverse from the traditional approach. The similarity variables have been utilized to alter the basic flow equations into the nonlinear ordinary differential equations. The result of the transformed equations is computed by BVPh 2.0 package. The performance of different constraints, for flow motion and temperature distributions are plotted and conferred. It has been observed that under the Marangoni convection the impact of the physical parameters varies after the point of inflection and the diverse impact of the embedding constraints provide space for the variation of the point of inflection for the desired spray analysis. Keywords: Marangoni convection, Steady flow, Thin film spray, Stretching cylinder, OHAM