## THERMAL SCIENCE

International Scientific Journal

### A FRACTAL-FRACTIONAL MODEL FOR COMPLEX FLUID-FLOW WITH NANOPARTICLES

**ABSTRACT**

Nanoparticles play an important role in nanofluids to enhance thermal conduction, and can be easily controlled by a magnetic force, so it can be widely used in nano/micro devices. This paper gives two mathematical models to describe the nanofluid flow, one is an approximate continuum model, in which the homotopy matching is used to deal the discontinuity between the fluid and nanoparticles, and the other is to use the conservation laws in a fractal space. The models give new physical insight into the particle fluid-flow.

**KEYWORDS**

PAPER SUBMITTED: 2021-12-20

PAPER REVISED: 2022-07-19

PAPER ACCEPTED: 2022-07-19

PUBLISHED ONLINE: 2023-06-11

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 3**, PAGES [2057 - 2063]

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