scholarly journals Entropy Generation on Nanofluid Thin Film Flow of Eyring–Powell Fluid with Thermal Radiation and MHD Effect on an Unsteady Porous Stretching Sheet

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 412 ◽  
Author(s):  
Mohammad Ishaq ◽  
Gohar Ali ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Sher Muhammad
Keyword(s):  
Thin Film ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Stretching Sheet ◽  
Film Flow ◽  
Thin Film Flow

scholarly journals Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation

Processes ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 262 ◽  
Author(s):  
Asad Ullah ◽  
Zahir Shah ◽  
Poom Kumam ◽  
Muhammad Ayaz ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Thin Film ◽  
Nusselt Number ◽  
Entropy Generation ◽  
Stretching Sheet ◽  
Film Flow ◽  
Analysis Method ◽  
Thin Film Flow ◽  
Nanofluid Flow ◽  
Boundary Layer Equations ◽  
Homotopy Analysis

The boundary-layer equations for mass and heat energy transfer with entropy generation are analyzed for the two-dimensional viscoelastic second-grade nanofluid thin film flow in the presence of a uniform magnetic field (MHD) over a vertical stretching sheet. Different factors, such as the thermophoresis effect, Brownian motion, and concentration gradients, are considered in the nanofluid model. The basic time-dependent equations of the nanofluid flow are modeled and transformed to the ordinary differential equations system by using similarity variables. Then the reduced system of equations is treated with the Homotopy Analysis Method to achieve the desire goal. The convergence of the method is prescribed by a numerical survey. The results obtained are more efficient than the available results for the boundary-layer equations, which is the beauty of the Homotopy Analysis Method, and shows the consistency, reliability, and accuracy of our obtained results. The effects of various parameters, such as Nusselt number, skin friction, and Sherwood number, on nanoliquid film flow are examined. Tables are displayed for skin friction, Sherwood number, and Nusselt number, which analyze the sheet surface in interaction with the nanofluid flow and other informative characteristics regarding this flow of the nanofluids. The behavior of the local Nusselt number and the entropy generation is examined numerically with the variations in the non-dimensional numbers. These results are shown with the help of graphs and briefly explained in the discussion. An analytical exploration is described for the unsteadiness parameter on the thin film. The larger values of the unsteadiness parameter increase the velocity profile. The nanofluid film velocity shows decline due the increasing values of the magnetic parameter. Moreover, a survey on the physical embedded parameters is given by graphs and discussed in detail.

scholarly journals Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3177 ◽  
Author(s):  
Kohilavani Naganthran ◽  
Ishak Hashim ◽  
Roslinda Nazar
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Differential Equations ◽  
Film Thickness ◽  
Stretching Sheet ◽  
Film Flow ◽  
Problem Solver ◽  
Thin Film Flow ◽  
Unsteady Stretching Sheet ◽  
Negative Film

Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.

scholarly journals Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer

2018 ◽  
Vol 57 (2) ◽  
pp. 1019-1031 ◽  
Author(s):  
Noor Saeed Khan ◽  
Saeed Islam ◽  
Taza Gul ◽  
Ilyas Khan ◽  
Waris Khan ◽  
...  
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Porous Medium ◽  
Stretching Sheet ◽  
Film Flow ◽  
Second Grade ◽  
Thin Film Flow ◽  
Second Grade Fluid ◽  
Grade Fluid

scholarly journals Darcy Forchheimer nanofluid thin film flow of SWCNTs and heat transfer analysis over an unsteady stretching sheet

AIP Advances ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 015223 ◽  
Author(s):  
Saleem Nasir ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Ebenezer Bonyah ◽  
Taza Gul
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Stretching Sheet ◽  
Film Flow ◽  
Heat Transfer Analysis ◽  
Thin Film Flow ◽  
Unsteady Stretching Sheet

scholarly journals Radiative MHD thin film flow of Williamson fluid over an unsteady permeable stretching sheet

Heliyon ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. e00825 ◽  
Author(s):  
Zahir Shah ◽  
Ebenezer Bonyah ◽  
Saeed Islam ◽  
Waris Khan ◽  
Mohammad Ishaq
Keyword(s):  
Thin Film ◽  
Stretching Sheet ◽  
Film Flow ◽  
Thin Film Flow ◽  
Williamson Fluid
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