Model Matematika Fluida Lapisan Tipis pada Bidang Miring
Keywords:
Bidang miring, Fluida lapisan tipis, Metode beda hingga, Newtonian, Non-NewtonianAbstract
Thin film fluid is a fluid characterized by a very small ratio of height to length, allowing the vertical velocity component to be neglected. This article presents a mathematical model of Newtonian and non-Newtonian thin film fluids on an inclined plane. The mathematical model consists of a system of partial differential equations built from two governing equations: the Navier-Stokes equations and the continuity equation. By utilizing the scaling method, small-order parameters can be neglected to obtain an equation that describes the changes in thin film fluid height. Numerical solutions are obtained using the finite difference method. In this research, simulations were conducted with various inclination values and fluid types. The simulation results indicate that differences in inclination and fluid types lead to distinct variations in fluid flow movement.
Keywords: Finite difference method, Inclined plane, Newtonian, Non-Newtonian, Thin film fluid
ABSTRAK
Fluida lapisan tipis adalah fluida dengan kondisi perbandingan tinggi fluida dan panjang fluida yang sangat kecil, sehingga komponen kecepatan arah vertikal dapat diabaikan. Pada artikel ini dipaparkan sebuah model matematika fluida lapisan tipis jenis Newtonian dan non-Newtonian pada bidang miring. Model matematika ini berupa sistem persamaan diferensial parsial yang terdiri dari dua persamaan pembangun, yaitu persamaan Navier-Stokes dan persamaan kontinuitas. Dengan metode penskalaan, parameter-parameter yang berorde kecil dapat diabaikan, sehingga diperoleh persamaan yang menggambarkan perubahan ketinggian fluida lapisan tipis. Solusi numerik diperoleh dengan metode beda hingga. Pada penelitian ini, simulasi dilakukan dengan beberapa nilai kemiringan dan jenis fluida. Hasil simulasi menunjukkan bahwa perbedaan kemiringan dan jenis fluida menyebabkan perbedaan pada pergerakan aliran fluida.
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