Effects of variable fluid properties on unsteady thin-film flow over a non-linear stretching sheet

2010 ◽  
Vol 53 (25-26) ◽  
pp. 5757-5763 ◽  
Author(s):  
B.S. Dandapat ◽  
S. Chakraborty
2018 ◽  
Vol 28 (7) ◽  
pp. 1596-1612 ◽  
Author(s):  
N. Faraz ◽  
Y. Khan

Purpose This paper aims to explore the variable properties of a flow inside the thin film of a unsteady Maxwell fluid and to analyze the effects of shrinking and stretching sheet. Design/methodology/approach The governing mathematical model has been developed by considering the boundary layer limitations. As a result of boundary layer assumption, a nonlinear partial differential equation is obtained. Later on, similarity transformations have been adopted to convert partial differential equation into an ordinary differential equation. A well-known homotopy analysis method is implemented to solve the problem. MATHEMATICA software has been used to visualize the flow behavior. Findings It is observed that variable viscosity does not have a significant effect on velocity field and temperature distribution either in shrinking or stretching case. It is noticed that Maxwell parameter has no dramatic effect on the flow of thin liquid fluid. It has been seen that heat flow increases by increasing the conductivity with temperature in both cases (shrinking/stretching). As a result, fluid temperature goes down when than delta = 0.05 than delta = 0.2. Originality/value To the best of authors’ knowledge, nobody has conducted earlier thin film flow of unsteady Maxwell fluid with variable fluid properties and comparison of shrinking and stretching sheet.


Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3177 ◽  
Author(s):  
Kohilavani Naganthran ◽  
Ishak Hashim ◽  
Roslinda Nazar

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.


2018 ◽  
Vol 57 (2) ◽  
pp. 1019-1031 ◽  
Author(s):  
Noor Saeed Khan ◽  
Saeed Islam ◽  
Taza Gul ◽  
Ilyas Khan ◽  
Waris Khan ◽  
...  

AIP Advances ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 015223 ◽  
Author(s):  
Saleem Nasir ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Ebenezer Bonyah ◽  
Taza Gul

Processes ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 262 ◽  
Author(s):  
Asad Ullah ◽  
Zahir Shah ◽  
Poom Kumam ◽  
Muhammad Ayaz ◽  
Saeed Islam ◽  
...  

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.


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