Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition: Effects of different thermal boundary conditions at the porous-fluid interface

Enhancement of forced convective heat transfer is analytically investigated in a channel partially filled with a porous medium under local thermal non-equilibrium (LTNE) condition. Thermally and hydrodynamically fully developed conditions are considered. The flow inside the porous material is modelled by the Darcy–Brinkman–Forchheimer equation. The thermal boundary conditions at the interface between the porous medium and the clear region are described by two different models. For each interface model exact solutions are developed for the solid and fluid temperature fields. The Nusselt number (Nu) associated with each interface model is derived in terms of the porous insert normalised thickness (S) and other pertinent parameters such as thermal conductivity ratio (k), Biot number (Bi), and Darcy number (Da). The differences between the two interface models in predicting the temperature fields of the solid and fluid phases and validity of the Local Thermal Equilibrium (LTE) assumption are examined. Subsequently, for each model the values of S, Bi, k and Da at which LTE holds are determined. Further, the maximum values of S up to that the two models predict LTE condition are found as a function of Bi, k and Da. For each model and for different pertinent parameters the optimum value of S, which maximises the Nu number, is then found. The results show that, in general, the obtained Nu numbers can be strongly dependent upon the applied interface model. For large values of k and Bi, there are significant disparities between the Nu numbers predicted by the two models. Nonetheless, for most values of k and Bi, and under different values of Da numbers both models predict similar trends of variation of Nu number versus S. The Nu number and pressure drop ratio are then used to determine the Heat Transfer Performance (HTP). It is found that for S < 0.9, HTP is independent of Da number and the model used at the porous-fluid interface. For S > 0.9, reduction of Da results in smaller values of HTP and signifies the difference between the values of HTP predicted by the two interface models

Numerical investigation of heat transfer enhancement in a pipe partially filled with a porous material under local thermal non-equilibrium condition

This paper examines numerically the heat transfer enhancement in a pipe partially filled with a porous medium under local thermal non-equilibrium (LTNE) condition. The flow inside the porous material is modelled using the Darcy–Brinkman–Forchheimer model. The effect of different parameters such as, inertia (F), Darcy number (Da), conductivity ratio, porosity and particle diameter on the validity of local thermal equilibrium (LTE) are studied. The optimum porous thickness for heat transfer enhancement under varying F and with reasonable pressure drop is determined. The pipe wall is under constant wall temperature boundary condition. Two models are considered at the interface between the porous medium and the fluid. The differences between these models in predicting the temperature of the fluid and solid phases as well as the Nusselt (Nu) number for different pertinent parameters are discussed. In general, the two interface models result in similar trends of Nu number variation versus porous thickness ratio. However, considerably different values of Nu number are obtained from the two interface models. The effects of inertia term on the Nu number and pressure drop are further studied. For a given model and for Da < 10−3, the Nu number is found independent of F. However, for Da > 10−3 as F increases the computed Nu number increase

Data-Driven Modal Analysis of Turbulent Momentum Exchange and Heat Transfer in Composite Porous Fluid Systems

This paper investigates the dynamics governing turbulent momentum exchange and heat transfer between pore flow within porous media and the turbulent flow passing over it. Employing high-fidelity pore-scale large eddy simulation, our investigation explores the fundamental mechanisms driving these phenomena. Modal analysis based on snapshot Proper Orthogonal Decomposition (POD) is employed to quantify the modes of interaction between porous and non-porous regions, providing a comprehensive understanding of the underlying processes. Spatial and temporal modes reveal the existence of localized flow structures at the pore scale, contributing to time-varying patterns of information exchange. At the commencement of the porous block, the mean flow (Mode = 0) from the porous to the non-porous region is the dominant mechanism in momentum exchange and heat transfer. This mode facilitates convective heat transfer from the porous to the non-porous region through upward and forward flow movements, showcasing positive flow leakage. In addition to the mean flow, the turbulent flux inherent in alternate POD modes (Mode ≠ 0) plays a substantial role in information propagation, influencing diverse directions. Spatial modes, complemented by statistical analysis, uncover a significant likelihood of observing negative vertical velocity values in the wake of the porous ligaments at the porous-fluid interface, indicative of negative flow leakage. This negative flow leakage precisely corresponds to the local penetration of fluid from the non-porous region into the porous region. Furthermore, our study reveals that information exchange via turbulence fluctuations manifests through complex outward and inward interactions in regions characterized by substantial positive flow leakage. Notably, these regions exhibit a distinct tendency for high-momentum streamwise-oriented flow to migrate outward from the porous region into the non-porous region (outward interactions). Conversely, inward interactions arise in these regions when the instantaneous magnitude of positive flow leakage is smaller than the mean value of positive flow leakage, emphasizing the pulsating nature of positive flow leakage. Finally, the distribution of the Nusselt number highlights that more than 60% of total heat transfer occurs within the initial one-third of the porous block length. Significantly, a notable portion of the porous ligaments experiences insufficient cooling due to positive flow leakage, underlining the critical implications of these findings for the understanding of turbulent momentum exchange and heat transfer in a composite porous-fluid system

Pulsating flow in a channel filled with a porous medium under local thermal non-equilibrium condition: an exact solution

The present work investigates analytically the problem of forced convection heat transfer of a pulsating flow, in a channel filled with a porous medium under local thermal non-equilibrium condition. Internal heat generation is considered in the porous medium, and the channel walls are subjected to constant heat flux boundary condition. Exact solutions are obtained for velocity, Nusselt number and temperature distributions of the fluid and solid phases in the porous medium. The influence of pertinent parameters, including Biot number, Darcy number, fluid-to-solid effective thermal conductivity ratio and Prandtl number are discussed. The applied pressure gradient is considered in a sinusoidal waveform. The effect of dimensionless frequency and coefficient of the pressure amplitude on the system's velocity and temperature fields are discussed. The general shape of the unsteady velocity for different times is found to be very similar to the steady data. Results show that the amplitudes of the unsteady temperatures for the fluid and solid phases decrease with the increase in Biot number or thermal conductivity ratio. For large Biot numbers, dimensionless temperatures of the solid and fluid phases are similar and are close to their steady counterparts. Results for the Nusselt number indicate that increasing Biot number or thermal conductivity ratio decreases the amplitude of Nusselt number. Increase in the internal heat generation in the solid phase does not have a significant influence on the ratio of amplitude-to-mean value of the Nusselt number, while internal heat generation in the fluid phase enhances this ratio