Modeling and analysis of entropy in MHD unsteady flow of water-based nanofluids with carbon nanoparticles

At a Glance

Metadata	Details
Publication Date	2025-07-01
Journal	Discover Applied Sciences
Authors	Vijendra Kumar Jarwal, Sushila Choudhary, Kalpna Sharma, Prasun Choudhary
Citations	1
Analysis	Full AI Review Included

Technical Analysis and Documentation: Carbon Nanoparticle Nanofluids for Advanced Thermal Management

Executive Summary

This technical documentation analyzes the research on entropy generation in Magnetohydrodynamic (MHD) unsteady flow of water-based nanofluids containing carbon nanoparticles. The findings underscore the critical role of high-conductivity carbon materials in optimizing thermal systems, directly aligning with 6CCVD’s core expertise in Chemical Vapor Deposition (CVD) diamond materials.

Core Research Focus: Comparative analysis of thermal performance and entropy generation using three carbon nanoparticles: Graphene, Nano-diamond (ND), and Single-Walled Carbon Nanotubes (SWCNT) in MHD flow.
Key Thermal Finding: SWCNT-water nanofluid exhibited the most superior heat transfer performance (highest Nusselt number) due to its exceptional thermal conductivity ($\kappa$).
Key Flow Finding: Nano-diamond (ND)-water nanofluid demonstrated the lowest skin friction coefficient, suggesting optimal flow characteristics for minimizing drag.
Methodology: The study relied on numerical solutions of non-linear Ordinary Differential Equations (ODEs), derived via similarity transformations, solved using the MATLAB bvp4c solver.
Application Relevance: The results are highly relevant for designing energy-efficient thermal systems, including electronics cooling, targeted drug delivery, and energy storage technologies.
6CCVD Value Proposition: CVD diamond (SCD/PCD) offers bulk, stable thermal conductivity significantly higher than the tested nanoparticles, providing a superior, stable platform for the advanced thermal management applications discussed.

Technical Specifications

The following table summarizes key material properties and numerical parameters extracted from the research, highlighting the performance metrics achieved by the carbon nanofluids.

Parameter	Value Range/Specific Value	Unit	Context
Magnetic Field Parameter (M)	0.0 to 3.0	Dimensionless	Higher M reduces velocity profiles due to Lorentz force.
Unsteadiness Parameter (A)	0.0 to 3.0	Dimensionless	Higher A reduces velocity and temperature profiles.
Suction/Injection Parameter (S)	-2.0 to 2.0	Dimensionless	S > 0 (Suction) reduces temperature; S < 0 (Injection) increases temperature.
Brinkman Number (Br)	0.5 to 3.5	Dimensionless	Measures ratio of viscous dissipation to thermal conduction.
Nanoparticle Volume Fraction ($\phi$)	0.05 to 0.25	Dimensionless	Augments thermal boundary layer thickness and temperature.
SWCNT Thermal Conductivity ($\kappa$)	6600	W/m K	Highest conductivity among tested nanoparticles (Table 1).
Graphene Thermal Conductivity ($\kappa$)	2500	W/m K	Nanoparticle property (Table 1).
ND Thermal Conductivity ($\kappa$)	1000	W/m K	Lowest conductivity among tested nanoparticles (Table 1).
Wall Velocity (Graphene, M=3)	0.10741	Dimensionless (f’(1))	Significant reduction in momentum profile due to magnetic damping.
Wall Temperature (SWCNT, $\phi$=0.10)	0.21466	Dimensionless ($\theta$(1))	Highest thermal boundary layer augmentation observed.
Skin Friction Hierarchy	Graphene > SWCNT > ND	Dimensionless	Graphene exhibits the highest skin friction value.
Heat Transfer Hierarchy (Nu)	SWCNT > Graphene > ND	Dimensionless	SWCNT demonstrates the most remarkable heat transfer performance.

Key Methodologies

The study employed a rigorous numerical approach to analyze the complex fluid dynamics and thermal behavior of the nanofluids:

Flow Model Definition: A 2D unsteady laminar flow of water-based nanofluids over a continuously stretching surface was considered, incorporating the effects of magnetic field (MHD) and suction/injection (S).
Nanoparticle Models: The Tiwari-Das nanofluid model was used to account for solid volume fractions ($\phi$). Thermal conductivity ($k_{nf}$) was modeled using the Hamilton-Crosser model (for ND and Graphene) and the Maxwell theory (for SWCNT).
Governing Equation Reduction: The governing Partial Differential Equations (PDEs) for mass, momentum, and energy were converted into a system of non-linear Ordinary Differential Equations (ODEs) using similarity transformations.
Numerical Solver Implementation: The resulting coupled ODEs (third-order for velocity, second-order for temperature) were solved using the robust bvp4c collocation method in MATLAB.
Entropy Analysis: Local entropy production rate ($S_G$) was calculated based on contributions from viscous dissipation, heat transfer, and the applied magnetic field, leading to the derivation of the Bejan number ($Be$).
Boundary Conditions: Time-dependent thermal boundary conditions were applied, where the stretching velocity $u_w(x, t)$ and magnetic strength $B(t)$ were functions of time $t$.

6CCVD Solutions & Capabilities

The research validates the critical need for materials with exceptional thermal conductivity and stability in advanced thermal management (electronics cooling) and microfluidic applications. While the paper focuses on carbon nanoparticles dispersed in fluid, 6CCVD provides the ultimate, stable, bulk carbon material—CVD Diamond—to address these exact engineering challenges with superior performance.

Applicable Materials & Performance	Research Requirement	6CCVD Capability Match
Thermal Grade Single Crystal Diamond (SCD)	Need for superior, stable heat transfer (SWCNT $\kappa$ up to 6600 W/m K).	SCD offers the highest known thermal conductivity (up to 2000 W/m K) in a stable, bulk solid form, ideal for high-power electronics heat spreaders and thermal interfaces.
High-Purity Polycrystalline Diamond (PCD)	Requirement for large-area thermal management and structural stability.	We provide PCD plates/wafers up to 125mm in diameter, with thicknesses up to 500 µm, suitable for large-scale industrial heat exchangers or robust substrates.
Boron-Doped Diamond (BDD)	Need for precise control over electrical conductivity ($\sigma$) for MHD flow and sensor applications.	BDD material offers tunable electrical properties, enabling researchers to replicate or extend the magnetic field (M) and electrical conductivity ($\sigma$) parameters used in the MHD simulations.
Ultra-Smooth Surfaces	Minimizing skin friction ($C_f$) and ensuring predictable boundary layer behavior in microfluidics.	SCD wafers are polished to achieve surface roughness $R_a < 1nm$, providing the ideal interface for microfluidic channels and boundary layer studies. Inch-size PCD is polished to $R_a < 5nm$.
Custom Metalization	Integration of electrodes or thermal contacts for advanced cooling systems.	6CCVD offers in-house metalization services (Au, Pt, Pd, Ti, W, Cu) for creating robust, high-performance electrical and thermal contacts directly onto diamond substrates.
Custom Dimensions & Substrates	Need for specific geometries for stretching surfaces or microfluidic channels.	We offer custom thickness control for SCD and PCD (0.1 µm to 500 µm) and bulk substrates up to 10mm, allowing for precise replication of experimental geometries.

Engineering Support

The research highlights the complex interplay between MHD, viscous dissipation, and entropy generation. 6CCVD’s in-house PhD team specializes in the thermal, electrical, and mechanical properties of CVD diamond. We provide expert consultation to assist engineers and scientists in selecting the optimal diamond material (SCD, PCD, or BDD) and geometry for similar electronics cooling, biomedical, or microfluidic projects focused on entropy minimization and enhanced heat transfer.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Abstract This study explores the entropy generation characteristics in the flow of nanofluids over an unsteady stretching surface under the combined effects of magnetic field and suction/injection. The primary objective is to investigate that three different carbon-based nanoparticles Graphene, nano-diamond, and single-walled carbon nanotubes, dispersed in a water-based fluid, influence thermal performance and entropy production in magnetohydrodynamic flow scenarios. This work presents a novel comparison of high-conductivity nanofluids for precise thermal regulation applications. The flow governing partial differential equations, describing the unsteady nanofluid flow and heat transfer, are reduced to a system of ordinary differential equations through similarity transformations. These ODEs are numerically solved using MATLAB’s built-in bvp4c solver. An increase in the magnetic parameter from $$M = 0$$ M = 0 to $$M = 3$$ M = 3 leads to a significant reduction in the momentum profiles from $$f^{\prime}\left( {\eta = 1} \right) = 0.38101$$ f ′ η = 1 = 0.38101 for graphene nanofluid to $$f^{\prime}\left( {\eta = 1} \right) = 0.10741$$ f ′ η = 1 = 0.10741 for nanodiamond fluid. Similarly, enhancing the injection parameter than a rise in velocity is noticed from $$f^{\prime}\left( {\eta = 1} \right) = 0.26662$$ f ′ η = 1 = 0.26662 (nanodiamond fluid) to $$f^{\prime}\left( {\eta = 1} \right) = 0.42372$$ f ′ η = 1 = 0.42372 (SWCNT-based nanofluid). Furthermore, an improvement in nanoparticle volume fraction $$\left( {0.05 \le \phi \le 0.10} \right)$$ 0.05 ≤ ϕ ≤ 0.10 augments the thermal boundary layer, with the wall temperature rising from $$\theta \left( {\eta = 1} \right) = 0.13774$$ θ η = 1 = 0.13774 for graphene nanofluid to $$\theta \left( {\eta = 1} \right) = 0.21466$$ θ η = 1 = 0.21466 for SWCNT-based nanofluid. The results highlight the potential of nanoparticle-enhanced fluids and magnetic/injection control for optimizing heat and momentum transfer in advanced cooling, biomedical, and microfluidic systems. These findings support applications in electronics cooling, targeted drug delivery, and energy storage technologies.

Tech Support

Original Source

DOI: https://doi.org/10.1007/s42452-025-07256-y