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Considering varying cusp numbers, we investigate the time-dependent, incompressible natural convective flow of an iron oxide-water nanofluid within an annulus formed between a square and a concentric hypocycloid. The vertical walls of the annulus are treated as relatively colder walls, while the bottom wall of the square disk and the inner hypocycloid wall act as heat sources. The outer upper wall of the square is considered adiabatic. We transform the dimensional, nonlinear, and strongly coupled fundamental equations of nanofluids in Cartesian coordinates into non-dimensional equations. We utilize the Galerkin finite element method to solve the governing equations. This study comprehensively explores the flow and heat transfer of nanofluids, considering the essential parameters relevant to the problem. The results highlight a remarkable observation, as the ferric oxide-water nanofluid exhibits significantly enhanced heat transfer compared to the conventional fluid. The precise positioning of the hypocycloid in the cusp configuration represents a critical phenomenon that substantially improves the flow and heat transfer rates of the nanofluid. The three cusped hypocycloids positioned on the inner wall of the annulus perpendicular to the horizontal axis result in a nanofluid flow configuration and heat transfer that surpasses other configurations and cusp numbers studied in the analysis. Notably, heat transfer exhibits a discernible increase with an increase in the nanoparticle volume fraction (maximum 3vol%), while it declines with an increase in the nanoparticle diameter. The intricate relationship between the nanoparticle diameter, volume fraction, cusp number, and hypocycloid configuration substantially influences the friction factor and particle-surface interactions. As the number of cusps on the inner surface increases, the velocity magnitude, Nusselt number, and concentration profiles near the boundary layer decrease, while the fluctuations of the middle annulus indicate the combined influence of nanoparticle dispersion and the formation of the annulus boundary layer due to the orientation of hypocycloidal cusps. Furthermore, an increase in the particle diameter and the sharpness of the corners of the hypocycloid lead to a proportional increase in the nanofluid flow resistance within the annulus.

We investigate the unsteady laminar convective magnetohydrodynamic nanofluids flow in a square cavity driven by an exothermic chemical reaction. Because exothermic chemical reactions are intrinsic in nanofluidic flow applications, we consider this exothermic chemical reaction in the analysis, which is governed by Arrhenius kinetics energy. A water-based nanofluid containing iron oxide (Fe3O4) nanoparticles is employed in the simulation. The square cavity is accurately propounded by a combination of suitable heating and flow conditions. The left vertical wall of the enclosure is considered a higher unevenly heated wall, the right vertical wall of the domain is considered a relatively cool constant temperature, and the upper and lower walls are considered insulating walls. Each wall assumes a no-slip condition. The nanofluid governing equations are transformed into the non-dimensional set of equations using similarity analysis and then modified into finite element equations. Galerkin's method in finite element analysis is used to obtain the results of the problem. The results show that the Rayleigh number, the Frank-Kamenetsky number, and the nanosolid volume ratio all have significant effects on the convective flow regime, and the average Nusselt number increases with these parameters. Due to the greater value of the Rayleigh number (Ra = 106), the average Nusselt number increased to 75.92%, and heat generation due to a strongly exothermic reaction (higher Frank-Kamenetskii number) can blow up the bounded solution. The water-Fe3O4 nanofluid achieves a greater rate of heat transfer (maximum 22.65%) than that of the base fluid.

Heat transfer in different nanofluids and understanding their characteristics through mathematical modeling will lead to the development of noble nanofluids with tunable hydrodynamics. A dynamic model has been utilized to analyze the convection and flow of a copper oxide-water nanofluid flow within a symmetrical isosceles triangular cavity with a rippled base wall. The Galerkin Finite Element (FEM) approach has been used in the simulation to analyze the governing equations, including the wall conditions. The walls are kept rigid, and a steady low temperature has been applied to the cavity's tending walls. We studied the isoconcentration levels, isotherms, streamlines, and heat transfer distribution by keeping the corrugated bottom wall equally heated. The heat transfer distributions for problem variables, nanoparticle size, time evolution, and nanoparticle volume fraction confirmed that the patterns of the heat transfer distribution for adjustments in nanoparticle volume fraction are inversely proportional to those for modifications in nanoparticle diameter. A noticeable heat transfer dissemination requires a 1-20 nm diameter of nanoparticle inside the mixture, while a stagnant distribution of heat transfer happens after this range. Our analysis revealed that the isosceles design and the size distribution of the nanoparticles play a crucial role in heat transmission. Compared to the base fluid tested in the research, nanofluid shows a lower coefficient of friction. The greater the friction coefficient within the cavity, the higher the Rayleigh number and nanoparticle diameter.

We explored natural convection of copper oxide-water nanofluid flow within a square domain having two wavy vertical surfaces in existence of the hydro-magnetic field using non-uniform dynamic model. Two vertical surfaces on the left and right are regarded as connecting outlets through which heat can pass and considered as the colder walls, the bottom surface is regarded as a uniform heat source, and the upper boundary line is regarded as an insulating surface through which heat cannot pass. The Galerkin's extension in the finite element analysis has been incorporated to design, transform, and solve the nanofluid equations. The results reveal that when the thermal Rayleigh number upturns, the amplitude of the velocity, streamlining, isotherms efficacy, and uniformity of the isoconcentration labeling increase for a nanofluid with reduced nanoparticle volume percentage. As the magnetic pitch intensifies, the flow strength drops, and effective flow occurs in the vertical magnetic field. Flow convolution develops as more waves are formed on a vertical surface. The average heat transmission rose by 158% as the Rayleigh number grew from 104 to 106. The mean heat transmission increases by 10.18% when the nanoparticle volume segment is increased from 0.025 to 0.05. The heat transmission rate is higher on the vessel's non-wave vertical surface. Heat transfer is reduced by 16.98% when the wave number is augmented to 2 and increased by 3.62% when the wave number is risen from 2 to 4.

Nanofluids have various operations and prospects in heat transfer engineering to produce novel technological equipment for cooling purposes. In response to nanofluid's possible application, the transient convective alumina-water nanofluid flow in a square vessel in the presence of magnetic field and exothermic chemical reaction has been numerically investigated. We consider a square vessel, where the lower boundary of the vessel is heated, the two vertical side walls are relatively cold, and the upper wall is insulated. The finite element method based on Galerkin scheme is used to solve the governing partial differential equations along the imposing boundary conditions. We verified the present results with the standard experimental published results. The flow and thermal forms, and local Nusselt number are investigated for the numerous appropriate parameters. The time effects on the heat transfer is examined. The result shows that as the Rayleigh number increased from 105 to 106, the heat transfer increased by 72.78%. Compared with the base fluid water, the heat transfer of the alumina-water nanofluid with a nanoparticle volume fraction of 6% increased by 10.42%. The magnetic field and the Arrhenius chemical reaction parameters regulates the nanofluid flow and the heat transfer.

In the present paper, unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically. The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated. The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations. In numerical simulations, four types of nanoparticles such as magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn-Zn ferrite (Mn-ZnFe2O4), and silicon dioxide (SiO2), and three types of base fluids such as water (H2O), engine oil (EO) and kerosene (Ke) have been considered. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various model parameters such as thermal Rayleigh number, nanoparticles volume fraction and nanoparticles shape factor are studied. The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify. The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles. Kerosene-based nanofluids exhibit higher heat transfer rate. Mn-ZnFe2O4-kerosene nanofluid has a higher average Nusselt number than that of other 11 types of nanofluids which are studied in the present analysis. Keywords: Nanofluids, Nanoparticles, Heat transfer, Natural convection, Square enclosure, Finite element method

In this paper, we have examined the magnetohydrodynamic flow of a nanofluid past a radiating sheet. The Navier velocity slip, Newtonian heating and passively controlled wall boundary conditions are considered. The governing equations are reduced into similarity equations with the help of Lie group. A collocation method is used for simulation. The influence of emerging parameters on velocity, temperature, nanoparticle volumetric fraction profiles, as well as on local skin friction factor and local Nusselt number is illustrated in detail. It is found that the friction (heat transfer rate) is lower (higher) for passively controlled boundary conditions as compared to the case of an actively controlled boundary condition. The magnetic field effects decrease both the skin friction and the rate of heat transfer. The findings are validated with existing results and found an excellent agreement. The model explores new applications in solar collectors with direct solar radiative input using magnetic nanofluids. Keywords: Lie group, Navier slip flow, Newtonian heating, Nonlinear radiation, Passively controlled boundary condition, MHD

Thermal energy management associated with the transmission of heat is one of the main problems in many industrial setups (e.g. pharmaceutical, chemical and food) and bio-engineering devices (e.g. hospital ventilation, heating, cooling devices, heat exchanger and drying food, etc). The current study aims to examine thermo-bioconvection of oxytactic microorganisms taking place in a nanofluid-saturated needle with the magnetic field. Stefan-blowing is applied. The leading equations of continuity, momentum and energy, species transport equations for oxygen concentration and population density of microorganisms are reduced dimensionless and Lie symmetry group transformations are used to generate appropriate invariant transformations. The resulting similarity boundary value problem (in which the blowing parameter is coupled with concentration) have been simulated using MATLAB (2015a) bvp5c built in function. The impact of the emerging factors on the nondimensional velocity, temperature, nanoparticle concentration and motile microorganism density functions and their slopes at the wall, are pictured and tabulated. Justification with published results are included. It is found that all physical quantities decrease with Stefan blowing and increase with power law index parameter. With elevation in magnetic field parameter i.e., Lorentzian drag force, the friction factor reduces while the local Nusselt number, local Sherwood number, and the local motile microorganism density wall gradient increase. Present study could be used in food and pharmaceutical industries, chemical processing equipment, fuel cell technology, enhanced oil recovery, etc.

A mathematical model is presented for forced convective slip flow of a nanofluid past a radiating stretching/shrinking sheet. Melting boundary condition is taken into account. The nanofluid model involves the Brownian motion and thermophoresis effects. Lie group transformation is used to the transport equations as well as the boundary conditions to develop the similarity equations, before being solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. To show the effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, skin friction factor, local Nusselt, and local Sherwood numbers, numerical results are presented both in graphical and tabular forms. It is found that the friction factor decreases with slip and melting parameters for both stretching/shrinking sheets. It is also found that the Nusselt number decreases with the first order slip while it increases with melting and radiation parameters in both cases. Also, the Sherwood number decreases with the melting parameter both for radiating and non-radiating stretching/shrinking sheets. An excellent agreement is found between the present numerical results and published results. Keywords: Nanofluid, Melting effect, Lie group, Thermal radiation, Slip boundary condition

A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing micro-organisms and taking into account Stefan blowing effect is presented theoretically and numerically. Appropriate transformations are used to transform the governing boundary layer equations into non-linear ordinary differential equations, before being solved numerically using the Runge-Kutta-Fehlberg method. The effect of the governing parameters on the dimensionless velocities, temperature, nanoparticle volume fraction (concentration), density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile microorganisms numbers are thoroughly examined via graphs. It is observed that the Stefan blowing increases the local skin friction and reduces the heat transfer, mass transfer and microorganism transfer rates. The numerical results are in good agreement with those obtained from previous literature. Physical quantities results from this investigation show that the effects of higher disk stretching strength and suction case provides a good medium to enhance the heat, mass and microorganisms transfer compared to blowing case.

Nanofluid based heat transfer approaches have a tremendous prospect to develop novel cost-effective cooling technologies. In response to this potential development, a problem of unsteady copper oxide-water nanofluid flow and natural convective heat transfer within a quadrilateral vessel with uniform heating of bottom wall using modified Buongiorno model are investigated. The sloping wall of the vessel is maintained at constant low temperature and the uniform thermal condition on the bottom heated wall is considered, whereas the upper horizontal wall is regarded as adiabatic. The governing equations along with boundary conditions are solved using the Galerkin finite element method. Partial differential equation solver COMSOL Multiphysics with Matlab interface is used in the simulation. The results of the present problem of a certain situation as a special case have been verified by the previously published standard numerical investigations. The flow, thermal and concentration fields, local and average Nusselt number for various pertinent parameters entered into the problem have been analyzed. The time evolutions for a steady-state solution are also examined. The results show that the adjustment factor with the optimal nanoparticle volume fraction and the thermal Rayleigh number controls the optimal heat transfer. The trapezoidal vessel having higher sloping angles with the vertical axis exhibits higher heat transfer. Heat transfer decreases rapidly in 1–10 nm size nanoparticles for a nanofluid solution.

The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate) for methanol are higher (lower) than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate) factor of Newtonian fluid is higher (lower) than the dilatant fluid.

Bionanofluid is a nanofluid in which bioconvection occurs. This paper studies the three dimensional steady stagnation point flow of a bionanofluid with variable transport properties. All the transport properties are dependent on the concentration. Zero mass flux and thermal convective boundary conditions are taken into account. The governing equations of the problem are nondimensionalized and transformed into a set of similarity equations using similarity transformation generated by Lie group analysis. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method (RKF45). The solutions depend on the viscosity parameter, thermal conductive parameter, mass diffusivity parameter, microorganism diffusivity parameter, Schmidt number, bioconvection Schmidt number and Péclet number. These controlling parameters affect the dimensionless velocity, temperature, nanoparticle volume fraction, microorganisms, the skin friction coefficient, the local Nusselt number and the Sherwood number as well as the motile microorganism rate and are displayed graphically. The results were found to be in good agreement with previous related studies.

A mathematical model for two dimensional unsteady magneto-convective flows with heat and mass transfer in the presence of a time dependent magnetic field is presented. The system of partial differential equations governing the transport problem is converted to a system of ordinary differential equations via two parameter scaling group transformations, before being solved using an implicit finite difference method. Computed results for non-dimensional velocity, temperature and concentration distributions as well as skin friction factor, local Nusselt number and Sherwood number are discussed for various values of the controlling parameters (Prandtl number, Schmidt number, Richardson number, magnetic field and buoyancy ratio). It is found that the magnetic field causes an increase in the rate of the heat and mass transfers. The buoyancy ratio increases the heat transfer rates and decreases the mass transfer rates.

A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM). The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number) on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.

This paper deals with an analytical solution of free convective flow of dilatant nanofluid past a vertical cone/plate. A two-phase mixture model is used for nanofluid in which the Brownian motion and thermophoretic diffusivities are the important slip mechanisms between solid and liquid phases. The governing transport equations along with physically realistic thermal and mass convective boundary conditions are reduced to similarity equations using relevant similarity transformations before being solved by homotopy analysis method. The effects of the governing parameters (Brownian motion, thermophoresis, convection–conduction, convection–diffusion, Lewis number, buoyancy ratio, and power-law) on the dimensionless velocity, temperature and nanoparticle volume fraction, friction and heat transfer rates are plotted and discussed. It is found that friction factor decreases with the increase in Le and Nr for both vertical plate and cone. The local Nusselt number decreases with the increase in the thermophoresis and Brownian motion parameters for both the plate and cone. The local Sherwood number increases with the Brownian motion parameter and decreases for thermophoresis parameter. The results have been compared with the published ones and an excellent agreement has been noticed.

A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD) free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z) coordinate system to a (ξ,η) coordinate system in terms of dimensionless x-direction velocity (∂F/∂η) and z-direction velocity (G) and dimensionless temperature function (H) under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM). The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

We present a mathematical model and numerical simulation of the unsteady 2-D g-jitter-free and forced the convective flow of water-based nanofluid from a flat plate, considering both the velocity slip and thermal slip conditions imposed on the wall of the plate. The Darcian model is used, and both cases of a calm and moving free stream are considered. In place of the extensively used linearly varying radiative heat flux, the nonlinearly varying heat flux calculation is applied to produce practically useful results. Further, we incorporate the “zero mass flux boundary condition” which is believed to be more realistic than the earlier extensively used “actively” controlled model. The parameter influences the non-dimensional velocity, temperature, nanoparticle volume fraction, skin friction and heat transfer rates are visualized graphically and discussed in detail. Special cases of the results are benchmarked with those existing in the literature, and a good arrangement is obtained. It is found that the rate of heat transfer is lower for the calm free stream rather than the moving free stream.

The aim of this study was to evaluate effect of non genetic factors on reproductive performance ofBali cattle. Data on reproduction performance were collected from Breeding Centre of Bali Cattle inDenpasar-Bali. Reproductive traits studied were age at first calving (AFC), calving interval (CI) andpregnancy rate (PR). To observe the effect of non genetic factors on the reproductive traits, a mixedmodel was used because all of the traits studied were measured repeatedly in individuals. The overallmeans for AFC, CI, PR and preweaning mortality were 43.86±0.70 months, 360.93±4.47 days,88.44±1.91% and 7.58±1.07%, respectively. The results showed that AFC and PR were significantly(P0.05) effect. Withregard to CI, dam year of birth and parity affected CI while mating system had no significantly affect(P>0.05) on CI. The preweaning mortality was only affected by the age of dam significantly (P