Linear Model for Two-Layer Porous Bed Suspended with Nano Sized Particles
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-02-19 |
| Journal | Energies |
| Authors | J. C. Umavathi, Mikhail Đ. Sheremet |
| Institutions | Gulbarga University, Ulyanovsk State Technical University |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: High-Performance Diamond Nanofluids in Porous Media
Section titled âTechnical Documentation & Analysis: High-Performance Diamond Nanofluids in Porous MediaâExecutive Summary
Section titled âExecutive SummaryâThis analysis reviews the modeling of combined convection and heat transfer in a two-layer porous bed system, highlighting the critical role of diamond nanoparticles in achieving superior thermal performanceâa direct application for 6CCVDâs advanced MPCVD diamond materials.
- Core Achievement: The study successfully modeled two immiscible fluids (nanofluid/viscous fluid) saturated in porous beds with differing permeabilities, simulating complex heat transfer scenarios relevant to advanced cooling and energy systems.
- Thermal Superiority of Diamond: Diamond nanoparticles, when suspended in water, demonstrated the best heat transfer rate (highest average Nusselt number) compared to copper and titanium oxide, confirming diamondâs status as the premier thermal material for nanofluids.
- Modeling Approach: The system utilized the Dupuit-Forchheimer model for porous media effects and the Tiwari-Das model for nanofluid properties, solved using the finite difference method.
- Flow Dynamics: Velocity is accelerated by high Darcy (Da) and Grashof (Gr) numbers but depleted by high inertia (I) and solid volume fraction ($\phi$).
- Material Impact: Increasing the solid volume fraction ($\phi$) significantly reduces flow velocity due to increased base fluid viscosity, emphasizing the need for highly efficient nanoparticles like diamond at low concentrations.
- Applications: The research directly supports the development of high-efficiency cooling gadgets in electronics, nuclear technology, and industrial heat exchangers.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the numerical analysis, focusing on the material parameters and dimensionless numbers influencing flow and heat transfer.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Nanoparticle Material (Best Nu) | Diamond (C) | N/A | Causes the highest rate of heat transfer at both plates (Table 5). |
| Maximum Solid Volume Fraction ($\phi$) | 0.5 | N/A | Tested range; high $\phi$ (0.5) achieved the highest Nu (3.973438). |
| Darcy Number (Da) Range | 0.001 to 2.0 | N/A | Da boosts flow rate (Q) and Nusselt number (Nu). |
| Grashof Number (Gr) Range | -25 to 25 | N/A | Gr expands velocity and surges volumetric flow rate (Q). |
| Brinkman Number (Br) Range | 0.0 to 2.0 | N/A | Br advances momentum and energy distribution. |
| Permeability Ratio ($\kappa$) Range | 0.1 to 2.0 | N/A | Ratio of Layer-1 to Layer-2 permeability ($\kappa_1 / \kappa_2$). |
| Inertia Parameter (I) Range | 0.0 to 8.0 | N/A | I suppresses velocity and depletes volumetric flow rate (Q). |
| Max Average Nusselt (Layer-1, y=0) | 3.973438 | N/A | Achieved using $\phi = 0.5$ (Diamond/Water). |
| Base Fluid Combination (Best Nu) | Engine oil-Mineral oil | N/A | Provides the highest Nu values at the left plate (Table 5). |
| Base Fluid Combination (Best Overall) | Ethylene glycol-Kerosene | N/A | Causes the rate of heat transfer to rise in both Layer-1 and Layer-2. |
Key Methodologies
Section titled âKey MethodologiesâThe experimental analysis relied on a robust mathematical and numerical framework to simulate the complex fluid dynamics and thermal transport within the porous media.
- Physical Configuration: A square duct filled with two immiscible Newtonian fluids (Layer 1: Nanofluid in porous matrix $\kappa_1$; Layer 2: Viscous fluid in porous matrix $\kappa_2$).
- Porous Media Modeling: The Dupuit-Forchheimer approach was applied to mathematically outline the permeability and inertia effects within the porous beds.
- Nanofluid Modeling: The Tiwari-Das model was used to define the thermophysical properties (density, viscosity, thermal conductivity) of the nanofluid in Layer 1.
- Governing Equations: The Navier-Stokes equations for momentum and energy conservation were utilized, incorporating Grashof (buoyancy), Darcy (porosity), and Brinkman (viscous dissipation) numbers.
- Boundary Conditions: No-slip velocity was enforced at all boundaries. Continuity of velocity, shear stress, temperature, and heat flux was assumed at the interface between Layer 1 and Layer 2.
- Numerical Solution: The conservation equations were solved using the finite difference method, employing the Southwell over-relaxation technique for iterative convergence (stopping condition: difference < 10-8).
- Validation: Code validation was confirmed via a grid independence test (101 x 101 nodes) and comparison of average Nusselt values against established literature.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe research confirms that diamond nanoparticles offer superior thermal performance in advanced cooling applications. 6CCVD is uniquely positioned to supply the high-quality MPCVD diamond materials and custom substrates required to replicate and advance this research into commercial thermal management solutions.
Applicable Materials
Section titled âApplicable MaterialsâTo achieve the peak heat transfer rates demonstrated by diamond nanoparticles, researchers and engineers require high-purity, high-thermal conductivity diamond materials.
| Research Requirement | 6CCVD Solution | Material Specification |
|---|---|---|
| High Thermal Performance Nanoparticles | Optical/Thermal Grade SCD | Single Crystal Diamond (SCD) precursors for synthesizing high-purity, defect-free diamond nanoparticles. |
| Porous Substrate/Heat Spreader | High-Purity PCD Plates | Polycrystalline Diamond (PCD) wafers up to 125mm in diameter, ideal for large-area heat dissipation and acting as robust porous bed substrates. |
| Active Thermal/Electrochemical Control | Boron-Doped Diamond (BDD) | BDD films and wafers for applications requiring simultaneous thermal management and electrochemical sensing or heating elements (e.g., controlling fluid temperature via Joule heating). |
Customization Potential
Section titled âCustomization PotentialâThe complexity of two-layer flow and porous media requires precise material dimensions and surface quality, especially at the fluid interface. 6CCVDâs custom manufacturing capabilities ensure materials meet the exact specifications needed for advanced thermal fluid dynamics research.
- Custom Dimensions: We provide SCD and PCD plates/wafers in custom sizes, including large-area PCD up to 125mm, suitable for scaling up experimental ducts and heat exchangers. Substrate thicknesses are available up to 10mm.
- Interface Quality: For minimizing interfacial drag and maximizing heat flux continuity (as required by the boundary conditions in the paper), 6CCVD offers ultra-smooth polishing capabilities:
- SCD: Surface roughness (Ra) < 1nm.
- Inch-size PCD: Surface roughness (Ra) < 5nm.
- Metalization Services: While the porous bed itself may not be metalized, associated electronic components or sensors often require robust contacts. 6CCVD offers in-house deposition of standard metals including Au, Pt, Pd, Ti, W, and Cu, allowing for integrated thermal and electrical designs.
Engineering Support
Section titled âEngineering SupportâThe successful implementation of diamond nanofluids relies heavily on understanding the interplay between material properties (viscosity, thermal conductivity ratio $K$) and flow parameters (Darcy number Da, Grashof number Gr).
6CCVDâs in-house PhD engineering team specializes in the material science of MPCVD diamond and can assist researchers in selecting the optimal diamond grade, thickness, and surface finish for Advanced Cooling Systems and Energy Conservation projects. We provide consultation on how material characteristics influence critical dimensionless numbers like the thermal conductivity ratio ($K$) and the resulting Nusselt number (Nu).
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Two immiscible fluids flows are materialized in science and technology; the combined convection of the two immiscible fluids in a square conduit is reviewed in this study. The nanofluid and pure viscous fluid which do not mix are discussed, and both layers saturated with a porous matrix have different permeabilities. The Dupuit-Forchheimer and Tiwari-Das models are applied to outline the permeability of the layer and nanofluids, respectively. The finite difference method is utilized to find the solutions of conservation equations along with suitable boundary and interface conditions. The boundary condition for the velocity is no slip at all the boundaries, while continuity of velocity and shear stress are used at the interface. The left and right walls are kept at constant but different temperatures, the top and bottom walls are isolated, and the continuity of temperature and heat flux is assumed at the interface. Grashof number, Brinkman number, Darcy number, inertia parameter, permeability ratio, solid volume fraction, thermal conductivity and viscosity ratios, different nanoparticles, and various base liquids of the two-layered fluids are engaged. The velocity is depleted by the inertia and viscosity ratio while it is accelerated with the Darcy and Grashof numbers. The energy distribution was not modulated significantly with any of the dimensionless numbers. Using copper nanoparticles doped in mineral oil and ethylene glycol produced the peak momentum. Diamond nanoparticles dropped in water catalysis showed the best heat transfer rate.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 2015 - Numerical investigation of heat transfer in three-fluid stratified flows [Crossref]
- 2014 - Heat transfer enhancement in a vertical tube confining two immiscible falling co-flows [Crossref]
- 2014 - Two immiscible layers of electro-osmotic driven flow with a layer of conducting non-Newtonian fluid [Crossref]
- 2012 - Multiphase lattice Boltzmann simulations of buoyancy-induced flow of two immiscible fluids with different viscosities [Crossref]
- 2010 - Generalised plain Couette flow heat transfer in a composite channel [Crossref]
- 2012 - Poiseuille-Couette flow and heat transfer in an inclined composite porous medium [Crossref]
- 2021 - Heat transfer of viscous fluid in a vertical channel sandwiched between nanofluid porous zones [Crossref]
- 1971 - Stratified laminar flow of two immiscible fluids [Crossref]
- 2011 - Numerical study of factors influencing relative permeabilities of two immiscible fluids flowing through porous media using lattice Boltzmann method [Crossref]