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In recent years, utilization of nano-technology in drugs and cancer growth treatment has produced a great deal of temptation in thermal properties of biological nanofluid, for example, blood with nanoparticles suspension. The objective of this research is to discover a MHD naturally bio-convective flow of non-Newtonian bio-nano-fluid containing blood as base fluid with ( A l 2 O 3 ) alumina nanoparticles suspension carrying effect of buoyancy, chemical reaction, moving microorganism and heat generation near stagnation region. The Buongiorno along Tiwari and Das nanofluid model is employed whereas Oldroyd-B model is capitalized for depicting the viscoelastic behavior of blood. The non-similarity transformations are exercised on governing nonlinear partial differential system (PDE’s) to transform them into system of non-dimensional PDE’s. After applying appropriate transformations the local non-similarity method via bvp4c algorithm is adopted to numerically deal with the problem. The significance of parameters such as Grashof numbers, magnetic field, Brownian motion, thermophoresis, Deborah numbers, Prandtl number, Schmidt number, Peclet number, heat generation/absorption number and chemical reaction on velocity, temperature, concentration and density of moving microorganism are computed in the graphical profiles to explain the physical state of problem. Physical quantities i.e. local Nusselt number, local Sherwood number and local microorganism density number are also calculated.

In the current study, we focused on the shape effects of copper (Cu) nano-particles on heat transmission of three-dimensional magnetohydrodynamic (MHD) nano-fluid. A particular type of flow is considered, i.e., rotating flow over an exponentially stretching sheet. Significant actions of thermal radiation and Grashof number are also formulated to study. The modified Chebyshev wavelets method is introduced to examine the numerical solutions of the accomplished model. Error analysis and further comparison with existing results reflect the appropriateness of the proposed modification. Graphical behavior of dimensionless velocities, temperature, Nusselt number, and skin friction under the inspiration of several parameters is also presented. The attained solutions propose that the modification is beneficial and can be protracted to other highly nonlinear problems. The modified Chebyshev wavelets technique lowers computing time, according to the study. The research takes into account the form impacts of nano-particles. There are three kinds of nano-particles to examine (spherical, laminar, and cylinder). The behavior of various particles varies depending on the flow and temperature profile. For microparticles with a laminar structure, velocity and temperature have higher values.

A numerical study is accomplished to analyze the Brownian motion of micro-polar hydromagnetic nano-fluid over a stretched surface with thermophoresis and thermal radiation effect. The dimensional equations of the proposed model are reformed by acceptable similarity transformations and the numerical approach using MATLAB in connection with bvp4c is implemented to solve the final equations. The convergence, salient features of the pertinent parameters on micro-polar nano-fluid flow for velocity, angular velocity, temperature and concentration are emphasized on the plots. We also discuss the effect on Skin friction, Nusselt number and Sherwood number and displayed via Tables. The influence of Grashof number is remarkable throughout the study. Outcomes obtained indicate that for enlarged values of micro-polar parameter, the angular velocity is raised. The validity and accuracy of the present model have been checked and found adequate agreement. The importance of such analysis over stretched sheet have numerous manufacturing, industrial and engineering applications in plastic sheets extrusion, polymer extraction, blowing of glass, manufacture of paper and rubber sheets.

This article has the objective of examining to perform unstable magnetohydrodynamic flow over an inclined plate enclosed in a penetrable mechanism with Soret-aligned magnetic field and chemical reaction. Once momentum and energy and mass are equal, they can be combined using the diffusion equation to yield the dimensionless momentum/energy/mass model. Aligned Magnetic field, Jeffrey Parameter, Inclined angle, and Chemical Reaction Model outlines are used to study the effect of numerous physical parameters on boundary layer properties, including Soret temperature, chemical reaction velocity, Temperature and concentration on the resulting heat accumulation profile, are tested using parametric models. The findings derived from skin friction, Nusselt number, and Sherwood numbers are included in the tables provided for several parameters. It is observed from the results that the velocity profile increases with increase Thermal and Mass Grashof Numbers, Jeffery Parameter and Porous media but the opposite trends are seen with increase in the magnetic field parameter, inclined parameter and Aligned magnetic field parameter. One of the important findings of this analysis includes that intensification in the Newtonian heating effect causes a gradual downfall in the rate of heat transfer at the plate and the concentration of the fluid decreases under the impact of chemical reaction. Their physic- Chemical features have been dealt with in detail. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

A hypothetical value of an MHD parabolic started perpendicular plate along with rotation with unvarying mass dispersion on thermal radiation. The heat plate is elevated on T’W then promoted the centre near the close plate was about C’W. The plate hotness along with the concentration point next to the plate is lifted consistently. Dimension-less equivalence realized by applying the Laplace transmute method. This Analytic method of the issue tackled with the limit condition for heat and fixation is one with thermal radiation. The interpretation for temperature profile, concentration, and velocity outline is used several bodily criteria Grashof quantity for thermal and mass, warm air energy limitation, prandtl quantity, Schmidt quantity. The value speed steps up along mounting ideals of Grashof number for thermal (or) Grashof number for mass. The vogue is presently inverted with abiding by thermal radioactivity stricture.

We study the effects of the thermal radiation and an induced magnetic field on the flow over a black isothermal plate for an optically thin gray fluid. The flowing medium absorbs and emit radiation, but scattering is not included. Numerical solutions are obtained for different values of radiation parameter, Prandtl number, Grashof number and magnetic Prandtl number.

Owing to the improved thermophysical properties of nano-materials, the nanofluid convey novel applications in industries, engineering as well as bio-medicals. With high efficiency performances, the nanoparticles include applications in various cooling and heating systems, energy production, aerospace engineering, thermal extrusion, bio-medical applications like treatment of diseases, brain tumour, surgical applications and many more. Moreover, the magneto-nanofluids have the characteristics in the flow of blood in the human artery. The current analysis deals with the free convective unsteady flow of viscous nanofluid subject to the magnetic force over a vertical plate in presence of porous space. The heat transfer phenomenon is accessed by utilizing the additional features like Joule heating, viscous dissipation and absorption coefficients. In addition to the volume fraction of the nanofluid, the effect of the chemical reaction is also introduced. The solution procedure for the modified time-dependent boundary value problem is performed by using the code in-build MATLAB namely Built-in-Shooting method. The change in velocity, temperature and concentration of nano-materials is examined through various graphs. The physical consequences of flow parameters like porosity parameter K p 1 ⩽ K p ⩽ 3 , thermal Grashoff number Gr 1 ⩽ G r ⩽ 3 , solutal Grashoff number Gc 1 ⩽ G c ⩽ 3 , magnetic field parameter M 1 ⩽ M ⩽ 3 , thermal radiation parameter Nr 0.1 ⩽ N r ⩽ 1 , radiation absorption parameter Q 0 ⩽ Q ⩽ 0.5 , Prandtl number Pr 2 ⩽ Pr ⩽ 21 , Eckert number Ec 0 ⩽ E c ⩽ 0.4 , heat source S - 0.2 ⩽ S ⩽ 0.2 , chemical reaction parameter Kc 1 ⩽ K c ⩽ 4 , nanoparticles volume fraction ϕ 0.0 ⩽ ϕ ⩽ 0.1 , Lewis number Le 1 ⩽ L e ⩽ 10 on velocity, temperature and concentration distributions is graphically analyzed. The results show that skin friction coefficients decline with buoyant forces. A lower numerical variation in Nusselt number is resulted with heat source parameter. Moreover, a sharp fall in nanofluid concentration is noticed with increment of chemical reactants and Lewis number.

The mixed convection flow of a hybrid nanofluid in an inclined channel with top wall-slip due to wall stripe and constant heat flux conditions is studied. Explicit analytical solutions are given to the flow velocity, temperature, as well as the pressure in non-dimensional forms. The flow regime domain, the velocity and temperature distributions, and the dependence of various physical parameters such as the hybrid nanoparticle volume fractions, the wall-slip, the Grashof number, the Reynolds number, and the inclined angle are analyzed and discussed. It is found that the hybrid nanofluid delays the appearance of flow reversal on both walls and the wall-slip postpones the flow reversal on the top wall.

The exploration addresses the effect of variable viscosity and thermal conductivity on the peristaltic mechanism of Bingham fluid. A two-dimensional non-uniform porous channel is considered for the fluid flow, which is assumed to be inclined. The impact of heat, slip conditions, wall properties, homogeneous and heterogeneous reactions are examined. The resulting nonlinear differential equations are solved by employing the perturbation method. The solutions acquired are analyzed and sketched through graphs that show that the variable viscosity renders a critical role in regulating the velocity of the fluid in the channel's central part. The stream function has been analyzed to observe the trapping phenomenon. Further, the obtained results find its application in understanding the flow of blood in micro arteries.

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

For the Korean design of the PCCS (passive containment cooling system) in an innovative PWR, the overall thermal resistance around a condenser tube is dominated by the heat transfer coefficient of steam condensation on the exterior surface. It has been reported, however, that the calculated heat transfer coefficients by thermal-hydraulic system codes were much lower than measured data in separate effect tests. In this study, a new empirical model of steam condensation in the presence of a noncondensable gas was implemented into the MARS-KS 1.4 code to replace the conventional Colburn-Hougen model. The selected correlation had been developed from condensation test data obtained at the JERICHO (JNU Experimental Rig for Investigation of Condensation Heat transfer On tube) facility, and considered the effect of the Grashof number for naturally circulating gas mixture and the curvature of the condenser tube. The modified MARS-KS code was applied to simulate the transient response of the containment equipped with the PCCS to the large-break loss-of-coolant accident. The heat removal performances of the PCCS and corresponding evolution of the containment pressure were compared to those calculated via the original model. Various thermal-hydraulic parameters associated with the natural circulation operation through the heat transport circuit were also investigated.

In this study we investigated unsteady mixed convection flow and heat transfer of radiating and reacting nanofluid with variable transport properties in a microchannel filed with a saturated porous medium by taking into account the convective boundary conditions. The Buongiorno’s nanofluid flow model is used to study the effects of the Brownian motion and the thermophoresis. The governing highly nonlinear partial differential equations corresponding to the momentum, energy and concentration profiles have been formulated and solved numerically by utilizing the semi-discretization finite difference method. The effect of each governing thermophysical parameters on the microchannel hydrodynamic and thermal behaviors is discussed with the usage of graphs. The numerical results indicate that the velocity and temperature profiles show an increasing behavior with the variable viscosity parameter, Eckert number, thermal Grashof number, solutal Grashof number, Prandtl number and chemical reaction parameter, whereas the concentration profile increases with increasing values of variable thermal conductivity parameter, porous medium shape parameter, Forchheimer number, Brownian motion parameter, Schmidt number, Biot number and radiation parameter. Moreover, the result reveals that the skin friction coefficient increases with suction/injection Reynolds number, porous medium shape parameter, thermal Grashof number, Schmidt number and Brownian motion parameter but decreases with Eckert number, thermophoresis parameter, Biot number and radiation parameter. Both the heat transfer and the mass transfer rates at both sides of the microchannel walls are higher for large values of suction/injection Reynolds number, porous medium shape parameter and variable viscosity parameter, while both are lower for large values of Eckert number, variable thermal conductivity parameter and radiation parameter. Besides, Grashof number, Schmidt number and Biot number indicate an increasing effect on both the heat transfer and mass transfer rates at the cold wall of the microchannel. The numerical simulation also reveals that Brownian motion parameter and thermophoresis parameter show an opposite effect on both heat transfer and mass transfer rates at both sides of the microchannel walls.

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies.

In this study, numerical investigation on heat transfer by mixed convection for air-cooling through a rectangular horizontal duct with three heat sources is conducted. These heat sources are rectangular ribs with different small aspect ratios and every heat source emits uniform heat flux with small space between each other. The investigation is to enhance forced convection that produced from fan through a rectangular horizontal duct with natural convection using perforated holes between each heat source. The study shows the effect of air entering through the holes at different open hole ratio β (0.01472, 0.02618, 0.04091, 0.05891, 0.08017) and with Reynolds number Re in the range (376, 900, 2073, 3428 and 6170) and at Grashof number Gr = 0.371 x 107 on the temperature of each heat source. The results show the best performance at open hole ratio 0.04091 for which the dimensionless temperature decreased by 5% for the first heater, 15% for the second one and 6% for the third one.

Nanofluids flow and heat transfer in micro-channels have a wide range of attributes in industrial process as well as engineering and biomedical applications. Therefore, the aim of this study is to analyze the hydrodynamic and thermal behaviors of unsteady mixed convection flow of nanofluid in a micro-channel filed with a saturated porous medium. The highly nonlinear governing partial differential equations corresponding to the momentum, energy and concentration profiles were formulated and solved numerically by utilizing the semi-discretization finite difference method. The effects of each governing thermophysical parameters on the micro-channel hydrodynamic and thermal behaviors are discussed with the usage of graphs. The numerical results indicate that the velocity and temperature profiles show an increasing behavior with pressure gradient parameter, variable viscosity parameter, Eckert number, thermal Grashof number, solutal Grashof number and thermophoresis parameter, whereas the concentration profile increases with increasing values of suction/injection Reynolds number, porous medium shape parameter, Forchheimer number, Prandtl number, Schmidt number and thermophoresis parameter. Moreover, the result reveals that the skin friction coefficient, the Nusselt number and the Sherwood number are higher for large values of pressure gradient parameter, thermal Grashof number, Prandtl number and Schmidt number.

Flow, heat transfer and entropy generation in a vertical microchannel made of two parallel porous plates (the injection plate kept at rest while the suction plate is moving in upward/downward direction) under the combined action of buoyancy force and transverse magnetic field are studied. Variable pressure gradient (favorable/adverse) due to Couette–Poiseuille (C–P) flow is considered here. This is one of the fundamental problems of applied science and engineering. Slip conditions for the velocity at plates are implemented for both moving-plate directions and pressure gradients with the help of classical C–P flow. The basic equations are solved numerically by using Runge–Kutta–Fehlberg method along with shooting technique. Numerical results are in concordance with previously published results for specific cases. The present results are frequently compared with those of the classical C–P flow. Influence of operational parameters (plate movement, pressure gradient, injection–suction rate, slip length, Grashof Number, temperature ratio (between hotter to colder side) and viscous dissipation effect) on the flow and heat transfer characteristics (velocity, temperature, Nusselt number (Nu) distribution, entropy generation and Bejan Number) are investigated here. An effort is made to search singularity in the variation of Nu with some parameters, and find the parameters’ values at which the global entropy is minimally generated in the channel. Finally, a critical analysis is conducted on the individual contribution of irreversibilities due to heat flow, fluid friction and Joule heating to the total entropy generation.

The aim of this paper is to study the combined effects of the concentration and the thermo-diffusion on the unsteady oscillation flow of an incompressible Carreau fluid through an inclined porous channel. The temperature is assumed to affect exponentially the fluid's viscosity. We studied fluid flow in an inclined channel under the non-slip condition at the wall. We used the perturbation series method to solve the nonlinear partial differential equations. Numerical results were obtained for velocity distribution, and through the graphs, it was found that the velocity of fluid has a direct relation with Soret number, Peclet number, and Grashof number, while it has a reverse variation with chemical reaction, Schmidt number, frequency of oscillation, and Froude number.

In this study, the pulsating flow of hydromagnetic nanofluid in a vertical porous channel has been investigated. Blood is considered as a base fluid that is non-Newtonian, and alumina $$(\mathrm{Al}_{2}\mathrm{O}_{3})$$ , copper (Cu), silver (Ag) and gold (Au) are considered as nanoparticles. The effects of Joule’s heating and velocity slip at the walls are taken into consideration. Numerical results are obtained by solving the transformed differential equations using the Runge–Kutta fourth-order in addition to the shooting method. Influences of several flow controlling parameters including Grashof number, cross-flow Reynolds number, Hartmann number and frequency parameter on velocity and temperature profiles are examined graphically. The results elucidates that the velocity-slip plays an important role in increasing the heat transfer and velocity of the nanofluid. Further, the heat transfer rate by means of Nusselt number against different parameters is studied and the numerical results obtained are presented. It shows that heat transfer rate at the injection wall increased with increasing Grashof number, frequency parameter and radiation parameter.

Purpose The purpose of this study is to analyze the heat transfer and flow enhancement of an Al2O3-water nanofluid filling an inclined channel whose lower wall is embedded with periodically placed discrete hydrophobic heat sources. Formation of a thin depletion layer of low viscosity over each hydrophobic heated patch leads to the velocity slip and temperature jump condition at the interface of the hydrophobic patch. Design/methodology/approach The mixed convection of the nanofluid is analysed based on the two-phase non-homogeneous model. The governing equations are solved numerically through a control volume approach. A periodic boundary condition is adopted along the longitudinal direction of the modulated channel. A velocity slip and temperature jump condition are imposed along with the hydrophobic heated stripes. The paper has validated the present non-homogeneous model with existing experimental and numerical results for particular cases. The impact of temperature jump condition and slip velocity on the flow and thermal field of the nanofluid in mixed convection is analysed for a wide range of governing parameters, namely, Reynolds number (50 ≤ Re ≤ 150), Grashof number ( 103≤Gr≤5×104), nanoparticle bulk volume fraction ( 0.01≤φb≤0.05), nanoparticle diameter ( 30≤dp≤60) and the angle of inclination ( −60°≤σ≤60°). Findings The presence of the thin depletion layer above the heated stripes reduces the heat transfer and augments the volume flow rate. Consideration of the nanofluid as a coolant enhances the rate of heat transfer, as well as the entropy generation and friction factor compared to the clear fluid. However, the rate of increment in heat transfer suppresses by a significant margin of the loss due to enhanced entropy generation and friction factor. Heat transfer performance of the channel diminishes as the channel inclination angle with the horizontal is increased. The paper has also compared the non-homogeneous model with the corresponding homogeneous model. In the non-homogeneous formulation, the nanoparticle distribution is directly affected by the slip conditions by virtue of the no-normal flux of nanoparticles on the slip planes. For this, the slip stripes augment the impact of nanoparticle volume fraction compared to the no-slip case. Originality/value This paper finds that the periodically arranged hydrophobic heat sources on the lower wall of the channel create a significant augmentation in the volume flow rate, which may be crucial to augment the transport process in mini- or micro-channels. This type of configuration has not been addressed in the existing literature.

The current survey’s primary purpose is to conduct the computational modeling of laminar mixed convection heat transfer of nanofluids inside a CESC using a finite volume method. Water/Cu nanofluid at 0–6% volume fractions was selected as a working fluid. The investigation was done at Grashof numbers of 10,000

A theoretical investigation for internal heat generation, suction/injection, diffusion-thermo and nano-particle volume fraction on a chemically reacting hydro-magnetic flow of Cu–water nano-fluid over a semi-infinite vertical surface is presented in this article. The surface has a uniform velocity which is placed in a saturated porous medium. Under thermal equilibrium state, here we consider that the nano-particles are of uniform shape and size. The small perturbation technique is utilized to solve the boundary layer equations, and the solutions are assumed to be oscillatory type. The significant outputs are presented via figures to explain the effects of different controlling variables on the velocity, temperature, concentration, shear stress and rate of heat transfer profiles. As the conductivity of Cupper particles are higher than those of water-based particles, and significantly it is found that the flow velocities are accelerated for the impact of diffusion-thermo/Grashof/internal heat generation. Increasing porosity parameter decelerate the flow velocity for both nano-fluid and base fluid, whereas enhance the temperature for the radiation parameter. For the impact of free convection and diffusion-thermo, growth values of flow velocity are detected for nano-fluid ( $$\mathrm{Cu}$$ ) than the base fluid (water). Furthermore, application of $$\mathrm{Cu}$$ nano-particles can be used in conductive coatings, medical devices, anti-biotic, and textiles. Comparison with previously published works in the limits shows excellent agreement.

The non-Newtonian fluid flows find its applications in the production of paints, pharmaceutical products, synthetic lubricant and biological fluid. Because of the significance of this aspect, the present paper describes the consequence of non-uniform surface heating on the natural convection of the Casson fluid past a vertical cone with a viscous dissipation effect. Firstly, the governing partial differential equations are derived in the dimensionless form. After that, the numerical solution is obtained using the Crank–Nicolson technique of the finite difference method. The obtained numerical solutions for the temperature profiles, velocity profiles, local Nusselt number and local skin friction are displayed by employing the graphs in order to judge the impact of the governing physical parameters of the model such as the Casson fluid parameter, Grashof number, Eckert number and semi-vertical angle of the cone. The major result is found that the velocity and temperature profiles are more at the center of the lateral side of the cone.

Experiments have found substantial morphological differences between buoyancy-driven flames developing on the upper and lower surfaces of inclined burning plates. These differences cannot be explained on the basis of existing analytical solutions of steady semi-infinite flames, which provide identical descriptions for the top and bottom configurations. To investigate the potential role of flame instabilities in the experimentally observed flow differences, a temporal linear stability analysis is performed here. The problem is formulated in the limit of infinitely fast reaction, taking into account the non-unity Lewis number of the fuel vapor. The stability analysis incorporates non-parallel effects of the base flow and considers separately spanwise traveling waves and Gortler-like streamwise vortices. The solution to the stability eigenvalue problem determines the downstream location at which the flow becomes unstable, characterized by a critical value of the relevant Grashof number, whose value varies with the plate inclination angle. The results for the flame formed on the underside of the fuel surface indicate that instabilities emerge farther downstream than they do for a flame developing over the top of the fuel surface, in agreement with experimental observations. Increased buoyancy-induced vorticity production is reasoned to be responsible for the augmented instability tendency of topside flames.

This paper deals with the numerical investigation of the convective mode of heat transfer across a vertical tube. Experiments were carried out using air as a fluid in a closed room by achieving a steady-state condition. Implicit scheme of finite difference method was adopted to numerically simulate the free convection phenomenon across vertical tube using LINUX based UBUNTU package. Numerical data were collected in the form of velocity, temperature profiles, boundary layer thickness, Nusselt number (Nu), Rayleigh's number (Ra), and heat transfer coefficient. The results of the Nusselt number showed a good agreement with the previous studies. Results data of heat transfer coefficient indicate that there were some minor heat losses due to radiation of brass tube and curvature of the tube.

This paper presents numerical simulations for a MHD convective process in curved channels. The worked suspension consists of water as a based hybrid nanofluid and two types of the nanoparticles, namely, Cu and Al2O3. Two systems of the governing equations are formulated for the hybrid nanofluid and dusty phases. The hybrid nanofluid system is modeled in view of lubrication approach. The governing equations are mapped to a regular computational domain then they solved numerically using the fourth order Runge-Kutta method. The obtained findings revealed that the growing in the Hartmann number causes a reduction in both of the hybrid nanofluid and dusty velocities while the mixture temperature is enhanced. Also, the temperature distributions are supported when either the Grashof number or the amplitude ratio is altered.

In this study, the magnetic hydrodynamic and scattering intake of the fluid flow movement preceding an exponentially augmented vertical plate through mass distribution with varying temperature and warmth basis via a heat porous medium. Dimensionless conditions with limitation and starting conditions is workout mathematically. The plate temperature is extended in straight line alongside period t also focus closer near the plate. The dimensionless administering conditions in the current examination are tackled utilizing the Laplace change method. The velocity outlines are graphically explained to various physical limits heat Grashof value, mass Grashof value, Schmidt value also duration. It has been found that the velocity raises through the increase of the thermal grashof number Gr also expansion time t of the plate but the velocity growths through rise in absorptivity of the permeable medium while the presence of hypnotic parameter decreases. The impacts of boundaries M, K, t, Sc, an and Gr on the velocity profiles are demonstrated graphically.

The aim of the present chapter is to investigate the problem of Study on MHD boundary layer flow over a moving vertical porous plate with heat generation and chemical reaction in the presence of thermal absorption. The governing equations of the flow are transformed into nonlinear ordinary differential equations and then solved by using Runge-Kutta-fourth order along with shooting method. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The influence of the various parameters like Magnetic parameter (M), thermal Grashof number (Gr), mass Grashof number (Gc), permeability parameter (K), Prandtl number (Pr), Dufour number (Df), Soret number (Sr), Schmidt number (Sc), Heat generation (B), Radiation Parameter (Ra) and Chemical reaction (Ch) on the flow are analyzed and discussed through graphs in detail. The values of the skin friction coefficient, Nusselt number and the Sherwood number for different physical parameters are also tabulated.

This paper reports on the numerical investigation of assisting and opposing mixed convection flows and heat transfer performance of nanofluids in a cubical enclosure under turbulent conditions. The enclosure side wall consists of a partially heated heat source and the nanofluid is pumped into the enclosure through the inlet port. A three-dimensional, turbulent two-phase mixture model is developed to investigate the thermal performance of nanofluids by considering the effects of Brownian motion and thermophoresis. The base fluid is considered as water into which different nanoparticles such as aluminum oxide (Al2O3), copper (Cu) and silver (Ag) are dispersed for different particle volume fractions (ϕ) varied from 0% to 4%. The Richardson number (Ri) and Reynolds number (Re) are varied between 0.01 ≤ Ri ≤ 10 and 3.1 × 103 ≤ Re ≤ 105 and the Grashof number (Gr) is maintained at a constant value of 108. The nanoparticles are considered as monodispersed spherical particles with a uniform diameter of 100 nm. The results indicate that the temperature and turbulent kinetic energy distributions for opposing flows are higher than assisting flows. It also found that the average heat transfer rate increases with decrease in Richardson number and increase in volume fraction for both assisting and opposing flows. The effects of Brownian motion and thermophoresis are more significant in assisting flows than opposing flows.

In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

The models, simulation, and validation were presented during the last decade over various moving particle investigations with thermal convection and disclosed the challenges as well. The present work provides the simulation and validation of the grinding mechanism of high-temperature nickel-based alloy with single abrasive grain. Several nickel-based alloys provide better performances for temperatures above 1000 °C and those suited for extremely difficult conditions as well. In this study, we simulate and analyze the grinding mechanism of high-temperature nickel-based alloy using single abrasive grain cutting. Using a grinding, it introduces variation in friction coefficient as per the variations of the grinding parameters. The grinding force system of single abrasive grain is designed and simulated to investigate high-temperature nickel-based alloy using various grinding conditions like particle settling modes such as rolling, horizontal, and vertical with thermal convection. The multi-grid finite element fictitious boundary method (FEM-FBM) is used to simulate and study the grinding mechanism of high-temperature nickel-based alloy in terms of fluid-particle sedimentations. The material used for this simulation study is Inconel 718 alloy. The simulation results investigate the various grinding force conditions of high-temperature nickel-based 718 alloys using the dimensional physical parameters and numbers such as Prandtl number and Grashof number. Finally, the simulation results were validated with a conventional FEM model.

This paper presents a computational modeling approach to analyze the peristaltic pumping of couple stress hybrid nanofluids regulated by the electroosmosis mechanism through a microchannel. The effects of applied magnetic field, Joule heating and buoyancy have also been computed. In this analytical model, water-based titanium dioxide (TiO2) and silver (Ag) hybrid nanofluids have been considered. For more relevant physical problem, the axial velocity slip and thermal slip conditions have also been introduced. The nonlinear differential equations are simplified by considering the Huckel–Debye approximations as well as lubrication theory, and then the equations have been solved numerically by Mathematica 10 software via the NDsolve commands. The pertinent influences of key parameters on the axial velocity, nanoparticle temperature, Nusselt number and streamlines in the microchannel have been visualized graphically. It is observed that an increase in the thermal Grashof number produces a maximum axial velocity, and temperature of nanoparticles for both water–titanium dioxide and water–silver nanofluids. The maximum axial velocity and nanoparticle temperature occur in water–titanium dioxide as compared with water–silver. The outcomes of this model shall be very useful in the designs of smart electro-peristaltic pumps for thermal systems and drug delivery systems.

In this paper, free convection of nanofluids flow with oscillating vertical parallel plates and mass diffusion were considered. Obtained equations were converted into ordinary differential equations with appropriate transformations. Method of Laplace transform was used to find the exact solutions of velocity, temperature and concentration profiles from the dimensionless governing equations. Discussion of graph pertaining to different embedded parameters such as Prandtl number, Schmidt number, Grashof and mass Grashof number, oscillating parameter and nanoparticles volume fraction parameter was also added. Skin friction, Nusselt and Sherwood number were also discussed and deliberated.

The development of advanced-performance thermal frameworks for increased heat transport has proved to be of remarkable interest these days. Therefore, present attempt is intended to deal with entropy generation and heat transfer analysis for the peristaltic flow of an electrically conducting silver-water nanoliquid through a symmetric channel. System is supposed to be affected by an external magnetic field and electrical conductivity of nanofluid is considered to vary with temperature. Mixed convection, joule heating aspects along with thermal and velocity slip conditions are considered in analysis. Two phase model of nanofluids is adopted. Mathematical modeling for entropy generation is carried out via second law of thermodynamics. Making use of numerical solver NDSolve, graphical analysis for entropy generation, heat transfer, Bejan number and velocity is presented. Results reveal that by enhancing electrical conductivity parameter entropy generation increases. It is further deduced that entropy generation can be minimized by addition of silver nanoparticles. Bejan number increases by increasing Grashoff number. For large values of Hartman number temperature increases. Temperature of nanofluid increases by enhancing thermal slip parameter. Increase in Grashoff number provides better rate of heat transport at the boundary. Moreover, velocity decreases by enhancing velocity slip parameter.

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.

This paper examined the fluid transport on boundary layer near a vertical wall with thermal radiation effect. The coupled nonlinear partial differential equations are reduced to a system of ordinary differential equations through similarity transformation. The resultant system of ordinary differential equations is integrated with maple software using RKF45 method. The effect of the active parameters such as Grashof number, thermal radiation parameter, temperature difference, Prandtl number, and local convective heat transfer parameter on the velocity profile, skin friction, temperature profile and Nusselt number are presented using graphs and tables. The outcome of the study revealed that the Prandtl number has a decreasing effect on thermal boundary layer thickness. It also revealed that the thermal radiation has an increasing effect on the Nusselt number, temperature distribution, temperature gradient and skin friction. The temperature distribution increases with increasing values of the temperature difference and local convective heat transfer parameter whereas decreases with Grashof number.

A numerical computation is performed to analyze the double diffusive convection in micropolar nanofluids flow governed by peristaltic pumping in an asymmetric microchannel, in the presence of thermal radiation and an external magnetic field. The highly nonlinear governing equations are diluted by using desirable physical assumptions such as lubrication approximation and low zeta potential. Convective boundary conditions are employed. This enables us to determine numerical estimates of various physical flow variables such as velocity, pressure gradient, spin velocity, temperature of the nanofluid, concentration of solute, and volume fraction of nanoparticles for sundry parameters like micropolar parameter, coupling parameter, solutal Grashof number, thermophoretic diffusion coefficient, Grashof number, thermal radiation parameter and Helmholtz–Smoluchowski velocity with the aid of bvp4c function built-in command of MATLAB 2012b. Influence of each relevant parameter on flow, thermal and species characteristics are computed in this study. Influence of Soret and Dufour parameters are also simulated. This model is applicable to the study of chemical fraternization/separation procedures and various thermal management systems like of heat sinks, thermoelectric coolers, forced air systems and fans, heat pipes, and many more.

The current investigation owns the mathematical and computational analysis of the forced and free convection in a square shape enclosure with inlet/outlet opening. The flow field is manifested with CuO nanoparticles along with the porous media assumption. The left boundary is uniformly heated while the right wall is taken cold. The force flow constraint is implemented on the openings ports and the remaining portions are kept adiabatic. To be more specific the mixed convection transportation in the regime persists because of thermal difference in-between the heated source and cold inflow of fluid. For possible insight, the physical model is translated in terms of the differential systems. To report solution the finite element method has been adopted. The quantities of interest include the flow and heat transportation individualities. The output of computational scheme towards various controlling parameters are offered by means of both the contour maps and line graphs. It is noticed that the flow patterns identify forced flow at low Grashof number while the higher porous permeability possess the natural convection transportation. Additionally, as the heated source length heightens thermal distributions inside the cavity becomes intensify.

In the present study, double-diffusive mixed convection related to the heat and mass transfer of the solid particles dissolution in a shear flow was numerically investigated. For this purpose, the study employed the combined two-dimensional thermal-concentration smoothed profile-lattice Boltzmann method scheme. The governing equations of the flow, concentration and temperature fields are solved by applying the LBM. The interplay amongst the fluid–solid particle and the boundary condition of the no-slip at the interface of the fluid–solid particle is treated by using the SPM. Initially, a comparison made amongst the results obtained in the present numerical method and to those that had been obtained in the previous works, showing a well compatibility. Then, the impacts of Reynolds number, thermal and concentration Grashof numbers and buoyancy ratio on the flow characteristics and dissolution process have been addressed. Following that, a comparison is made amongst the impacts of pure forced convection and double-diffusive mixed convection on the solid particle dissolution behavior. It is shown that different competitive mechanisms have impact on the migration of the solid particles under the double-diffusive mixed convection; these are the particle mass force, the buoyancy force resulting from the fluid weight, the thermal convection and finally, the concentration convection. The numerical results also revealed the identification of the critical buoyancy ratio, with the dissolution time of the solid particles being sensitive to it.

PurposeNaturally, all the materials are not viscous (i.e. milk, mayonnaise, blood, vaccines, syrups, cosmetics, oil reservoirs, paints, etc.). Here present analysis focuses on the usage of non-Newtonian fluid rheological properties enhancing, damping tools, protection apparatus individuals and in various distinct mechanical procedures. Industrial applications of non-Newtonian liquids include minimum friction, reduction in oil-pipeline friction, scale-up, flow tracers and in several others. The peristaltic mechanism is used as a non-Newtonian material carrier here. This mechanism occurs because of continuous symmetrical and asymmetrical propulsion of smooth channel walls. Peristalsis is a very significant mechanism for carrying drugs and other materials during sensitive diseases treatments.Design/methodology/approachKeeping in mind the considered problem assumptions (Rabinowitsch fluid model, thermal Grashof number, Prandtl number, density Grashof number, wall properties, etc.), it is found that the modeled equations are coupled and nonlinear. Thus here, analytical results are quite challenging to acquire and very limited to extremely venerated circumstances unsettled to their nonlinearity. Hence various developments found in computing proficiencies, numerical procedures that provides accurate, stable and satisfying solutions for non-Newtonian material flows exclusively in complex dimensions play a significant role. Here BVP4C numerical technique is developed to evaluate the nonlinear coupled system of equations with appropriate boundary constraints.FindingsDue to convectively heated surface fluid between the walls having a small temperature. Sherwood and Nusselt numbers both deduce for fixed radiation values and different Rabinowitsch fluid quantity. Skin friction is maximum in the case of Newtonian, while minimum in case of dilatant model and pseudoplastic models. The influence of numerous parameters associated with flow problems such as thermal Grashof number, density Grashof number, Hartman number, Brownian motion, thermophoresis motion factor and slip parameters are also explored in detail and plotted for concentration profile, temperature distribution and velocity. From this analysis, it is concluded that velocity escalates for largerOriginality/valueThe work reported in this manuscript has not been investigated so far by any researcher.

The problem of natural convection of a viscous incompressible fluid between two concentric cylinders is investigated. It is assumed that the inner cylinder can rotate around its axis without friction. Convection in the area is created due to the constant temperature difference at the outer boundary. The movement of fluid in the annular cavity, due to viscous friction, will cause the rotation of the inner cylinder. This rotation can be used to perform mechanical work. This system can be considered as a stationary heat engine, operating in the presence of a gravitational field, where the work is done through an irreversible process - viscous friction. In the work, two limiting cases were considered: the inner cylinder is thermally insulated, the inner cylinder is made of a material having a very high thermal conductivity. The work analyzed the amount of kinetic energy of the rotating cylinder depending on the inner radius, the size of the area where the temperature is maintained and the location of these areas. It has been found that the kinetic energy of the cylinder depends strongly on the thermal conductivity and the radius. For both types of the inner cylinder, the values of the inner radius were established at which the maximum kinetic energy of the cylinder is reached. It has also been found that this radius does not depend on the size of the area over which the temperature is maintained, or on the location of these areas. The Boussinesq approximation was chosen as the mathematical model. To solve this problem, the control volume method and the SIMPLER algorithm were used. The calculations were carried out at Pr = 1,104 ≤ Gr ≤ 2 ⋅ 104, 0

Nanoparticles have great potential to improve thermophysical properties and thermal execution. At different polymer fixations, hybridization of Eyring–Powell nanofluid model with peristaltic flow is done due to its high accuracy and consistency as found in the measurements of fluid time frame. The transport equations of the problem have been incorporated under the assumptions of long wave length and lubrication approximations. The conditions of wavelength include the impacts of thermophoretic dissemination of nanoparticles with Brownian movement. The coupled nonlinear boundary value problem has been analytically solved employing the homotopic approach. Key consideration includes material constant, thermophoresis parameter, Brownian movement parameter, Eyring–Powell parameter, local temperature Grashof number and local nanoparticles Grashof number. Key findings of the analysis reveal that fluid axial velocity enhances with larger aspect ratio and thermophoresis parameter but decays for Brownian motion and fluid factors. On the other hand, the channel aspect ratio exhibits inverse relation with peristaltic pressure, fluid temperature and nanoparticles concentration.

Applications of mixed convection due to lid-driven cavities can be found in different engineering technologies. A computational study was conducted to explore the effects of different parameters on mixed convection in a porous media filled lid-driven cavity with one side opening in the presence of heat generation. The cavity has a flush mounted heater on its bottom wall. The governing equations were solved by developing a computer code by using finite volume technique for different parameters as length of heater (1/5, 2/5, 4/5), Richardson number (0.1, 1, 10) and Darcy number (0.1, 0.01, 0.001). It is found that heat transfer and flow field inside the cavity is so complex due to moving lid, open side wall and heater. Heat transfer increases with increasing of Grashof numbers, heater length and decreased with Darcy numbers.

Nanoparticles play a radical role in oncology treatment especially nanoparticles of gold (Au NPs). Among the substantial properties of Au NPs is the possession of a large atomic number, which helps in the treatment of tumors. Furthermore, it is employed to encapsulate large numbers of therapeutic compounds. Also, the alternating electric field therapy (AC electro-kinetics, called tumor treating fields TTF), is used in malignancy oncology therapy (MOT). The aim of this article is to investigate the blood flow characteristics under the influence of AC electric field and heat transfer in the presence of Au and Cu-NPs through a symmetric elastic sinusoidal channel. The governing equations of the Jeffrey fluid (blood model) along with total mass, thermal energy, and the electric potential equations are simplified by using the postulate of long wavelength approximation. The expressions of the axial velocity field, stream function, pressure gradient, the temperature distribution, and the electric potential field are obtained by using DSolve program in Mathematica software (version 10). Influence of the materialistic parameters like the Jeffrey parameter, volume fraction, Grashof number, and electric Rayleigh number on the velocity profile, temperature distribution, electrical potential, pressure gradient, pressure rise, and entropy generation are considered. Two different nanofluid suspensions are investigated (Au and Cu NPs). The results pointed out that the Au-NPs are efficacious for drug carrying and drug delivery systems, this is evidenced by the velocity in the case of Au-NPs greater than in the case of Cu-NPs. Also, when the electrical Raleigh number increases, an electric force is generated to reverse the wave propagation.

In the present paper, the free convection oscillatory flow of a micropolar fluid determined by a vertical an infinite surface plane has fluctuates harmonically temperature with a relaxation time is studied. The surface has a constant suction and oscillates free steam velocity, and absorbs the fluid. The Eringen model for micropolar fluid is applied to solve the problem. The components of velocity, induced magnetic field, and concentration profiles have been obtained. The technique of regular perturbation is considered to solve the equations governing to a set of linear coupled and uncoupled ordinary differential equations. The problem has been solved for the small values of the micropolar perturbing parameter χ . The effects of Prandetl number P r , Grashof number G r , material parameter χ , β , γ are discussed. The cooling and heating effect on the fluid has been discussed. The numerical results indicate that the external parameters are affected strongly on the electrically conducting micropolar concentration fluid. If the electrically conducting and thermal relaxation time, the results obtained deduce to the results obtained by Sharma and Gupta (1995) [31].

Conclusion The solution of thermal radiation and variable pressure effects of a viscous,incompressible and electrically conducting fluid between vertical porous medium is gained. In the absence of mass transfer equation [3] and Gr = N =M = K = Sc = δ, our present result agrees with available work [7]. The dimensionless governing equations are solved analytically by perturbation method. The effects of various parameters were discussed. From the study it’s concludes that: i. Increase in thermal radiation parameter, Schmidt number, magnetic field parameter chemical reaction, decreases velocity, temperature and concentration. ii. Thermal Grashof number increases the velocity. iii. Thermal Grashof number (Gr), and sustention parameter (N), enhances skin friction , while increase in chemical reaction parameter (Rc), magnetic field parameter (M), thermal radiation parameter (R), Schmidt number (Sc), and permeability parameter (K), retard skin friction. It is noticed from the table that an increase in Pr, S and δ decreases the rate of heat transfer and increase in radiation parameter (R), increases the rate of heat transfer.

The current and potential applications of bioconvection renewed drive for theoretical research on synthesis and process control in biofuel cells and bioreactors. Thus, this work devoted to solving the problem of free convection in micropolar boundary layer fluid flow and heat transfer past a vertical flat stretching plate within a porous medium. Scaling group of transformation was performed to achieve the appropriate similarity solutions, which was later applied to modify the governing boundary layer system to a nonlinear ordinary differential equations system. The Runge–Kutta method in association with the shooting technique in the Maple software exercised to attain the numerical solutions. There is a strong dependence of momentum transportation on the increment of the Darcy number, the suction/injection parameter and the Grashof number, respectively. The temperature distribution within the thermal boundary layer aided by augmenting the magnitude of the microrotation density.

In this study, mixed convection heat transfer and fluid flow is numerically investigated in an open system enclosure containing a heated obstacle. Effects of the positions of both obstacles and fluid flow outlet on the flow field and heat transfer within the enclosure were studied. Richardson number ranging from 0.1 to 10 was examined for a constant Grashof number at different Reynolds numbers in both base fluid and fluid mixed with Cu nanoparticles (0 to 4% of volume fractions). It is found that the obstacle and outlet position as well as the Richardson number greatly affect the flow field and heat transfer rate. The maximum heat transfer rate occurs for Richardson number 0.1, when the outlet and obstacle position are located at the bottom of the right side of the enclosure (P3) and near right side of the enclosure (8H), respectively. Also, the heat transfer rate is higher when the obstacle is placed close to the inlet (2H) and outlet (8H) compared to the center of the enclosure (5H). It is shown that although the change of volume fraction of nanofluid does not have significant effect on the flow pattern, however, it enhances the heat transfer rate through improving the effective thermo-physical properties of the base fluid.