This study explores the mathematical modeling of magnetohydrodynamics (MHD) in a two-dimensional dynamic scenario involving free convection (FC) and heat transfer (HT) with entropy generation (Egen) within a wavy octagonal cavity filled with blade-shaped kerosene-Ag nanofluids, where nanoparticles exhibit Brownian motion. The lower wall maintains uniform thermal boundary conditions (TBC), while the undulating wall remains at a cooler temperature. All other boundaries of the domain are assumed to be adiabatic. The finite element method, combined with the central composite design (CCD) based response surface method (RSM) and artificial neural networks (ANN), is used to solve nonlinear PDE problems. Various parameters are investigated, including Hartmann number (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$0\le Ha\le 100$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>H</mi> <mi>a</mi> <mo>≤</mo> <mn>100</mn> </mrow> </math></EquationSource> </InlineEquation>), Rayleigh number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${10}^{3}\le Ra\le {10}^{6},$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mn>3</mn> </msup> <mo>≤</mo> <mi>R</mi> <mi>a</mi> <mo>≤</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> nanoparticles volume concentration <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$(0\le \phi \le 0.04),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>≤</mo> <mi>ϕ</mi> <mo>≤</mo> <mn>0.04</mn> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> nanoparticles diameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$10 nm\le {d}_{p}\le 40 nm$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10</mn> <mi>n</mi> <mi>m</mi> <mo>≤</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>≤</mo> <mn>40</mn> <mi>n</mi> <mi>m</mi> </mrow> </math></EquationSource> </InlineEquation>, and wave numbers (1 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\le \lambda \le 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≤</mo> <mi>λ</mi> <mo>≤</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>). Streamlines and isotherms contour plots are used to display the thermal and flow behavior under various conditions. Increasing Ha shows that higher magnetic field strengths tend to suppress convective flow, thereby reducing the overall HT rate, while buoyancy forces enhance thermal transport. A higher concentration of Ag nanoparticles improves thermal conductivity and HT rate, whereas larger nanoparticle sizes reduce HT. Notably, the domain with three waves demonstrates superior HT rates compared to those with one or two waves as ϕ increases. In addition, the statistical analysis testing for the response function indicates high R2 values (95.07%), which suggests a well-suited technique for estimating the Nusselt number (average). ANN shows a good alternative for predicting response function analysis. Furthermore, this research highlights the considerable potential for advancing industrial and engineering applications by exploring fluid flow and HT in intricate domains, including wavy octagonal cavities with kerosene-Ag nanofluids.

Thermal performance investigation of blade-shaped kerosene-Ag nanofluid in a top wavy octagonal cavity using RSM and ANN

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2026年3月10日

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Tinni Saha,
Nazma Parveen,
Goutam Saha,
Md. Mohi Uddin,
Tarikul Islam

摘要

This study explores the mathematical modeling of magnetohydrodynamics (MHD) in a two-dimensional dynamic scenario involving free convection (FC) and heat transfer (HT) with entropy generation (E_gen) within a wavy octagonal cavity filled with blade-shaped kerosene-Ag nanofluids, where nanoparticles exhibit Brownian motion. The lower wall maintains uniform thermal boundary conditions (TBC), while the undulating wall remains at a cooler temperature. All other boundaries of the domain are assumed to be adiabatic. The finite element method, combined with the central composite design (CCD) based response surface method (RSM) and artificial neural networks (ANN), is used to solve nonlinear PDE problems. Various parameters are investigated, including Hartmann number ( $0\le Ha\le 100$ $0 \leq H a \leq 100$ ), Rayleigh number ${10}^{3}\le Ra\le {10}^{6},$ $10^{3} \leq R a \leq 10^{6},$ nanoparticles volume concentration $(0\le \phi \le 0.04),$ $(0 \leq ϕ \leq 0.04),$ nanoparticles diameter $10 nm\le {d}_{p}\le 40 nm$ $10 n m \leq d_{p} \leq 40 n m$ , and wave numbers (1 $\le \lambda \le 3$ $\leq λ \leq 3$ ). Streamlines and isotherms contour plots are used to display the thermal and flow behavior under various conditions. Increasing Ha shows that higher magnetic field strengths tend to suppress convective flow, thereby reducing the overall HT rate, while buoyancy forces enhance thermal transport. A higher concentration of Ag nanoparticles improves thermal conductivity and HT rate, whereas larger nanoparticle sizes reduce HT. Notably, the domain with three waves demonstrates superior HT rates compared to those with one or two waves as ϕ increases. In addition, the statistical analysis testing for the response function indicates high R² values (95.07%), which suggests a well-suited technique for estimating the Nusselt number (average). ANN shows a good alternative for predicting response function analysis. Furthermore, this research highlights the considerable potential for advancing industrial and engineering applications by exploring fluid flow and HT in intricate domains, including wavy octagonal cavities with kerosene-Ag nanofluids.