scholarly journals Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

scholarly journals Heat transfer analysis of the mixed convective flow of magnetohydrodynamic hybrid nanofluid past a stretching sheet with velocity and thermal slip conditions

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260854
Author(s):  
Muhammad Ramzan ◽  
Abdullah Dawar ◽  
Anwar Saeed ◽  
Poom Kumam ◽  
Wiboonsak Watthayu ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Skin Friction ◽  
Heat Generation ◽  
Higher Order ◽  
Eckert Number ◽  
Hybrid Nanofluid ◽  
Radiation Parameter ◽  
Slip Conditions

The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag − MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Slip flow of hybrid nanofluid in presence of solar radiation

2021 ◽  
pp. 2250017
Author(s):  
Kalidas Das ◽  
Nilangshu Acharya ◽  
Md Tausif SK ◽  
Pinaki Ranjan Duari ◽  
Tanmoy Chakraborty
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Uniform Heat Flux ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Fifth Order ◽  
The Impact ◽  
Final System

A theoretical model on MHD hybrid nanofluid flow in accordance with non-uniform heat flux and solar energy radiation has been studied in our work. Also, the impact of multiple slip conditions is presumed at the boundary. Comparative flow analyses for hybrid nanofluid (Al2O3/Cu–H2O) and single nanoparticle-based nanofluid (Cu–H2O) are addressed here with graphs and charts. The leading partial differential equations with boundary conditions have been converted into ordinary differential equations with the aid of similarity transformation. The final system is tackled via the fifth-order Runge–Kutta–Felberg method with shooting procedure and the computation is done using Maple 17. One of the interesting results shows that with the growth of thermal radiation, the Nusselt number for Cu–H2O is reduced by 26.16%, whereas for the same, Nusselt number for Al2O3/Cu–H2O is lessened by 27.38%. Fallout shows that with the growing values of velocity slip parameter, the thermal boundary layer thickness enlarges faster for Al2O3/Cu–H2O in comparison to Cu–H2O.

scholarly journals Stagnation Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in CNT with Homogeneous–Heterogeneous Reaction: Stability Analysis

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 522 ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Heterogeneous Reaction ◽  
Shrinking Sheet ◽  
Multi Wall Carbon Nanotubes ◽  
Exponentially Stretching ◽  
The Impact

This study focuses on the flow of stagnation region and heat transfer of carbon nanotubes (CNTs) over an exponentially stretching/shrinked sheet in the presence of homogeneous–heterogeneous reactions. Kerosene and water are considered base fluids in both single-wall and multi-wall carbon nanotubes. After employing the appropriate similarity variables, the system of partial differential equations is transformed to a system of nonlinear ordinary differential equations. Solution of the problems is obtained numerically using the bvp4c solver in MATLAB software. The impact of physical parameters, such as solid volume fraction, stretching/shrinking parameter, homogeneous and heterogeneous reaction rate, Schmidt number on the velocity, temperature and concentration profiles, skin friction, and heat transfer rate are discussed graphically and interpreted physically. The results indicate that for an exponentially shrinking sheet, dual solutions exist for a certain range. It is clear from figures that the concentration profile increases for increasing values of heterogeneous parameter and decreasing values of homogeneous parameter. Heat transfer and skin friction were observed to have a greater impact for single-wall carbon nanotubes (SWCNTs) compared to multi-wall carbon nanotubes (MWCNTs). A stability analysis has been performed to show which solutions are linearly stable.

Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Current Work ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin ◽  
Content Type

Purpose This paper aims to discuss a stability analysis on Cu-Al2O3/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

scholarly journals Computational Modeling of Hybrid Sisko Nanofluid Flow over a Porous Radially Heated Shrinking/Stretching Disc

Coatings ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1242
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Anuar Ishak ◽  
Fahad S. Al-Mubaddel ◽  
Sakhinah Abu Bakar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Flow Problem ◽  
Shear Thickening ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Shear Thinning Fluids ◽  
Water Based ◽  
New Type ◽  
The Impact ◽  
The Magnetic Field

The present study reveals the behavior of shear-thickening and shear-thinning fluids in magnetohydrodynamic flow comprising the significant impact of a hybrid nanofluid over a porous radially shrinking/stretching disc. The features of physical properties of water-based Ag/TiO2 hybrid nanofluid are examined. The leading flow problem is formulated initially in the requisite form of PDEs (partial differential equations) and then altered into a system of dimensionless ODEs (ordinary differential equations) by employing suitable variables. The renovated dimensionless ODEs are numerically resolved using the package of boundary value problem of fourth-order (bvp4c) available in the MATLAB software. The non-uniqueness of the results for the various pertaining parameters is discussed. There is a significant enhancement in the rate of heat transfer, approximately 13.2%, when the impact of suction governs about 10% in the boundary layer. Therefore, the heat transport rate and the thermal conductivity are greater for the new type of hybrid nanofluid compared with ordinary fluid. The bifurcation of the solutions takes place in the problem only for the shrinking case. Moreover, the sketches show that the nanoparticle volume fractions and the magnetic field delay the separation of the boundarylayer.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

Impact of Joule heating and viscous dissipation on magnetohydrodynamics boundary layer flow of viscous nanofluid subject to the stretched surface

2021 ◽  
pp. 095440892110641
Author(s):  
M. Riaz Khan ◽  
Awatef Abidi ◽  
Jamel Madiouli ◽  
Kamel Guedri ◽  
A.M. Al-Bugami ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Base Fluid ◽  
Fluid Temperature ◽  
Suction Parameter ◽  
Nanoparticles Concentration ◽  
The Impact

The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surface is investigated with the existence of viscous dissipation and Joule heating. Moreover, the impact of the convective condition and mass suction is applied with the viscous nanofluid containing copper nanoparticles and the base fluid water. The similarity variables have been employed to transform the coupled nonlinear partial differential equations into the ordinary differential equations and the numerical scheme bp4c is implemented for the further analysis of the solution. The diverse results of temperature, skin friction coefficient, velocity, and the Nusselt number according to numerous parameters have been shown graphically. It appears that the Nusselt number and the skin friction reduces, which is caused by the enhancement of both Hartman number and nanoparticles concentration. Moreover, the fluid temperature surges with the growth of Biot number, and Eckert number whereas the growth of nanoparticles concentration and suction parameter diminishes the velocity and temperature profile. The inclusion of a significant quantity of nanoparticles in the base fluid increases the density of the corresponding nanofluids and accordingly the temperature of the coupled nanoparticles in the base fluids can be modified. Hence, nanofluids build an outstanding performance in electronic components appliances and other electrical devices. The existing research is further effective in refrigerators for stabilizing their rate of cooling.

scholarly journals Unsteady MHD Bionanofluid Flow in a Porous Medium with Thermal Radiation near a Stretching/Shrinking Sheet

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Internal Heat ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
The Impact

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter A , magnetic parameter M , and porosity parameter Kp . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number Lb and Peclet number Pe and decreases with the increasing values of an unsteady parameter A .

scholarly journals Entropy Generation and Heat Transfer Analysis in MHD Unsteady Rotating Flow for Aqueous Suspensions of Carbon Nanotubes with Nonlinear Thermal Radiation and Viscous Dissipation Effect

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 492 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Aurungzeb Khan ◽  
Waris Khan ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Shrinking Sheet ◽  
Bejan Number ◽  
Nanofluid Flow ◽  
The Impact

The impact of nonlinear thermal radiations rotating with the augmentation of heat transfer flow of time-dependent single-walled carbon nanotubes is investigated. Nanofluid flow is induced by a shrinking sheet within the rotating system. The impact of viscous dissipation is taken into account. Nanofluid flow is assumed to be electrically conducting. Similarity transformations are applied to transform PDEs (partial differential equations) into ODEs (ordinary differential equations). Transformed equations are solved by the homotopy analysis method (HAM). The radiative source term is involved in the energy equation. For entropy generation, the second law of thermodynamics is applied. The Bejan number represents the current investigation of non-dimensional entropy generation due to heat transfer and fluid friction. The results obtained indicate that the thickness of the boundary layer decreases for greater values of the rotation parameter. Moreover, the unsteadiness parameter decreases the temperature profile and increases the velocity field. Skin friction and the Nusselt number are also physically and numerically analyzed.

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