scholarly journals Dual Solutions and Stability Analysis of Magnetized Hybrid Nanofluid with Joule Heating and Multiple Slip Conditions

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 332 ◽  
Author(s):  
Liang Yan ◽  
Sumera Dero ◽  
Ilyas Khan ◽  
Irshad Ali Mari ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Heat Transfer Rate ◽  
Joule Heating ◽  
Transfer Rate ◽  
Numerical Results ◽  
Eckert Number ◽  
Hybrid Nanofluid ◽  
Thermal Slip

This paper investigates the steady, two dimensional, and magnetohydrodynamic flow of copper and alumina/water hybrid nanofluid on a permeable exponentially shrinking surface in the presence of Joule heating, velocity slip, and thermal slip parameters. Adopting the model of Tiwari and Das, the mathematical formulation of governing partial differential equations was constructed, which was then transformed into the equivalent system of non-linear ordinary differential equations by employing exponential similarity transformation variables. The resultant system was solved numerically using the BVP4C solver in the MATLAB software. For validation purposes, the obtained numerical results were compared graphically with those in previous studies, and found to be in good agreement, as the critical points are the same up to three decimal points. Based on the numerical results, it was revealed that dual solutions exist within specific ranges of the suction and magnetic parameters. Stability analysis was performed on both solutions in order to determine which solution(s) is/are stable. The analysis indicated that only the first solution is stable. Furthermore, it was also found that the temperature increases in both solutions when the magnetic parameter and Eckert number are increased, while it reduces as the thermal slip parameter rises. Furthermore, the coefficient of skin friction and the heat transfer rate increase for the first solution when the magnetic and the suction parameters are increased. Meanwhile, no change is noticed in the boundary layer separation for the various values of the Eckert number in the heat transfer rate.

scholarly journals Mixed convective hybrid nanofluid flow in lid-driven undulated cavity: effect of MHD and Joule heating

2019 ◽  
Vol 16 (2) ◽  
pp. 109-126 ◽  
Author(s):  
Ishrat Zahan ◽  
R Nasrin ◽  
M A Alim
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Rate ◽  
Joule Heating ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Hybrid Nanoparticles ◽  
Wave Number ◽  
Hybrid Nanofluid

A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid,  TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

scholarly journals Double Solutions and Stability Analysis of Micropolar Hybrid Nanofluid with Thermal Radiation Impact on Unsteady Stagnation Point Flow

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 276
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Thermal Radiation ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Stable Solution ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Micropolar Nanofluid

The mathematical modeling of unsteady flow of micropolar Cu–Al2O3/water nanofluid driven by a deformable sheet in stagnation region with thermal radiation effect has been explored numerically. To achieve the system of nonlinear ordinary differential equations (ODEs), we have employed some appropriate transformations and solved it numerically using MATLAB software (built-in solver called bvp4c). Influences of relevant parameters on fluid flow and heat transfer characteristic are discussed and presented in graphs. The findings expose that double solutions appear in shrinking sheet case in which eventually contributes to the analysis of stability. The stability analysis therefore confirms that merely the first solution is a stable solution. Addition of nanometer-sized particle (Cu) has been found to significantly strengthen the heat transfer rate of micropolar nanofluid. When the copper nanoparticle volume fraction increased from 0 to 0.01 (1%) in micropolar nanofluid, the heat transfer rate increased roughly to an average of 17.725%. The result also revealed that an upsurge in the unsteady and radiation parameters have been noticed to enhance the local Nusselt number of micropolar hybrid nanofluid. Meanwhile, the occurrence of material parameter conclusively decreases it.

scholarly journals MHD Flow and Heat Transfer of Hybrid Nanofluid over an Exponentially Shrinking Surface with Heat Source/Sink

2021 ◽  
Vol 11 (17) ◽  
pp. 8199
Author(s):  
Mohamad Nizam Othman ◽  
Alias Jedi ◽  
Nor Ashikin Abu Bakar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Mhd Flow ◽  
Hybrid Nanofluid ◽  
Flow And Heat Transfer ◽  
Source Sink ◽  
Shrinking Surface

In nanotechnology research, nanofluid technology contributes many applications to engineering applications and industry, such as power generation, solar collection, heat exchangers for cooling, and many more. However, there are still a few constraints in terms of heat transfer enhancement, although nanofluid properties show the best heat transfer rate compared with conventional fluids. Thus, this study was conducted for the purpose of investigating the behaviors of flow and heat transfer of hybrid nanofluid with carbon nanotubes (CNTs) on a permeable exponentially shrinking surface, as well as investigating the effects of a magnetic field and heat source/sink. This study was conducted by developing a mathematical model, which was the Tiwari–Das model for momentum and energy equations, and then transforming the model’s partial differential equations (PDEs) to ordinary differential equations (ODEs) using a similarity solution. Next, these equations were solved numerically using the MATLAB bvp4c boundary value problem solver. The authors particularly explored these behaviors with a few variations. Based on the results obtained, it was found that dual solutions exist in a specific range of the shrinking case, and that the critical point also exists in a range of −1.5 < < −1 with different parameters. For the heat source/sink effect, the Nusselt number was higher when heat sink case ε < 0, whereas it decreased when the heat source case ε > 0. Therefore, this study deduced that the heat transfer rate of hybrid nanofluid (CNTs/Cu–water) is better than regular nanofluid (CNT–water) and conventional fluid (water). The present study took into consideration the problem of MHD flow and heat transfer analysis of a hybrid nanofluid towards an exponentially shrinking surface with the presence of heat source/sink and thermal radiation effects. The authors show that dual solutions exist within a specific range of values due to the shrinking case. The current work is predicted to have numerous benefits in equivalent real-world systems.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

Non-axisymmetric Homann stagnation point flow and heat transfer past a stretching/shrinking sheet using hybrid nanofluid

2020 ◽  
Vol 30 (10) ◽  
pp. 4583-4606 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Strain Rate ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Hybrid Nanofluid ◽  
Ambient Fluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat plate. Design/methodology/approach The similarity transformation which fulfils the continuity equation is opted to transform the coupled momentum and energy equations into the nonlinear ordinary differential equations. Numerical solutions which are elucidated in the tables and graphs are obtained using the bvp4c solver. Findings Non-unique solutions (first and second) are feasible for both stretching and shrinking cases within the specific values of the parameters. First solution is the physical/real solution based on the execution of stability analysis. An upsurge of the ratio of the ambient fluid strain rate to the plate strain rate can delay the boundary layer separation, whereas a boost of the ratio of the ambient fluid shear rate to the plate strain rate only accelerates the separation of boundary layer. The heat transfer rate of hybrid nanofluid is greater for the stretching case than the shrinking case. However, for the shrinking case, the heat transfer rate intensifies with the increment of the copper (Cu) nanoparticles volume fraction, whereas a contrary result is found for the stretching case. Originality/value The present numerical results are original and new. It can contribute to other researchers on electing the relevant parameters to optimize the heat transfer process in the modern industry, and the right parameters to generate non-unique solution so that no misjudgment on flow and heat transfer features.

Unsteady axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable stretching/shrinking disc

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan M. Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Axisymmetric Flow ◽  
Hybrid Nanofluid ◽  
Uniqueness Of Solutions ◽  
Suction Parameter ◽  
Content Type ◽  
Comparison Results

Purpose This study aims to analyze the unsteady flow of hybrid Cu-Al2O3/water nanofluid over a permeable stretching/shrinking disc. The analysis of flow stability is also purposed because of the non-uniqueness of solutions. Design/methodology/approach The reduced differential equations (similarity) are solved numerically using the aid of bvp4c solver (Matlab). Two types of thermophysical correlations for hybrid nanofluid (Type 1 and 2) are adopted for the comparison results. Using correlation Type 1, the heat transfer and flow analysis including the profiles (velocity and temperature) are presented in the figures and tables with different values control parameters. Three sets of hybrid nanofluid are analyzed: Set 1 (1% Al2O3 + 1% Cu), Set 2 (0.5% Al2O3 + 1% Cu) and Set 3 (1% Al2O3 + 0.5% Cu). Findings The comparison of numerical values between present (Types 1 and 2 correlations) and previous (Type 2 correlations) results are in a good compliance with approximate percent relative error. The appearance of two solutions is noticed when the suction parameter is considered and the unsteady parameter is less than 0 (decelerating flow) for both stretching and shrinking disc while only one solution is possible for steady flow. The hybrid nanofluid in Set 1 can delay the separation of boundary layer but the hybrid nanofluid in Set 3 has the greatest heat transfer rate. Moreover, the inclusion of wall mass suction for stretching case can generate a significant increment of heat transfer rate approximately 90% for all fluids (water, single and hybrid nanofluids). Originality/value The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids.

scholarly journals Unsteady Three-Dimensional MHD Non-Axisymmetric Homann Stagnation Point Flow of a Hybrid Nanofluid with Stability Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 784 ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

The hybrid nanofluid under the influence of magnetohydrodynamics (MHD) is a new interest in the industrial sector due to its applications, such as in solar water heating and scraped surface heat exchangers. Thus, the present study accentuates the analysis of an unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid Al2O3-Cu/H2O nanofluid with stability analysis. By employing suitable similarity transformations, the governing mathematical model in the form of the partial differential equations are simplified into a system of ordinary differential equations. The simplified mathematical model is then solved numerically by the Matlab solver bvp4c function. This solving approach was proficient in generating more than one solution when good initial guesses were provided. The numerical results presented significant influences on the rate of heat transfer and fluid flow characteristics of a hybrid nanofluid. The rate of heat transfer and the trend of the skin friction coefficient improve with the increment of the nanoparticles’ concentration and the magnetic parameter; however, they deteriorate when the unsteadiness parameter increases. In contrast, the ratio of the escalation of the ambient fluid strain rate to the plate was able to adjourn the boundary layer separation. The dual solutions (first and second solutions) are obtainable when the surface of the sheet shrunk. A stability analysis is carried out to justify the stability of the dual solutions, and hence the first solution is seen as physically reliable and stable, while the second solution is unstable.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Squeezed Hybrid Nanofluid Flow Over a Permeable Sensor Surface

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 898 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Dual Solutions ◽  
Hybrid Nanoparticles ◽  
Squeeze Flow ◽  
Flow Index ◽  
Hybrid Nanofluid ◽  
Sensor Surface ◽  
Nanofluid Flow

This paper examines the squeezed hybrid nanofluid flow over a permeable sensor surface with magnetohydrodynamics (MHD) and radiation effects. The alumina (Al2O3) and copper (Cu) are considered as the hybrid nanoparticles, while water is the base fluid. The governing equations are reduced to the similarity equations, using the similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain the numerical solutions. It was found that the heat transfer rate was greater for the hybrid nanofluid, compared to the regular nanofluid. It was observed that dual solutions exist for some values of the permeable parameter S. The upper branch solutions of the skin friction coefficient ( Re x 1 / 2 C f ) and the heat transfer rate at the surface ( Re x − 1 / 2 N u x ) enhance with the added Cu nanoparticle ( φ 2 ) and for larger magnetic strength ( M ). Moreover, the values of Re x 1 / 2 C f decrease, whereas the values of Re x − 1 / 2 N u x increase for both branches, with the rise of the squeeze flow index ( b ). Besides, an increment of the heat transfer rate at the sensor surface for both branches was observed in the presence of radiation ( R ). Temporal stability analysis was employed to determine the stability of the dual solutions, and it was discovered that only one of them was stable and physically reliable as time evolves.

scholarly journals Hybrid Nanofluid Flow Past a Permeable Moving Thin Needle

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 612 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Temporal Stability ◽  
Skin Friction Coefficient ◽  
Hybrid Nanoparticles ◽  
Problem Solver ◽  
Hybrid Nanofluid ◽  
Nanoparticle Concentration

The problem of a steady flow and heat transfer past a permeable moving thin needle in a hybrid nanofluid is examined in this study. Here, we consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles, and water as a base fluid. In addition, the effects of thermophoresis and Brownian motion are taken into consideration. A similarity transformation is used to obtain similarity equations, which are then solved numerically using the boundary value problem solver, bvp4c available in Matlab software (Matlab_R2014b, MathWorks, Singapore). It is shown that heat transfer rate is higher in the presence of hybrid nanoparticles. It is discovered that the non-uniqueness of the solutions is observed for a certain range of the moving parameter λ . We also observed that the bifurcation of the solutions occurs in the region of λ < 0 , i.e., when the needle moved toward the origin. Furthermore, we found that the skin friction coefficient and the heat transfer rate at the surface are higher for smaller needle sizes. A reduction in the temperature and nanoparticle concentration was observed with the increasing of the thermophoresis parameter. It was also found that the increase of the Brownian motion parameter leads to an increase in the nanoparticle concentration. Temporal stability analysis shows that only one of the solutions was stable and physically reliable as time evolved.

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