scholarly journals Thermal Radiation in Nanofluid Penetrable Flow Bounded with Partial Slip Condition

CFD letters ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 32-44
Author(s):  
Nadia Diana Mohd Rusdi ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan Md. Arifin ◽  
Norfifah Bachok
Keyword(s):  
Boundary Conditions ◽  
Thermal Radiation ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Slip Boundary ◽  
Exponentially Shrinking Sheet ◽  
Layer Flow

Thermal radiation enhances heat transfer, and it is used widely in manufacturing and materials processing applications. Thus, steady two-dimensional boundary layer flow over an exponentially porous shrinking sheet of nanofluids was considered in the influence of thermal radiation related to partial slip boundary conditions and suction. This paper aims to study the nanofluid penetrable flow over an exponentially shrinking sheet with thermal radiation and partial slip. The effects of silver (Ag) nanoparticles with two different types of base fluids named water and kerosene oil are investigated in this study. First, the governing equations and boundary conditions are transformed to a non-linear ordinary differential equation and then solved using bvp4c solver. Using Matlab software, it is found that the dual solution exists in some values from the suction parameter. Furthermore, we identified both nanoparticle volume fraction and suction parameter increase, leading to the rise in velocity profile. Moreover, the suction parameter increases both skin friction coefficient and Nusselt number increase.

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.

Unsteady Flow of a Power–Law Fluid past a Shrinking Sheet with Mass Transfer

2012 ◽  
Vol 67 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Nor Azizah Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Power Law ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Shrinking Sheet ◽  
Power Law Fluid ◽  
Suction Parameter ◽  
Shooting Technique ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Power Law Index

The unsteady two-dimensional boundary layer flow past a shrinking sheet in a non-Newtonian power-law fluid is investigated. The governing partial differential equations are transformed into a nonlinear ordinary differential equation using a similarity transformation before being solved numerically by the Runge-Kutta-Fehlberg method and the NAG Fortran library subroutine DO2HAF with shooting technique. The results obtained by both methods are in good agreement. It is found that dual solutions exist for a certain range of the unsteadiness parameter and the suction parameter. Moreover, by increasing the power-law index n, the skin friction coefficient is enhanced.

scholarly journals Micropolar ferrofluid flow via natural convective about a radiative isoflux sphere

2021 ◽  
Vol 13 (2) ◽  
pp. 168781402199439
Author(s):  
Saber EL-Kabeir ◽  
Ahmed Rashad ◽  
Waqar Khan ◽  
Zeinab Mahmoud Abdelrahman
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Magnetic Force ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Partial Slip ◽  
Convection Flow

Current investigation scrutinizes the magnetohydrodynamic (MHD) natural convection flow of micropolar ferrofluid across an isoflux sphere with the impacts of thermal radiation and partial slip. Cobalt-nanoparticles with kerosene as the base fluid are considered. The governing partial differential conservation equations and convenient boundary conditions are rendered into a nondimensional form. The finite difference method (FDM) is then applied to determine the solution of a collection of resultant equations. The outcomes obtained by FDM have also compared with cited investigation. Illustrations describing influences of prominent parameters which provides physical interpretations of velocity, angular velocity, and temperature fields as well as the skin friction coefficient and Nusselt number are examined in detail with the help of graphical representations. This investigation determined that the skin-friction coefficient and heat transport rate reduced along with augmentation in the magnetic force and micropolar parameter, while opposite performance is adhered with elevating in the thermal radiation. Moreover, the boosted nanoparticle volume fraction reduced the skin friction coefficient and improved the Nusselt number.

scholarly journals Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 788 ◽  
Author(s):  
Anuar Jamaludin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Source Sink

In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.

Heat and Mass Transfer of MHD Dissipative Casson Nanofluid Flow over a Stretching or Shrinking Sheet with Multiple Slip Boundary Conditions

2019 ◽  
Vol 393 ◽  
pp. 103-120 ◽  
Author(s):  
Emmanuel O. Titiloye ◽  
Jacob A. Gbadeyan ◽  
A.T. Adeosun
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Shrinking Sheet ◽  
Nanoparticle Volume Fraction ◽  
Slip Boundary Conditions ◽  
Nanofluid Flow ◽  
Slip Boundary ◽  
Stretching Or Shrinking Sheet

The present study concerns steady two-dimensional laminar mixed convective boundary layer Casson nanofluid flow along a stretching or shrinking sheet with multiple slip boundary conditions in a non-Darcian porous medium. The effect of viscous dissipation and non-linear radiation are considered. The governing partial differential equations, together with boundary conditions are transformed into a system of dimensionless coupled ordinary differential equations. Galerkin weighted residual method is then employed to solve the transformed coupled ordinary differential equations. The effect of various controlling parameters on dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient and nanoparticle volume fraction gradient are presented graphically and discussed. The present approach is validated by comparing the result of this work and those available in the literature, and they are found to be in excellent agreement.

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