MHD Hybrid Cu-Al2O3/ Water Nanofluid Flow with Thermal Radiation and Partial Slip Past a Permeable Stretching Surface: Analytical Solution

2020 ◽  
Vol 64 ◽  
pp. 75-91 ◽  
Author(s):  
Nur Syahirah Wahid ◽  
Norihan Md Arifin ◽  
Mustafa Turkyilmazoglu ◽  
Mohd Ezad Hafidz Hafidzuddin ◽  
Nor Aliza Abd Rahmin
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Radiation Effects ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Exact Analytical Method

The influence of velocity slip and thermal radiation effects on the magnetohydrodynamic hybrid Cu-Al2O3/water nanofluid flow over a permeable stretching sheet is reported in this paper. The similarity transformation is adopted to reduce the partial differential equations to the ordinary differential equations. Exact analytical method is implemented to solve the problem. Maple program is used to facilitate the calculation process. The new additional effects which are the velocity slip and thermal radiation effects are considered towards the model to scrutinize the impacts. The effects of various parameters towards the velocity and temperature profiles are demonstrated through graphs, meanwhile the skin friction coefficient and the local Nusselt number are exhibited through the tabulation of data. The existence of velocity slip reduced the velocity profile but enhanced the temperature profile. The thermal radiation effect has increased the temperature profile. The heat transfer rate are enhanced for the case of hybrid nanofluid compared to the mono nanofluid.

scholarly journals Partial slip and thermal radiation effects on hydromagnetic flow over an exponentially stretching surface with suction or blowing

2018 ◽  
Vol 22 (2) ◽  
pp. 797-808 ◽  
Author(s):  
Santosh Chaudhary ◽  
Mohan Choudhary
Keyword(s):  
Thermal Radiation ◽  
Radiation Effects ◽  
Computational Simulation ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Slip Parameter ◽  
Stretching Surface ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

This paper is devoted to analyze computational simulation to study the partial slip and thermal radiation effects on the flow of a viscous incompressible electrically conducting fluid through an exponentially stretching surface with suction or blowing in presence of magnetic field. Using suitable similarity variables, the non-linear boundary-layer PDE are converted to ODE and solved numerically by Runge-Kutta fourth order method in association with shooting technique. Effects of suction or blowing parameter, velocity slip parameter, magnetic parameter, thermal slip parameter, thermal radiation parameter, Prandtl number, and Eckert number are demonstrated graphically on velocity and temperature profiles while skin friction coefficient and surface heat transfer rate are presented numerically. Moreover, comparison of numerical results for non-magnetic case is made with previously published work under limiting cases.

scholarly journals Radiative Magnetohydrodynamics Casson Nanofluid Flow and Heat and Mass Transfer past on Nonlinear Stretching Surface

2021 ◽  
Author(s):  
Gurrala Thirupathi ◽  
Kamatam Govardhan ◽  
Ganji Narender
Keyword(s):  
Differential Equations ◽  
Velocity Slip ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Casson Nanofluid ◽  
Order Four

The magnetohydrodynamics (MHD) stagnation point Casson nanofluid flow towards stretching surface with velocity slip and convective boundary condition has been investigated in this article. Effects of thermal radiation, viscous dissipation, heat source and chemical reaction have also been incorporated. Using appropriate similarity transformation Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) and shooting technique along with Adams–Moulton method of order four has been used to obtain the numerical results. Different physical parameters effects on velocity, temperature and concentration of nanofluid flow have been presented graphically and discussed in detail. Numerical values of the skin friction coefficient, Nusselt number and Sherwood number are also and discussed.

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.

MHD hybrid nanofluid flow over a permeable stretching/shrinking sheet with thermal radiation effect

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ubaidullah Yashkun ◽  
Khairy Zaimi ◽  
Nor Ashikin Abu Bakar ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Thermal Radiation ◽  
Radiation Effects ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects. Design/methodology/approach Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results. Findings It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al2O3/H2O) is greater than the nanofluid (Cu/H2O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists. Practical implications In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc. Originality/value In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.

Double Stratification in Flow by Curved Stretching Sheet With Thermal Radiation and Joule Heating

2017 ◽  
Vol 10 (2) ◽  
Author(s):  
Tasawar Hayat ◽  
Sumaira Qayyum ◽  
Maria Imtiaz ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Joule Heating ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Curvilinear Coordinates ◽  
Double Stratification ◽  
Curvature Parameter ◽  
Basic Equations

Magnetohydrodynamic (MHD) flow of viscous fluid by curved stretching surface is presented in this paper. Heat and mass transfer analysis is studied with double stratification and thermal radiation effects. Joule heating is also taken into consideration. Basic equations of flow problem are obtained using curvilinear coordinates. The partial differential equations are reduced to the nonlinear ordinary differential equations using suitable transformations. Graphical results are shown and analyzed for the effect of different parameters on fluid characteristics. It is noted that thermal and solutal stratification parameters have opposite effect on temperature and concentration distributions. Magnitude of pressure, skin friction coefficient, and Nusselt number decreases for larger curvature parameter.

scholarly journals STEADY MHD SLIP FLOW OVER A PERMEABLE STRETCHING CYLINDER WITH THERMAL RADIATION

2021 ◽  
Vol 8 (11) ◽  
pp. 23-36
Author(s):  
Sharad Sinha ◽  
Deepak Kumar ◽  
Anil Sharma
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Fourth Order Method

Aim of the paper is to investigate the effects of thermal radiation and velocity slip on steady MHD slip flow of viscous incompressible electrically conducting fluid over a permeable stretching cylinder saturated in porous medium in the presence of external magnetic field. The governing nonlinear partial differential equations are transformed into ordinary differential equations by suitable similarity transformation and solved numerically using Runge-Kutta fourth order method with shooting technique. Effect of various physical parameters on fluid velocity, temperature, skin –friction coefficient and Nusselt number are presented through graphs and discussed numerically.

Stability and statistical analysis on melting heat transfer in a hybrid nanofluid with thermal radiation effect

2021 ◽  
pp. 095440892110331
Author(s):  
Md Faisal Md Basir ◽  
Joby Mackolil ◽  
B Mahanthesh ◽  
Kottakkaran S Nisar ◽  
Taseer Muhammad ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Transfer Rate ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Melting Heat ◽  
Melting Heat Transfer

The dual solutions for the stagnation point flow in a cobalt–CeO2/kerosene hybrid nanofluid with melting heat transfer and thermal radiation are analyzed. The partial differential equations are solved by the conversion of the partial differential equations into nonlinear ordinary differential equations by utilizing suitable scaling group transformations. Numerical solutions are obtained by employing the built-in function in the MATLAB software (bvp4c). Physically recoverable solutions are found employing stability analysis. The factor variables of interest (melting parameter, the nanoparticle volume fraction of cobalt and CeO2) are then further analyzed by utilizing the sensitivity analysis (based on the response surface methodology model) for heat transfer rate, as well as the skin friction coefficient. It is found that the heat transfer and skin friction tend to be significantly higher in a hybrid nanofluid due to the radiation and melting heat transfer. The lower branch is found to be unstable, whereas the upper branch is found to be stable. Also, the heat transfer rate and skin friction coefficient are found to be negatively sensitive toward the melting parameter. The model in this study can be applied for microscopic propulsion systems and the nano-electromechanical systems integrated with a nano-based system.

scholarly journals Flow towards a Stagnation Region of a Vertical Plate in a Hybrid Nanofluid: Assisting and Opposing Flows

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 448
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Radiation Effects ◽  
Vertical Plate ◽  
Similarity Transformation ◽  
Fluid Motion ◽  
Hybrid Nanoparticles ◽  
Problem Solver ◽  
Hybrid Nanofluid ◽  
Al2o3 Nanoparticles ◽  
Nanofluid Flow ◽  
Stagnation Region

This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water nanofluid. The stagnation point flow describes the fluid motion in the stagnation region of a solid surface. In this study, both buoyancy assisting and opposing flows are considered. The similarity equations are obtained using a similarity transformation and numerical results are obtained via the boundary value problem solver (bvp4c) in MATLAB software. Findings discovered that dual solutions exist for both opposing and assisting flows. The heat transfer rate is intensified with the thermal radiation (49.63%) and the hybrid nanoparticles (32.37%).

MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fazle Mabood ◽  
Anum Shafiq ◽  
Waqar Ahmed Khan ◽  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Design Parameters ◽  
Hybrid Nanofluid ◽  
Nonlinear Thermal Radiation ◽  
Content Type

Purpose This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source. Design/methodology/approach This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. Findings The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes. Originality/value This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

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