Stability analysis for heat transfer flow in micropolar hybrid nanofluids

Objective: hybrid nanofluids have superior thermal efficiency and physical durability in contrast to regular nanofluids. The stagnation point flow of MHD micropolar hybrid nanofluids over a deformable sheet with viscous dissipation is investigated. Methodology: the controlling partial differential equations are converted to nonlinear ordinary differential equations using the transmuted similarity, and are subsequently solved using the bvp4c solver in MATLAB. The hybrid nanofluids consist of aluminum and copper nanoparticles, dispersed in a base fluid of water. Results: multiple solutions are obtained in the given problem for the case of shrinking as well as for the stretching sheet due to the variation in several influential parameters. Non-unique solutions, generally, exist for the case of shrinking sheets. In addition, the first branch solution is physically stable and acceptable according to the stability analysis. The friction factor is higher for the branch of the first solution and lower in the second branch due to the higher magnetic parameters, while the opposite behavior is seen in the case of the local heat transfer rate. Originality: the novelty of this model is that it finds multiple solutions in the presence of Cu and Al2O3 nanoparticles and also performs the stability analysis. In general, non-unique solutions exist for the phenomenon of shrinking sheets.

Viscous dissipation effects on hybrid nanofluid flow over a non-linearly shrinking sheet with power-law velocity

This research intends to investigate the effect of the nonlinearity of the surface velocity on the hybrid nanofluid flow behavior. Here, the total composition of Al2O3 (alumina) as well as Cu (copper) volume fractions, are implemented in a one-to-one ratio and then dispersed in water. The similarity equations are gained employing a similarity transformation, which is programmed in MATLAB software. The dual solutions are attainable for certain ranges with respect to the mass flux parameter S and the power-law index n . Also, the turning point occurs in the region of S < 0 and n > 1 . Besides, the rise of n led to reduce the skin friction as well as the heat transfer coefficients with 39.44 % and 11.71 % reduction, respectively. Moreover, 14.39 % reduction of the heat transfer rate is observed in the presence of viscous dissipation (Eckert number). It is found that only the first solution is stable as time progresses. Generally, this study gives scientists and engineers a starting point for predicting how to control the parameters to achieve the best results for relevant practical applications.

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Cooling and heating are two critical processes in the transportation and manufacturing industries. Fluid solutions containing metal nanoparticles have higher thermal conductivity than conventional fluids, allowing for more effective cooling. Thus, the current paper is a comparative exploration of the time-independent buoyancy opposing and heat transfer flow of alumina nanoparticles scattered in water as a regular fluid induced via a vertical cylinder with mutual effect of stagnation-point and radiation. Based on some reasonable assumptions, the model of nonlinear equations is developed and then tackled numerically employing the built-in bvp4c MATLAB solver. The impacts of assorted control parameters on gradients are investigated. The outcomes divulge that the aspect of friction factor and heat transport upsurge by incorporating alumina nanoparticles. The involvement of the radiation parameter shows an increasing tendency in the heat transfer rate, resulting in an enhancement in thermal flow efficacy. In addition, the temperature distribution uplifts due to radiation and curvature parameters. It is discerned that the branch of dual outcomes exists in the opposing flow case. Moreover, for higher values of the nanoparticle volume fraction, the reduced shear stress and the reduced heat transfer rate increased respectively by almost 1.30% and 0.0031% for the solution of the first branch, while nearly 1.24%, and 3.13% for the lower branch solution.

Heat transfer characteristics of magnetized hybrid ferrofluid flow over a permeable moving surface with viscous dissipation effect

Hybrid ferrofluid is a unique heat transfer fluid because it can be magnetically controlled and ideal in various applications. Further exploration to unleash its potential through studying heat transfer and boundary layer flow is crucial, especially in solving the thermal efficiency problem. Hence, this research focuses on the numerical examination of flow behaviour and heat transfer attributes of magnetized hybrid ferrofluid Fe3O4-CoFe2O4/water across a permeable moving surface considering the mutual effects of magnetohydrodynamic (MHD), viscous dissipation, and suction/injection. The problem was represented by the Tiwari and Das model with duo magnetic nanoparticle hybridization; magnetite Fe3O4 and cobalt ferrite CoFe2O4 immersed in water. The governing equations were transformed into ordinary differential equations using appropriate similarity variables and solved with bvp4c MATLAB. A dual solution is obtained, and via stability analysis, the first solution is stable and physically reliable. The significant influence of governing effects on the temperature and velocity profiles, the local skin friction coefficient and the local Nusselt number are analyzed and visually shown. The surge-up value of suction and CoFe2O4 ferroparticle volume concentration enhances the local skin friction coefficient and heat transfer rate. Additionally, the magnetic parameter and Eckert number reduced the heat transfer. Using a 1% volume fraction of Fe3O4 and CoFe2O4; the hybrid ferrofluid's convective heat transfer rate was shown to be superior to mono-ferrofluid and water by enhancing 2.75% and 6.91%, respectively. This present study also suggests implying a greater volume concentration of CoFe2O4 and lessening the magnetic intensity to maintain the laminar flow phase.

Time-Dependent Flow of Water-Based CoFe2O4-Mn-ZnFe2O4 Nanoparticles over a Shrinking Sheet with Mass Transfer Effect in Porous Media

The use of hybrid nanoparticles to increase heat transfer is a favorable area of research, and therefore, numerous scientists, researchers, and scholars have expressed their appreciation for and interest in this field. Determining the dynamic role of nanofluids in the cooling of microscopic electronic gadgets, such as microchips and related devices, is also one of the fundamental tasks. With such interesting and useful applications of hybrid nanofluids in mind, the main objective is to deal with the analysis of the unsteady flow towards a shrinking sheet in a water-based hybrid ferrite nanoparticle in porous media, with heat sink/source effects. Moreover, the impact of these parameters on heat and mass transfers is also reported. Numerical results are obtained using MATLAB software. Non-unique solutions are determined for a certain shrinking strength, in addition to the unsteadiness parameter. The mass transfer and friction factor increase for the first solution due to the hybrid nanoparticles, but the heat transfer rate shows the opposite effect.

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

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

Thermal Progress of Unsteady Separated Stagnation Point Flow with Magnetic Field and Heat Generation in Hybrid Ferrofluid

This paper examines the unsteady separated stagnation point (USSP) flow and thermal progress of Fe₃O₄-CoFe₂O₄/H₂O on a moving plate subject to the heat generation and MHD effects. The model of the flow includes the boundary layer and energy equations. These equations are then simplified with the aid of similarity variables. The numerical results are generated by the bvp4c function and then presented in graphs and tables. The magnetic and acceleration (strength of the stagnation point flow) parameters are the contributing factors in the augmentation of the skin friction and heat transfer coefficients. However, the enhancement of heat generation parameter up to 10% shows a reduction trend in the thermal rate distribution of Fe₃O₄-CoFe₂O₄/H₂O. This finding reveals the effectiveness of heat absorption as compared to the heat generation in the thermal flow process. From the stability analysis, the first solution is the physical solution. The streamline for the first solution acts as a normal stagnation point flow, whereas the second solution splits into two regions, proving the occurrence of reverse flow.

Exact Solutions for Wall Jet Flow of Hybrid Nanofluid

Hybrid nanofluid wall jet problem of Glauert type has been investigated under effects of the thermal radiation, suction parameter, moving parameter, slip velocity and temperature jumps. Via similarity variables governing equations are converted to system of ODEs. Then, resulted equations are solved exactly for velocity and temperature field in the view of gamma and hypergeometric functions. Further, to confirm the similarity solutions, a relationship between the free stream velocity, slip parameter along with suction parameter, moving parameter and solid volume fractions were introduced. In addition, we discussed the physical existence of the slip parameter and asymptotic behavior in a relation with the moving and suction parameters. Further, the obtained outputs are matched with the previous works. It is seen that adding the copper nanoparticles to the nanofluid titanium dioxide/water has effective part in the velocity behavior. Moreover, they warm the hybrid nanofluid on increasing the thermal radiation parameter. However, effects of suction and temperature jump parameters lead to cooling the hybrid nanofluid temperature. Furthermore, for enlarging the wall velocity, the hybrid nanofluid is much better rather than the classical nanofluid. The current analysis has important applications; such as liquid crystal solidification and polymer process.

Aqua Cobalt Ferrite/Mn–Zn Ferrite Hybrid Nanofluid Flow Over a Nonlinearly Stretching Permeable Sheet in a Porous Medium

In the present article, the problem of ferro hybrid nanofluid flow over a nonlinearly stretching permeable sheet in a porous medium has been studied. The main motivation of this research is to present a comprehensive analysis of the hydrodynamics and thermal boundary layers as well as the skin friction and heat transfer as two important quantities of engineering interest for the relevant ferro hybrid nanofluid flow. The ferro hybrid nanofluid is a nanofluid that can be composed of several nanoparticles and has a magnetic property; it means that has its own behavior in the magnetic field. Two different types of ferroparticles, namely, Mn–Zn ferrite (Mn–ZnFe2O4) and cobalt ferrite (CoFe2O4) are considered with water as a base fluid. The similarity solution is used to decrease the governing set of partial differential equations (PDEs) to the nonlinear ordinary differential equations (ODEs) system, which is solved numerically by the bvp4c function of MATLAB. The effects of pertinent parameters, namely, magnetic parameter, nonlinear velocity parameter, permeability parameter, and volume fraction of the second nanoparticle on velocity and temperature profiles, skin friction coefficient, and local Nusselt number are computed and shown through graphs. The prominent novelty of this research is related to the use of ferro hybrid nanofluid as a working fluid, where many studies have been carried out in the field of the determination of heat transfer and skin friction in nanofluids/ferro nanofluids on different geometries. To the best of our knowledge, no one has ever attempted to study the present boundary layer problem with applying ferro hybrid nanofluid. The results of this paper indicate that Nusselt number and skin friction coefficient decrease with increasing magnetic field.

Free Convection Boundary Layer Flow from a Vertical Truncated Cone in a Hybrid Nanofluid

The present study investigates the mathematical model of free convection boundary layer flow from a vertical truncated cone immersed in Cu/water nanofluid and Al2O3-Cu/water hybrid nanofluid. The governing non-linear equations are first transformed to a more convenient set of partial differential equations before being solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number and the reduced skin friction coefficient are obtained and illustrated graphically as well as temperature profiles and velocity profiles. Effects of the alumina Al2O3 and copper Cu nanoparticle volume fraction for hybrid nanofluid are analyzed and discussed. It is found that the high-density and highly thermal conductivity nanoparticles like copper contributed more in skin friction and convective heat transfer capabilities. The appropriate nanoparticles combination in hybrid nanofluid may reduce the friction between fluid and surface but yet still gave the heat transfer capabilities comparable to metal nanofluid.

Lateral sinus thrombosis in a young patient with sudden neurosensorial hearing loss and genetic thrombophilia: A case report

Sensorineural hearing loss (SSHL) with a sudden onset is frequently encountered as a medical emergency in the ear, nose and throat (ENT) practice. The exact pathophysiology of the disease remains unknown, with the most likely etiologies being viral infection, inflammation, drug toxicity, trauma, or autoimmune response. Even though thrombophilia and cerebrovascular complications may lead, among others, to sudden neurosensorial hearing loss, its diagnosis is most often made following the onset of thrombotic complications. A case of a young female patient with unknown congenital hypercoagulation status complicated with lateral sinus thrombosis and unilateral drug-induced reversible hearing loss is presented. Molecular testing confirmed the diagnosis of genetic thrombophilia, due to the homozygous V Leiden, homozygous MTHFR A1298C, and heterozygous MTHFR C677T mutations. Although hereditary thrombophilia is a well-known topic in medical practice, current guidelines require continuous improvement, especially among patients treated in departments where this pathology is more difficult to recognize and manage.

The Impact of Thermal Radiation on Maxwell Hybrid Nanofluids in the Stagnation Region

Previous research has recognised the study of stagnation point flow by focusing Maxwell nanofluid on a stretching sheet surface. Motivated by this research idea, our main objective is to formulate and analyse a new mathematical model of stagnation point flow in Maxwell fluid that highlights the dual types of fluid known as hybrid nanofluids. The effects of thermal radiation and heat transfer are also considered. The partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) via similarity variables that generate similarity solutions. Following that, the bvp4c approach is employed to discover the approximate solutions of the reduced ODEs. The significance of various parameters is graphically presented and considers the physical quantities of interest. A remarkable observation found in this study is the enhancement of the heat transfer rate in Maxwell hybrid nanofluids, which is steadily amplified in contrast to traditional fluids. Indeed, the Maxwell parameter in hybrid nanofluids embarks on a substantial increment of the heat transfer rate. The current study succeeds in establishing more than one solution along the stretching/shrinking sheet. Thus, the stability analysis is conducted to confirm the sustainability of the solutions.

Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

Oblique Stagnation-Point Flow Past a Shrinking Surface in a Cu-Al2O3/H2O Hybrid Nanofluid

To fill the existing literature gap, the numerical solutions for the oblique stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid past a shrinking surface are computed and analyzed. The computation, using similarity transformation and bvp4c solver, results in dual solutions. Stability analysis then shows that the first solution is stable with positive smallest eigenvalues. Besides that, the addition of Al2O3 nanoparticles into the Cu-H2O nanofluid is found to reduce the skin friction coefficient by 37.753% while enhances the local Nusselt number by 4.798%. The increase in the shrinking parameter reduces the velocity profile but increases the temperature profile of the hybrid nanofluid. Meanwhile, the increase in the free parameter related to the shear flow reduces the oblique flow skin friction.

Aliran Titik Genangan MHD dan Pemindahan Haba terhadap Permukaan Telap Meregang/Mengecut dalam Nanobendalir Hibrid

Aliran mantap dan pemindahan haba dua matra terhadap titik genangan pada permukaan telap yang meregang/mengecut dalam nanobendalir hibrid dengan kesan medan magnet dikaji. Persamaan menakluk bagi masalah tersebut dijelmakan kepada satu set persamaan keserupaan dengan menggunakan penjelmaan keserupaan. Persamaan keserupaan yang terhasil kemudiannya diselesaikan secara berangka menggunakan penyelesai masalah nilai sempadan (bvp4c) dalam perisian Matlab. Kesan beberapa parameter terhadap pekali geseran kulit dan nombor Nusselt setempat serta profil halaju dan suhu dibentangkan dan dibincangkan. Keputusan berangka menunjukkan bahawa penyelesaian dual wujud bagi julat tertentu parameter regangan/kecutan dan fluks jisim. Didapati juga bahawa kadar pemindahan haba meningkat dengan peningkatan pecahan isi padu nanozarah tembaga (Cu) dan parameter fluks jisim. Analisis kestabilan dilakukan untuk menentukan kestabilan penyelesaian dual dalam jangka masa panjang dan keputusan menunjukkan bahawa hanya satu daripada penyelesaian tersebut yang stabil manakala yang lain adalah tidak stabil.

Radiation and Mixed Convection Magnetohydrodynamics Boundary Layer of Hybrid Cu–Al2O3/Water Nanofluid Flow Over a Wall Jet

The mixed convection MHD boundary layer flow of the hybrid nanofluid (copper–titanium dioxide/water) over a permeable wall jet surface subject to thermal radiation was studied with the effects of suction/injection and thermal energy. The governing PDEs were converted into non-linear ODEs by using the proper similarity transformations. Then, these equations were numerically solved applying the method of Chebyshev pseudo spectral differentiation matrix (ChPDM). The results were deduced for the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number. It was found that the hydrodynamic and thermal boundary layers decreases and increases, respectively, as the strength of the magnetic field increases. Further, in the industrial applications, the normal angle is to be applied if low velocity and high temperature is needed. Moreover, as the mixed convection parameter rises, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can control the thermal boundary layer. Finally, the Cu-nanoparticles volume fraction plays a very important role in the velocity variation.

Thermal Convection of Nanoliquid in a Double-Connected Chamber

Thermogravitational convective thermal transmission, inside a square differentially-heated chamber with a nanoliquid, has been examined in the presence of internal adiabatic or a thermally-conducting solid body. A single-phase nanoliquid approach is employed, based on the experimentally-extracted relations for nanofluid heat conductivity and dynamic viscosity. The governing equations have been written using non-primitive parameters such as stream function and vorticity. Such approach allows a decrease in computational time due to a reduction of equation numbers. One of the main challenges in such a technique is a determining the stream function magnitude at the inner body walls. A solution of this problem has been described in detail in this paper. Computational scrutinizing has been performed by employing the finite difference technique. The mesh sensitivity analysis and comparison with theoretical and experimental results of other researchers have been included. An influence of the Rayleigh number, nanoparticles concentration, internal block size, heat conductivity ratio and non-dimensional time on nanofluid motion and energy transport has been studied.

Mixed Convective Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Induced by a Permeable Stretching/Shrinking Sheet

The present study accentuates the magnetohydrodynamics (MHD) flow and heat transfer characteristics of a dual stratified micropolar fluid over a permeable stretching/shrinking sheet. Thermal and solutal buoyancy forces are also included to incorporate with the stratification effect. Similarity, transformation is applied to reduce the governing model (partial differential equations) into a set of nonlinear ordinary differential equations (ODEs) due to its complexity. Using bvp4c solver in the MATLAB software, numerical results for some limiting cases are in favorable agreement with the earlier published results. Both assisting and opposing buoyancy flows have dual similarity solutions within specific range of suction and stretching/shrinking parameters, whereas only a distinctive solution is observed for pure forced convective flow. The micropolar fluid shows a disparate pattern of flow, heat and mass transfer characteristics between stretching and shrinking cases. Unlike the shrinking flow, the surface velocity gradient, local Nusselt and Sherwood numbers for stretching flow intensify with the increment of the material parameter. The result from stability analysis reveals that the first solution is the real solution, whereas the second solution is virtual.

Axisymmetric rotational stagnation point flow impinging radially a permeable stretching/shrinking surface in a nanofluid using Tiwari and Das model

In this paper, the problem of normal impingement rotational stagnation-point flow on a radially permeable stretching sheet in a viscous fluid, recently studied in a very interesting paper, is extended to a water-based nanofluid. A similarity transformation is used to reduce the system of governing nonlinear partial differential equations to a system of ordinary differential equations, which is then solved numerically using the function bvp4c from Matlab. It is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable, while the lower branch solution is unstable. Sample velocity and temperature profiles along both solution branches are graphically presented.

Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet

In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

Genetic Correlates of Maladaptive Beliefs: COMT VAL(158)MET and Irrational Cognitions Linked Depending on Distress

Maladaptive/irrational beliefs are significant cognitive vulnerability mechanisms in psychopathology. They are more likely to be associated with a genetic vulnerability marker under conditions of emotional distress when irrational beliefs are more salient. Therefore, in the current study we investigated the COMT Val(158)Met gene variation in relation to irrational beliefs, assuming this relationship depended on the level of emotional distress. Two hundred and sixty-seven genotyped volunteers were assessed for core/general maladaptive beliefs, as well as trait emotional distress. We focused on context-independent measures of irrational beliefs and emotional distress in the absence of a stressor. As expected, the relationship between COMT Val(158)Met and irrational beliefs depended on the level of emotional distress (f(2)=.314). The COMT Val(158)Met-irrationality association was significant only when individuals fell in the average to above average range of emotional distress. Furthermore, within this range the Met allele seemed to relate to higher irrational beliefs. These results were significant for overall irrational beliefs and its subtypes, but not for rational beliefs, the functional counterpart of irrationality. In light of the study's limitations, the results should be considered as preliminary. If replicable, these findings have potential implications for therapygenetics, changing the view that COMT Val(158)Met might be of greater relevance when treatment modality does not rely on cognitive variables.