Nanoparticle Shape Factor Research Articles

Significance of nanoparticle shape factor and buoyancy effects on a parabolic motion of EMHD convective nanofluid past a Riga plate with ramped wall temperature

Significance of nanoparticle shape factor and buoyancy effects on a parabolic motion of EMHD convective nanofluid past a Riga plate with ramped wall temperature

MXene (Ti3C2) embedded blood flow on curved stretching artery: Thermal analysis due to nanoparticle shape factor

The 2-D MXene material has garnered immense attention in the multidisciplinary region due to its high surface area, excellent electrical conductivity, good biocompatibility, and tunable physicochemical properties. MXene nanoparticles can be utilized in thermal ablation to destroy unwanted tissues and tumors without invasive surgery. Therefore, this work investigates MXene (Ti3C2) embedded blood flow over a curved shape stretching artery. The mathematical model for hybrid blood flow is developed to see the thermal changes due to external pressure and diffusion. Furthermore, the flow model PDEs are equipped with Darcy-Forchheimer’s condition, external magnetic force, thermal radiation, and heat source/sink. These PDEs are converted into a system of ODEs by a proper similarity conversion. The solution of governing equations are acquired numerically, the flow and thermal performance outputs are exhibited through pictorial and tabular representations. It is revealed that the thermal performance is enhanced due to sphere shaped MXene (Ti3C2) nanoparticles. The outcomes of this study can be utilized in photothermic therapy and other applications where heat transfer plays an essential role.

Study of Nanoparticle Diffusion in Capillary-Tissue Exchange System using Jeffrey Nanofluid Model: Effects of Shapes of Nanoparticles

The present work concerns the diffusion of nanoparticles in capillary-tissue exchange system. Nanoparticle are inoculated into the patient’s body by intertumoral administration. Thus, nanoparticles diffuse into tumoral tissues through diseased capillary walls. Blood in the capillaries is modelled as Jeffrey fluid. The resultant fluid is called Jeffrey nanofluid. In this model we have described diffusion occurring through the capillary walls into the surrounding tissue. The mathematical results are obtained analytically and have been compared with numerical solution. Graphs have been plotted using MATLAB. The effects of shape factor of nanoparticles, volume fraction of nanoparticles, Jeffrey fluid parameter, viscosity index and viscosity parameter has been observed on velocity and concentration of nanoparticles diffusing into the tissues. A noticeable observation states that brick shaped nanoparticles diffuse most rapidly i.e., have higher diffusion rates than other shapes

Biosynthesis and numerical investigation of radiative heat transfer in silver-blood nanofluid flow through cosine-shaped stenosed artery: a biomedical application

Silver is a well-acknowledged antimicrobial and has wider usage to kill bacteria, as a topical treatment for burns, and as anticancer therapy. Because of this, the current work combines experimental and theoretical examinations on the impact of the external magnetic field, nanoparticle shape factor, and radiative heat in human blood flow. Here the blood is embedded with silver nanoparticles and passes through the cosine-shaped stenosis artery with unobstructed size. The biosynthesis of silver nanoparticles is prepared with moringa oleifera leaves. A mathematical exemplary was developed to scrutinize the control of physical quantities on movement and heat relocation in silver-blood nano liquid. The transformed central equalities are solved mathematically, and outcomes are explored in graphical and tabular illustrations. The obtained results validated the limiting case and found a good agreement. It is remarkable to mention that the silver-blood-lamina mixture heat relocation rate is more advanced than the silver-blood-platelet mixture. Therefore, the suspension of lamina-shaped silver nanoparticles in the blood may help to kill bacteria effectively.

Irreversibility analysis of electromagnetic hybrid nanofluid for Cattaneo–Christov heat flux model using finite element approach

To get a better heat transmission capacity of ordinary fluids, new hybrid nanofluids (HNFs) with a considerably greater exponent heat than nanofluids (NFs) are being used. HNFs, which have a greater heat exponent than NFs, are being applied to increase the HT capacities of regular fluids. Two-element nanoparticles mixed in a base fluid make up HNFs. This research investigates the flow and HT features of HNF across a slick surface. As a result, the geometric model is explained by employing symmetry. The technique includes nanoparticles shape factor, Magnetohydrodynamics (MHD), porous media, Cattaneo–Christov, and thermal radiative heat flux effects. The governing equations are numerically solved by consuming a method known as the Galerkin finite element method (FEM). In this study, H2O-water was utilized as an ironic, viscous improper fluid, and HNF was investigated. Copper (Co) and Titanium Alloy (Ti6Al4V) nanoparticles are found in this fluid. The HT level of such a fluid (Ti6Al4V-Co/H2O) has steadily increased in comparison to ordinary Co-H2O NFs, which is a significant discovery from this work. The inclusion of nanoparticles aids in the stabilization of a nanofluid flowing and maintains the symmetry of the flow form. The thermal conductivity is highest in the boundary-lamina-shaped layer and lowest in sphere-shaped nanoparticles. A system's entropy increases by three characteristics: their ratio by fractional size, their radiated qualities, and their heat conductivity modifications. The primary applications of this examination are the biological and medical implementations like dental and orthopedic implantable devices, as well as other devices such as screws and plates because they possess a favorable set of characteristics such as good biomaterials, corrosion resistance and wear, and great mechanical characteristics.

Engine oil enhanced performance with hybrid graphene-SWCNT nanomaterials over a Riga curvy surface

Hybrid graphene nanomaterials and single-wall carbon nanotubes (SWCNTs) saturated in a steady laminar viscous incompressible engine oil over a permeable and stretchable curvy Riga surface are focussed in the present study. The effects of nanoparticle shape factor, nanoparticle volume fraction and thermal radiation towards the non-Newtonian flow are considered. The proposed partial differential governing equations are initially transformed into non-linear ODEs aided with similarity expressions. Subsequently, the numerical MATLAB's bvp4c package is utilized to solve the equations. Then, the parameters' influences on dimensionless velocity and temperature distributions, reduced skin friction coefficient and reduced Nusselt number are presented tabularly and graphically. Hybrid graphene-SWCNTs/engine oil has the least velocity, yet the greatest temperature profile when φ1= 0.04 and φ2= 0.02 are considered. It is also observed that the heat transfer performance enhances as the values of nanoparticle shape factor and thermal radiation increase. The lamina-shape nanomaterials are highly recommended to elevate the heat transfer performance of hybrid graphene-SWCNTs/engine oil for realistic applications. The present hybrid nanofluid flow with consideration of thermal radiation and nanoparticle shape factor allows enhancement in the heat and mass transfer for various engineering, technological and industrial operations especially in the design of submarines, thermal reactors and micro-coolers.

Numerical analysis of magneto-radiated annular fin natural-convective heat transfer performance using advanced ternary nanofluid considering shape factors with heating source

ApplicationsThe fins performance under natural convection is essential to make it more functional for large scale applications more specifically in thermal engineering. For this, it is important to introduce new techniques to enhance the fins performance instead of traditional way. Thus, this study introduces a new way to make the fin more efficient using ternary nanomaterial under nanoparticles shape factor. The annular fin significantly contributes in electronics to exhaust the hot air, injector pumps and applied thermal engineering. Purposeand Methodology: This work focuses on the fin energy model using shape factors. Therefore, the ternary nanofluid, natural convection, thermal radiation and magnetic field used to develop the model. Then, the RKF-45 implemented to investigate physical results. Core findingsKeen analysis of the physical results reveal that the coefficient of thermal conductivity ranging from 0.0% < α1 < 3.0% and natural convection have major role in the fins energy performance. Induction of magnetic field and thermal radiation Rd are reliable for the fin cooling and, heating source Q1 = 0.2,0.4,0.6,0.8 promote the fin energy capability in the existence of (Al2O3–CuO–Cu) ternary nanomaterial with concentration factor up to 2%. On the comparative basis, ternary nanomaterial makes the fin more efficient than hybrid nanomaterial.

HOMOTOPY PERTURBATION ANALYSIS ON SHAPE EFFECT OF VASODILATORS DURING ARTERIAL FLOW

In this study, the homotopy perturbation method was employed to study the influence of the thermal and applied magnetic fields on the movement and efficiency of differently shaped nanoparticles. Extensive Hartmann number, nanoparticle shape factor, and nanofluid volume fraction values were used to investigate the influence of differently shaped nanoparticles in a flow-through diseased artery. To analyze the flow and heat conduction behavior of nanoparticles in an artery, the wall impedance and local Nusselt number values were evaluated using the homotopy perturbation method and the results were compared with existing results for the same case. The results of both approaches were compared graphically for the volume fraction and magnetic interaction parameters. In addition, a graph was plotted to compare the behavior of nanoparticles in both the Hamilton-Crosser and modified Hamilton-Crosser models.

Changing the physical behavior of phase change material by means of numerical technique

Numerical simulation was offered for scrutinizing the freezing of water within the complex container. The container has elliptic left adiabatic wall while the right wall is sinusoidal wall and maintained at cold temperature. The drawback of water has been removed by adding alumina nanoparticles. For this modeling, different ranges of volume and shape factor of nanoparticles have been scrutinized by incorporating FEM. The configuration of grid alters with change of time and verification test has been presented which proved good accuracy. As bigger shape factor has been selected, the time of process decline less than 4% for cylinder shape and this percentage augments around 78.22% for blade shape. As nanoparticle fraction increases, the required time declines around 26.84%. The impact of blade shape in view of adding nanoparticles is 25.74% greater than that of cylinder shape.

The role of nanofluids and fins in a heat exchanger on waste energy recovery from a diesel engine: An experimental and numerical study

A 3.7 kW diesel engine and a shell-and-tube heat exchanger were used in this study to decrease the temperature of exhaust gases and reduce the effects of greenhouse gases, respectively. The innovations utilized in this paper include the use of four novel non-linear arrangements of fins on the heat exchanger body, two different types of nanofluids (Ag, Fe3O4) in single and hybrid forms, and using the nanoparticles shape factor. The embedded simulation in the ANSYS-FLUENT commercial software was evaluated under the K-epsilon (κ−ɛ) turbulence modeling. The study results showed that the exhaust gases’ temperature drops by an average of 7.0% by increasing the curvature of the fins, while this value was obtained as 5.80% by enhancing the height of the fins from 8 mm to 24 mm. Examining the effect of the shape of the used nanoparticles revealed that changing the shape factor from Spherical to Lamina led to the increase of heat transfer rate by 4.33%. Also, at a constant shape factor, increasing the number of fins caused a 47.12% growth in the heat transfer rate. Therefore, one can say that the arrangement and number of fins have a larger influence on increasing the heat transfer rate than the nanoparticles shape factor. Moreover, increasing the concentration of nanofluids from 1% to 5% led to a 0.67% drop in the temperature of the exhaust gases. According to the research results, we can recognize the parameters of the number, shape, and arrangement of the fins, the type of nanofluid, and the nanoparticles shape factor as factors effective in reducing the temperature of exhaust gases from a diesel engine.

Thermal performance of ternary-hybrid nanofluids through a convergent-divergent nozzle using distilled water - ethylene glycol mixtures

A computational analysis is conducted based on ternary-nanoparticles performance for base fluid mixture through a convergent-divergent (CD) nozzle. Since the thermal phenomena through a CD nozzle exposes many attention-grabbing performances, it deserves additional investigation for laminar flow characteristics. Using ternary-nanoparticles at different base fluid mixture makes the study more robust and interesting to analyze the real situation better. In this study, the properties of cobalt (Co), silver (Ag), and zinc (Zn) nanoparticles along with base fluid mixtures of distilled-water (DW) and ethylene glycol (EG) as (100:0), (60:40), (50:50), and (0:100), are employed. A wide range of inlet velocity, solid concentrations, nanoparticle size and magnitude of nanoparticle shape factor is considered in this research. The mixtures of nanoparticles are considered as a ratio of (0:1/2:1/2), (1/2:0:1/2), (1/2:1/2:0), (1/6:1/6:2/3), (1/6:2/3:1/6), (2/3:1/6:1/6) and (1/3:1/3:1/3). The mathematical model is formulated using Navier-Stokes equations, energy conservation with proper boundary conditions, and solved using finite element method. Among the considered base fluid mixtures, the highest heat transfer rate is obtained for EG-Co-Ag-Zn nanofluid. A relatively higher heat transfer rate is found for all base fluid mixtures with nanoparticles ratio (1/6:2/3:1/6) compared to other combinations. Furthermore, advanced rate of thermal transport is found using laminar shape nanoparticles.

Nanomaterial efficacy on freezing of PCM with involvement of numerical simulation

To reduce the freezing time for a unit with curved walls which filled with water, nanoparticles has been dispersed. The shapes of CuO nano-powder can affect the conductivity of mixture and this factor efficacy has been scrutinized in current article. Freezing process is mostly affected by condition and due to negligible magnitude of velocity, only the energy equation with neglecting advection term should be considered as main equation which has been solved via FEM. The proposition of utilizing homogeneous mixture is applicable for condition of low concentration of additives and for this study, this is practical assumption. Conduction mode is significant for freezing and dispersing nanoparticle especially with greater shape factor can expedite the process. When shape factor of copper oxide nanoparticles augments with fraction of 0.04, the freezing time decline about 10.71%. The required time declines about 31.39% with raising the fraction of particles from zero to 0.04.

Hybrid Nanofluid Flow Induced by an Oscillating Disk Considering Surface Catalyzed Reaction and Nanoparticles Shape Factor.

Lately, a new class of nanofluids, namely hybrid nanofluids, has been introduced that performs much better compared with the nanofluids when a healthier heat transfer rate is the objective of the study. Heading in the same direction, the present investigation accentuates the unsteady hybrid nanofluid flow involving CuO, Al2O3/C2H6O2 achieved by an oscillating disk immersed in the porous media. In a study of the homogeneous and heterogeneous reactions, the surface catalyzed reaction was also considered to minimize the reaction time. The shape factors of the nanoparticles were also taken into account, as these play a vital role in assessing the thermal conductivity and heat transfer rate of the system. The assumed model is presented mathematically in the form of partial differential equations. The system is transformed by invoking special similarity transformations. The Keller Box scheme was used to obtain numerical and graphical results. It is inferred that the blade-shaped nanoparticles have the best thermal conductivity that boosts the heat transfer efficiency. The oscillation and surface-catalyzed chemical reactions have opposite impacts on the concentration profile. This analysis also includes a comparison of the proposed model with a published result in a limiting case to check the authenticity of the presented model.

Thermal strategy due to flame shape source in a carbon nanotubes-water enclosed by trapezoidal cavity

Thermal performance of working fluids is an important aspect in current industrial age. Single wall carbon nanotubes (SWCNTs) mixed with water can perform better as compared to the ordinary water in terms of thermal properties. SWCNTs nanofluids is considered within the trapezoidal cavity with flame shape heated source to examine the effects on thermal distribution of heat inside the cavity and flow pattern. To analyze the significant behavior of isotherm and steam lines, variation of Rayleigh number, heat generation parameter and size of flame is adjusted. Mathematical model is developed through continuity, momentum and energy equations that stand in the form of a system of nonlinear partial differential equations emerged with the nanofluid's relations to handle the viscosity, density, shape of nanoparticles, and thermal conductivity. Constraints are adjusted according to the natural convection due to flame shape source within the trapezoidal cavity. Since the shape factor of nanoparticles also has a dominant effect on fluid that is why, various shape of nanoparticles is considered to attain the best thermal performance. All the emerging parameters are analyzed through variation of velocities, temperature profiles, isotherms, and streamlines. Entire analysis demonstrates that free convection and heat generation deliver significant variation in isotherm and streamlines with respect to increasing values of Rayleigh number. Nanoparticle volume fraction gives a considerable increase in the heat transfer rate inside the cavity. It is observed that heat transfer rate is maximum when r=0.6. Local Nusselt number increase for buoyancy driven flow. The presence of carbon nanotubes increases the temperature profile within the cavity.

Performance of hybrid two-phase nanofluid neighboring to permeable plates exposed to elevated temperatures

Hybrid nanofluid becomes a fascinating research topic due to its thermophysical properties and stability which provide better performance compared to typical nanofluids. Two-phase model for mixed convection magnetohydrodynamic (MHD) flow was investigated incorporating hybrid nanoparticles of Alumina (Al2O3) and Copper (Cu) while the base fluid is water (Cu-Al2O3/water). Three parameters group transformation method (GTM) was employed to transform the mathematical model into a simpler system. The analysis included the effect of magnetic parameter, permeability coefficient, nanoparticle shape factor, temperature ratio, radiation parameter, nanoparticles fraction ratio, Brownian parameter, thermophoresis parameter and Nusselt, Reynold, Prandtl and Sherwood numbers relations. The results showed that the fluid velocity and shear stress were more sensitive to the change of magnetic parameter, M, Prandtl number, Pr, and permeability coefficient, . Moreover, the temperature distribution and the heat flux inside the boundary layer were more sensitive to changing Pr, radiation parameter, Nr , and nanoparticles relative ratio, Nf , while it was less sensitive to changing M. Nusselt–Reynolds number, , reached its highest value 242.7 at then 28.11 at and . Sherwood–Reynolds number, , scored its highest value 83.68 at then 11.03 at temperature ratio difference, , of 10 and .

Investigation of Nanoparticles Shape Effects on Aligned MHD Casson Nanofluid Flow and Heat Transfer with Convective Boundary Condition

This study focuses on the investigation of aligned MHD natural convection flow and heat transfer of a Casson nanofluid past a vertical plate with convective boundary condition. Casson nanofluid are found in a wide range of commercial and technological applications, including dissolved polymers, biological solutions, paints, asphalts, and glues. The governing partial differential equations (PDE) is transformed to ordinary differential equations (ODE) by using similarity transformation. Keller box method is employed to numerically solve the transformed partial differential equations and then the system is solved by Fortran programming. The results for both the velocity and temperature profiles of Casson nanofluid as well as the skin friction and Nusselt number that are affected by nanoparticles shape factor considering parameters aligned angle of magnetic, interaction of magnetic field, volume fraction of nanoparticles, Local Grashof number, Casson parameter and Biot number are presented graphically and in tabulated form. It is also found that the velocity increases while the temperature decreases when the aligned angle of magnetic, interaction of magnetic field, Casson parameter and Local Grashof number increase. The skin friction and Nusselt number increases for all parameters except for Casson nanofluid parameter. For convective boundary condition, Biot number increases when both velocity and temperature profiles increase. The nanoparticles shape of laminar has the highest velocity and temperature while the spherical shape has the lowest for all parameters.

Coupled flow and heat transfer of power-law nanofluids on non-isothermal rough rotary disk subjected to magnetic field

We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field. The problem is formulated in terms of specified curvilinear orthogonal coordinate system. An improved BVP4C algorithm is proposed, and numerical solutions are obtained. The influence of volume fraction, types and shapes of nanoparticles, magnetic field and power-law index on the flow, and heat transfer behavior are discussed. The obtained results show that the power-law exponents (PLE), nanoparticle volume fraction (NVF), and magnetic field inclination angle (MFIA) have almost no effects on velocities in the wave surface direction, but have small or significant effects on the azimuth direction. The NVF has remarkable influences on local Nusselt number (LNN) and friction coefficients (FC) in the radial direction and the azimuth direction (AD). The LNN increases with NVF increasing while FC in AD decreases. The types of nanoparticles, magnetic field strength, and inclination have small effects on LNN, but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate, while the inclination is negatively correlated with heat transfer rate. The size of the nanoparticle shape factor is positively correlated with LNN.

Experimental investigation and artificial intelligent estimation of thermal conductivity of nanofluids with different nanoparticles shapes

Determining and modelling the effective thermal conductivity of nanofluids is always a concern of investigators. The effect of nanoparticles' shape on the effective thermal conductivity of nanofluids has not been accurately correlated with other influencing factors such as temperature and nanoparticle concentration. The main purpose of this study is to reveal the effects of influencing factors on the effective thermal conductivity of nanofluids by experimental investigation and artificial intelligence (AI). We prepared the TiO2/water nanofluids with four shapes of TiO2 nanoparticles (spherical, ellipsoidal, clubbed, and sheet) and measured the effective thermal conductivities of the samples with nanoparticles concentrations from 0.5 to 4.0 vol% as a function of temperature from 20 to 60 °C. Besides, 389 experimental datasets collected from literature and 80 datasets from our experiment were used to determine the optimum structure of AI-based models. Temperature, concentrations, shape factor, and thermal conductivity of nanoparticles were selected as independent variables, and the relative thermal conductivity of nanofluids was selected as the dependent variable. Six AI-based models were examined, including four artificial neural networks of multi-layer perceptron, cascade feedforward, radial basis function, and generalized regression neural network, adaptive neuro-fuzzy inference systems, and least-squares support vector machines, and the estimating performances were compared. The experimental results showed that increasing temperature and nanoparticles concentrations led to a remarkable improvement in the relative thermal conductivity of nanofluids, attributed to the intensified Brownian motion of nanoparticles with the high temperature and the effective collision of nanoparticles with the high concentrations. Besides, nanoparticles with a large aspect ratio provided the fast pathway with seldom crossing an interparticle boundary or junction point for effective heat transfer in the nanofluids, resulting in higher relative thermal conductivity of nanofluids. Statistical analyses confirmed that the cascade feed-forward neural network with ten hidden neurons and the Levenberg–Marquardt training algorithms was the optimized AI-based model for estimating the relative thermal conductivity of nanofluids. This model estimated allover experimental data by MSE = 0.0039, RMSE = 0.0622, AARD% = 2.66%, and R2 = 0.9908.

Computational simulation of rheological blood flow containing hybrid nanoparticles in an inclined catheterized artery with stenotic, aneurysmal and slip effects

Influenced by nano-drug delivery applications, the present article considers the collective effects of hybrid biocompatible metallic nanoparticles (Silver and Copper), a stenosis and an aneurysm on the unsteady blood flow characteristics in a catheterized tapered inclined artery. The non-Newtonian Carreau fluid model is deployed to represent the hemorheological characteristics in the arterial region. A modified Tiwari-Das volume fraction model is adopted for nanoscale effects. The permeability of the arterial wall and the inclination of the diseased artery are taken into account. The nanoparticles are also considered to have various shapes (bricks, cylinders, platelets, blades) and therefore the influence of different shape parameters is discussed. The conservation equations for mass, linear momentum and energy are normalized by employing suitable non-dimensional variables. The transformed equations with associated boundary conditions are solved numerically using the FTCS method. Key hemodynamic characteristics i.e. velocity, temperature, flow rate, wall shear stress (WSS) in stenotic and aneurysm region for a particular critical height of the stenosis, are computed. Hybrid nanoparticles (Ag–Cu/Blood) accelerate the axial flow and increase temperatures significantly compared with unitary nanoparticles (Ag/blood), at both the stenosis and aneurysm segments. Axial velocity, temperature and flow rate are all enhanced with greater nanoparticle shape factor. Axial velocity, temperature, wall shear stress and flow rate magnitudes are always comparatively higher at the aneurysm region compared with the stenotic segment. The simulations provide novel insights into the performance of different nanoparticle geometries and also rheological behaviour in realistic nano-pharmaco-dynamic transport and percutaneous coronary intervention (PCI).

Stagnation point flow of a micropolar fluid filled with hybrid nanoparticles by considering various base fluids and nanoparticle shape factors

PurposeThe boundary-layer analysis is required to reveal the fluid flow behavior in several industrial processes and enhance the products’ effectiveness. Therefore, this research aims to investigate the buoyancy or mixed convective stagnation-point flow (SPF) and heat transfer of a micropolar fluid filled with hybrid nanoparticles over a vertical plate. The nanoparticles silver (Ag) and titanium dioxide (TiO2) are scattered into various base fluids to form a new-fangled class of (Ag-TiO2/various base fluid) hybrid nanofluid along with different shape factors.Design/methodology/approachThe self-similarity transformations are used to reformulate the leading requisite partial differential equations into renovated non-linear dimensionless ordinary differential equations. The numerical dual solutions are gained for the transmuted requisite equations with the help of the bvp4c built-in package in MATLAB software. The results are validated by comparing them with previously available published data for a particular case of the present study.FindingsThe impact of various pertaining parameters such as nanoparticle volume fraction, material parameter, shape factor and mixed convective on temperature, heat transfer, fluid motion, micro-rotation and drag force are visualized and scrutinized through tables and graphs. It is observed that dual or non-uniqueness outcomes are found for the case of buoyancy assisting flow, whereas the solution is unique in the buoyancy opposing flow case. Additionally, the fluid motion and micro-rotation profiles decelerate in the presence of nanoparticle volume fraction, while the temperature augments.Originality/valueThe mixed convective stagnation point flow conveying TiO2/Ag hybrid nanofluid with micropolar fluid with various shape factors is the significant originality of the current investigation where multiple outcomes are obtained for the assisting flow. The various base fluids such as glycerin, water and water–ethylene glycol (50%:50%) are considered in the present problem. The bifurcation values of the considered problem do not exist, probably because of various base fluids. To the best of the authors’ knowledge, this work is new and original which were not previously reported.