# Numerical study of flow and heat transfer in circular T-shaped junction of different cross-sections

## TL;DR

This paper numerically studies fluid flow and heat transfer in T-shaped junctions with different cross-sections to improve heat exchanger and piping designs.

## Contribution

The study introduces a numerical investigation of flow and heat transfer in T-shaped junctions with varying cross-sections and flow parameters.

## Key findings

- Lower flow rate ratios (r) cause stronger vortex formation and asymmetry in flow and temperature fields.
- Increasing Reynolds number (Re) enhances heat transfer and leads to unsteady flow regimes.
- Wider outlet configurations promote recirculation and thermal mixing.

## Abstract

This study investigates fluid flow and convective heat transfer within a smooth, two-dimensional T-shaped junction using a numerical approach. Simulations were conducted by varying the volumetric flow rate ratio r (0.25, 0.5, 0.75, and 1), the Reynolds number Re (500 to 2500), the Prandtl number Pr (1), and the cross-sectional width ratio w (0.5 to 2.5) of the outlet. The fluid dynamics were solved using the vorticity–stream function formulation with a compact upwind finite difference scheme and the Implicit-Explicit (IMEX) method, implemented in MATLAB. Flow behavior was analyzed through streamline and isotherm contours, while local and average Nusselt numbers were computed along the junction walls. The results show that lower r values lead to stronger vortex formation and asymmetry in the flow and temperature fields, while r = 1 yields symmetric and stable patterns. Increasing Re enhances heat transfer and transitions the flow toward unsteady regimes. Similarly, wider outlet configurations (higher w) promote recirculation and thermal mixing. This study provides valuable insights into how inlet flow, outlet shape, and fluid characteristics interact to influence heat transfer and flow behavior in a smooth T-shaped junction. It also provides insights that can help improve the design of heat exchangers, microfluidic systems, and industrial piping.