Numerical study of magnetic field interaction with fully developed flow in a vertical duct

Ducts are conduits or passages used to supply, return, or exhaust air, needed for heating, ventilation, or air conditioning in multistory gigantic building structures. Rapid growth in population (especially in industrially concentrated regions) has led to the culture of constructing skyscrapers of tens of storeys, in which vertical ducts are the natural choice for removing polluted air. Due to the compactness of the building design, high voltage current-carrying wires are usually located very close to exhaust ducts carrying polluted air. Consequently, a natural motivation is to study how the magnetic field produced by such a wire affects the flow, driven by an external pressure gradient (for example, exhaust fan, vacuum pump, etc.) in a vertical duct. Therefore, the paper is devoted to understanding the interaction of the developed (thermally and hydrodynamically) flow in a vertical square duct with the magnetic field produced by a nearby placed current-carrying wire. The flow is assumed to be laminar and is driven by a constant external pressure gradient. For the thermal boundary condition, we assume a uniform heat flux across the unit axial length whereas a fixed temperature is also assumed over the peripheral surface of the duct. As a result of the mathematical modeling of the problem, we come across a system of coupled Poisson-like equations which are solved numerically by following a finite volume approach. We have noted that a sufficiently higher Rayleigh number may cause a reverse flow while reducing and flattening the thermal distribution in the middle of the duct. In addition the magnetic field further reduces the flow velocity, particularly near the duct wall where the current-carrying wire (causing the magnetic field) is positioned.