Properties of Solutions in a Fourth-Order Equation of Squeezing Flows
- PDF / 1,409,062 Bytes
- 9 Pages / 595.276 x 790.866 pts Page_size
- 47 Downloads / 183 Views
RESEARCH ARTICLE-CHEMICAL ENGINEERING
Properties of Solutions in a Fourth‑Order Equation of Squeezing Flows Samer Al‑Ashhab1 Received: 19 September 2019 / Accepted: 26 April 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract We investigate properties of solutions for a squeezing flow problem governed by a fourth-order nonlinear ODE. The findings obtained reveal significant mathematical features with crucial physical implications. Those findings are obtained via the use of appropriate mathematical equations and approximations, as well as very careful mathematical analysis and derivations, which lead to mathematical formulas for relevant parameters, and results that enable us achieve a new understanding for the physical problem. The derived formulas for the parameters are compared with computations obtained using MATLAB built-in integrators to illustrate the accuracy of those derived formulas. In addition to doing the computations and generating the tabulated results, the MATLAB software is used to generate the figures and illustrations which highlight the main results and conclusions. Existence of solutions is discussed, and some special case solutions are obtained. Properties of parameters and their interdependence are determined, where relevant relations are derived. Keywords Squeezing flow · Boundary layer problem · Nonlinear IBVP · Radial speed · Dynamic viscosity
1 Introduction Squeezing flow studies date back to more than a century ago, cf. [1, 2], even though earlier studies in this field remain rare. However, it is noted that more studies took place during the second half of the past century, cf. [3–8] where many of those aforementioned investigations involved Newtonian fluids. A good number of applications of squeezing flows can be found within chemical engineering and food industry; observing that food industry applications involve more of the non-Newtonian fluids such as ketchup and mustard, however squeezing flow applications with Newtonian fluids such as water and oil can still be found in food industry. Squeezing flows also appear in liquid metal lubrication systems, polymer processing, as well as compression and injection moulding. Additional examples of Newtonian fluids are gasoline and glycerine with many applications in industry. Classically, squeezing flows are generated by a moving boundary, so that in fact, they result from external normal * Samer Al‑Ashhab [email protected] 1
Deanship of Scientific Research, Al Imam Mohammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh 11623, Saudi Arabia
stresses and velocities. More recent studies concerning the squeezing flow of fluids can be found in [9–12] for example; however, most of those focused on modelling, as well as obtaining numerical and graphical solutions. More needs to be done regarding the qualitative nature of solutions and their dependence on the physical parameters. In [13], the authors used the homotopy analysis method to solve the corresponding nonlinear differential equation, where they obtained seve
Data Loading...
