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Computations of the interface in two-fluid Couette flow

de Oliveira, Ebenezer
http://rave.ohiolink.edu/etdc/view?acc_num=osu1587032365434615

Abstract Details

2020, Master of Mathematical Sciences, Ohio State University, Mathematics.
Thin liquid films have helped improve efficiency in applications of heat or mass transport by exploiting the contrast in film thickness relative to substrate length. A thin film evolution equation is derived to describe the interface of two viscous, equal density fluids residing between parallel plates. The bottom fluid is of thin thickness relative to the channel height and the upper plate moves at constant velocity to drive the two-fluid flow. The recent work of Papageorgiou and Tanveer (2019) [5] proves the existence of steady-state solutions of this equation in a neighborhood of numerically obtained solutions by showing that Banach contraction theorem applies in a suitable space and providing rigorous error bounds between computational and true solutions. The same numerical approach is taken here by applying Newton’s method to determine Fourier coefficients. We find new steady-state and time-periodic numerical solutions and verify that the steady-state solutions satisfy conditions of the theorem in [5]. Wave profiles and bifurcation diagrams are provided for computed solutions.
Saleh Tanveer (Advisor)
Yulong Xing (Committee Member)
Janet Best (Committee Member)
55 p.
Applied Mathematics
thin films; Couette flow

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Citations

  • de Oliveira, E. (2020). Computations of the interface in two-fluid Couette flow [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587032365434615

    APA Style (7th edition)

  • de Oliveira, Ebenezer. Computations of the interface in two-fluid Couette flow. 2020. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1587032365434615.

    MLA Style (8th edition)

  • de Oliveira, Ebenezer. "Computations of the interface in two-fluid Couette flow." Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587032365434615

    Chicago Manual of Style (17th edition)

osu1587032365434615
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