The effect of the magnetic field on Couette flow in a porous-filled duct under local thermal non-equilibrium (LTNE) is examined in the present analysis. The bottom plate is moving and experiencing isoflux boundary conditions, whereas the top plate is stationary and adiabatic. The porous region's unidirectional flow fits the Darcy Brinkman (DB) model. The investigations further quantify the impact of the thermal conductivity ratio (κ), Hartmann number (MH), and Biot number (BiH), on heat transfer enhancement. For the coupled energy equations, a successive accelerated replacement (SAR) method is used to generate numerical solutions. The present investigation gives the temperatures in the solid and, the fluid phases in dimensionless form, dimensionless temperature based on the bulk mean temperature and, the local Nusselt number profiles. In the Couette flow model, the magnetic field influences the temperature field in both phases. Additionally, for each Hartmann number, the temperature of the solid phase is greater than that of the fluid phase, validating LTNE. For the thermal field, the fully developed condition is validated in the LTNE model. This study is primarily concerned with modeling high-performance matrix heat exchangers.
In this article, the numerical study of the influence of a magnetic field at the laminar forced convection in a thermally developing region coming under the influence of local thermal non-equilibrium (LTNE) of parallel plate channels completely immersed in the porous material is investigated. Constant wall heat flux boundary conditions are applied to the walls of the channel. In the nonlinear flow model, the Darcy-Brinkman-Forchheimer equation governs the flow field in the porous region, which is assumed to be unidirectional. The system is defined by certain well-known parameters, these being Darcy number (Da), thermal conductivity ratio (κ), Forchheimer number (F), Hartmann number (M), and Biot number (Bi). Numerical solutions have been obtained by applying a successive accelerated replacement (SAR) scheme. Exact solutions for the dimensionless temperature and the fully developed Nusselt number in the absence of the Forchheimer number (F = 0), for the fully developed thermal field, are obtained for the linear flow model, the Darcy-Brinkman model. Plots are given for the dimensionless temperature profiles in the fluid and solid phases, wall temperature, as well as the local Nusselt number at the parallel plate channel, which has been displayed. The effect of the magnetic field and the thermal conductivity ratio has a significant effect on the local Nusselt number.
This study analyses the influence of axial conduction and Biot number on the forced convective heat transfer characteristics in a duct filled with porous material that is thermally developing under local thermal non-equilibrium (LTNE). Channel walls are subjected to heat flux. The unidirectional flow in the porous region corresponds to the Darcy Brinkman model. A successive accelerated replacement (SAR) approach has been used to obtain numerical solutions. The investigations further quantify the impact of the Biot number on heat transfer enhancement. For fluid-solid phases, dimensionless temperatures, and local Nusselt number (<i>Nu<sub>ξ</sub></i>), profiles are given in the present investigation. Validation of fully developed conditions for LTNE is done. The axial conduction effect is more at the low Peclet number <i>Pe<sub>H</sub></i> for all the Biot numbers Bi. For large <i>Pe<sub>H</sub></i>, the axial conduction effect is negligible. The <i>Nu<sub>ξ</sub></i> decreases as the ratio of thermal conductivities, <i>κ</i> and <i>Bi</i>, increases. LTNE is equivalent to local thermal equilibrium (LTE) for a large Bi.
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