A numerical study of the longitudinal thermoconvective rolls in a mixed convection flow in a horizontal channel with a free surface

TL;DR

This numerical study investigates how mixed convection, buoyancy, and thermocapillary effects influence the formation of longitudinal convective rolls in a horizontal channel with a free surface, affecting flow patterns and heat transfer.

Contribution

It introduces a detailed numerical analysis of the combined effects of buoyancy, thermocapillarity, and forced convection on flow instabilities in a horizontal channel with a free surface.

Findings

Development of steady longitudinal convective rolls depends on flow parameters.

Flow patterns are influenced by Reynolds, Rayleigh, and Biot numbers.

Thermocapillary effects significantly alter heat transfer characteristics.

Abstract

This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier-Stokes and energy equations are solved numerically by the finite volume method taking into account the thermocapillary effects (Marangoni effect). When the strength of the buoyancy, thermocapillary effects and forced convective currents are comparable $(Ri\backsimeq O(1)$ and $Bd=Ra/Ma \backsimeq O(1))$, the results show that the development of instabilities in the form of steady longitudinal convective rolls is similar to those encountered in the Poiseuille-Rayleigh-B\'enard flow. The number and spatial distribution of these rolls along the channel depend on the flow conditions. The objective of this work is to study the influence of parameters, such as the Reynolds, Rayleigh and Biot numbers, on the flow patterns and heat transfer characteristics. The effects of variations in the surface tension with temperature gradients (Marangoni effect) are also considered.