Published July 3, 2026 | Version v1
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Numerical Investigation of Turbulent Water Flow Behavior in a Horizontal Pipe

Authors/Creators

  • 1. Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Juja, Kenya.

Description

Abstract

In this article turbulent flow of water through a horizontal pipe, considering sediment suspension under steady state is analyzed, inhomogeneity of temperature and effects of buoyancy and viscous dissipation have been taken into account. The effect of buoyancy forces has been analyzed using Grashof number (Gr), while that of viscous heating has been analyzed through the Eckert number (Ec). The Navier–Stokes, energy, and continuity equations in dimensionless form were numerically solved using the collocation method through MATLAB and the Boussinesq approximation was utilized to address buoyancy through temperature only. It is found that the Inhomogeneous ambient temperature of hot and cold fluid behaves as a potential source of sound, Nusselt number and suction, Grashof number increases the buoyancy induced flow structures become more upgraded resulting stronger velocity gradients with enhanced mixing, similarly the effects of viscous dissipation are higher in localized temperature increase. Flattening of the velocity profile and less radial variation led to a more uniform axial distribution of velocity compared to that of the laminar flow. The present results show the ability of the collocation technique in modeling complex thermally affected turbulent flows and suggest guidelines for optimizing pipe flow systems affected by buoyancy and viscous heating.

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Additional details

Identifiers

ISSN
3049-0669
DOI
10.5281/zenodo.21154762
URL
https://msipublishers.com/volume-3-issue-7-2026-msijmr/

Dates

Accepted
2026-07-03
This research presents a numerical investigation of turbulent water flow in a horizontal pipe, focusing on the combined effects of sediment suspension, buoyancy forces, viscous dissipation, and non-uniform ambient temperature under steady-state conditions. The study provides valuable insights into the complex thermal and fluid dynamic interactions that influence turbulent pipe flow and offers guidance for optimizing engineering systems involving heat transfer and fluid transport. The mathematical model is based on the dimensionless Navier–Stokes, energy, and continuity equations, with buoyancy effects incorporated through the Boussinesq approximation. The governing equations were solved numerically using the collocation technique implemented in MATLAB. The analysis evaluates the influence of the Grashof number (Gr), representing buoyancy-driven flow, and the Eckert number (Ec), representing viscous heating, on velocity distribution, temperature profiles, and heat transfer characteristics in turbulent flow conditions. The results demonstrate that inhomogeneous ambient temperature significantly affects turbulent flow behavior, heat transfer, and fluid mixing. Increasing the Grashof number enhances buoyancy-induced flow structures, producing stronger velocity gradients and improved mixing, while higher Eckert numbers lead to localized temperature increases due to viscous dissipation. Compared with laminar flow, turbulent flow exhibits a flatter velocity profile and a more uniform axial velocity distribution, contributing to improved transport efficiency. The findings also confirm the effectiveness of the collocation technique as a reliable numerical method for modeling thermally influenced turbulent flows in engineering applications. This study contributes to computational fluid dynamics, applied mathematics, and thermal engineering by advancing the understanding of buoyancy- and heat-induced turbulent pipe flow. The findings are relevant to researchers, engineers, and practitioners working in fluid mechanics, heat transfer, pipeline engineering, industrial process optimization, and numerical simulation of complex flow systems. Keywords: Turbulent flow, Horizontal pipe, Computational fluid dynamics, Collocation technique, Navier–Stokes equations, Grashof number, Eckert number, Buoyancy effects, Viscous dissipation, Heat transfer, MATLAB simulation, Fluid mechanics.

Software

Repository URL
https://msipublishers.com/volume-3-issue-7-2026-msijmr/

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