Enhancing Heat Transfer in the Developing Thermal Field in a Fluid Saturated Porous Filled Duct with Local Thermal Non-equilibrium

Abstract

This thesis introduces the local thermal non-equilibrium (LTNE) model as a framework for analyzing the forced convection heat transfer in the context of laminar flow within a thermally developing region within a parallel plate channel filled with porous media. Additionally, a transverse application of the magnetic field is imposed along the channel walls. Specific well-known parameters define the system, these being the Darcy number (Da), thermal conductivity ratio (κ), Forchheimer number (F), Hartmann number (M), Biot number (Bi), Peclet number (Pe), and Brinkman number (Br). Numerical solutions have been obtained by applying a successive accelerated replacement (SAR) scheme. The numerical solutions have been obtained for the following values of the parameters characterizing the different problems studied. Darcy number: 0.001 ≤ Da ≤ 1.0. Forchheimer number: 1≤ F ≤ 100. Hartmann number: 0.5 ≤ M ≤ 65. Biot number: 10 ≤ Bi ≤ 100. When axial conduction is considered, Peclet number: 5 ≤ Pe ≤ 100. When axial conduction is neglected, designated by Ac = 0, Pe is absorbed in ξ* and does not appear explicitly. When viscous dissipation is included, the Brinkman number: is 0.8 ≤ Br ≤ 100. The effect of Darcy number, Hartmann number, Biot number, and thermal conductivity ratio is discussed for the thermally developing region. The study presents outcomes concerning dimensionless temperature profiles in both the fluid and porous phases, the wall temperature and the local Nusselt number within the parallel plate channel. Notably, the local Nusselt number is influenced by a magnetic field and variations in the thermal conductivity ratio. A fully developed condition is validated when LTNE is used. It serves the purpose of the downstream boundary condition when axial conduction is used (elliptic PDE). The influence of axial conduction on the forced convective heat transfer characteristics in a duct filled with porous material at a thermally developing zone under LTNE is discussed. The axial conduction effect is more at the low Peclet number, Pe, for all the Biot numbers, Bi. For large Pe, the axial conduction effect is negligible. The vi validation of fully developed conditions for the local thermal non-equilibrium (LTNE) model is conducted. The effect of two viscous dissipation models, the form drag (FD) model and the clear fluid compatible (CFC) model, is employed at the thermal entrance. The results include the effects of viscous dissipation on temperature profiles and local Nusselt numbers. The increment in the Brinkman number, Biot number, and thermal conductivity ratio improves the temperature distribution. The parametric structure of this study permitted mapping LTNE and local thermal equilibrium (LTE) areas across a wide range of these dimensionless parameters. Enhancement in the local Nusselt number is obtained in the CFC model compared to the value in the FD model. Synergistic impact of axial conduction and viscous dissipation combined in the thermal-developing zone under LTNE framework in a duct packed with saturated porous medium. It explores the thermal characteristics of fluid flow through a porous medium confined within a channel defined by parallel plates. The channel walls are subject to a boundary condition with a constant wall heat flux. Enhancements in the Peclet number, Brinkman number, Biot number, and thermal conductivity ratio lead to improved temperature distribution. The parametric approach in this study enables the mapping of LTNE and local thermal equilibrium (LTE) regions across a broad spectrum of these dimensionless parameters.