Hartmann Flow and Heat Transfer of Two Immiscible Fluids between Two Parallel Porous Plates under Constant Pressure Gradient

Ibrahim, Mohamed Ahmed; Abbas, Wael; Ali, Ahmed

doi:10.21608/erj.2024.313588.1090

Hartmann Flow and Heat Transfer of Two Immiscible Fluids between Two Parallel Porous Plates under Constant Pressure Gradient

Document Type : Original Article

Authors

¹ Engineering Physics and Mathematics Department, Faculty of Engineering - Helwan university – Mataria Branch, Cairo, Egypt.

² Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt.

10.21608/erj.2024.313588.1090

Abstract

Unsteady Hartman flow and heat transfer of two immiscible fluids between two infinite porous parallel plates are studied in this work. Uniform magnetic field is applied on the fluids perpendicular to the plates and Hall Effect under constant pressure gradient are considered. The equations solution is acquired by applying the finite difference technique in both ﬂuid regions. Effects of physical parameters such as viscosity ratio, conductivity ratio, Hartman number, Prandtl number and Eckert number are presented graphically on both the velocity and temperature profile. It was found that, Hall parameter is direct proportional to main component of the velocity and temperature profiles. With the increase of the viscosity ratio, the temperature and velocity profiles decrease. In both regions, the temperature distribution in-creases with a rise in the Prandtl and Eckert numbers at any given point, whereas it drops with an in-crease in the thermal conductivity ratio. This research holds significant importance as it focuses on the extensive utilization of The Hartmann fluid flows in cooling electronic components that produce substantial heat during their operation.

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