<p>Artificial neural networks (ANNs) are becoming more popular because they can solve complex, nonlinear mathematical problems. The complicated domains of biotechnology, fluid dynamics, and cellular computation all find applications for artificial neural networks. This study uses machine learning techniques to analyze heat transfer and entropy production in unsteady <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\text{TiO}}_{2}/\text{EG}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>TiO</mtext> <mn>2</mn> </msub> <mo stretchy="false">/</mo> <mtext>EG</mtext> </mrow> </math></EquationSource> </InlineEquation> nanofluid flow, taking into account nonlinear thermal radiation, Darcy–Forchheimer effects, and mass suction on a spinning sphere. This study examines aggregation and non-aggregation phenomena in terms of dynamic viscosity and thermal conductivity. Skin friction coefficient, heat transfer rate, entropy generation, velocity, and temperature-related nonlinear versions of classic mathematical problems may be solved using the bvp4c solver in MATLAB. Data selection, network creation, training, and performance evaluation using the mean square error metric are all part of the model's artificial neural network architecture. Tables and graphics demonstrate the impact of parameters on subjective profiles. The velocity profile in the x-direction increases with nanoparticle volume fraction <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\phi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>, unsteadiness <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$A$</EquationSource> <EquationSource Format="MATHML"><math> <mi>A</mi> </math></EquationSource> </InlineEquation>, porous media permeability <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$K,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> and magnetic parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$M$</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation>, but decreases with the Darcy–Forchheimer coefficient <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\delta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> parameter. The z-direction velocity profile declines with increasing <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\phi , A, K, M$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>,</mo> <mi>A</mi> <mo>,</mo> <mi>K</mi> <mo>,</mo> <mi>M</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\delta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>. As <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$A$</EquationSource> <EquationSource Format="MATHML"><math> <mi>A</mi> </math></EquationSource> </InlineEquation> grows, the temperature profile lowers, but bigger values of the radiation parameter, Biot number, Eckert number, and temperature ratio parameter increase. Skin friction in the x-direction increases with higher (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$K, M, \phi$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>,</mo> <mi>M</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$S$</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>) but decreases with <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\delta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>. Similarly, skin friction in the z-direction rises with higher values of <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$K, \phi , M, \delta .$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>,</mo> <mi>ϕ</mi> <mo>,</mo> <mi>M</mi> <mo>,</mo> <mi>δ</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> As <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$Ec$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Ec</mi> </mrow> </math></EquationSource> </InlineEquation> increases, the local Nusselt number decreases and rises with <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$Bi, \phi , Rd$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mi>i</mi> <mo>,</mo> <mi>ϕ</mi> <mo>,</mo> <mi>R</mi> <mi>d</mi> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq16"> <EquationSource Format="TEX">${\theta }_{w}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>θ</mi> <mi>w</mi> </msub> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> As Brinkmann numbers and radiation parameters grow, entropy production increases, showing dual behavior for the magnetic parameter.</p>

Analyzing Heat Transfer and Irreversibility via Aggregation Dynamics in Darcy-Forchheimer Flow and Nonlinear Thermal Radiation Effects Utilizing Artificial Neural Networks

期刊论文
发表日期：

2025年8月21日

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Zafar Mahmood,
Khadija Rafique,
Mushtaq Ahmad Ansari,
Naveed Ahmed,
Umar Khan,
Abhinav Kumar

摘要

Artificial neural networks (ANNs) are becoming more popular because they can solve complex, nonlinear mathematical problems. The complicated domains of biotechnology, fluid dynamics, and cellular computation all find applications for artificial neural networks. This study uses machine learning techniques to analyze heat transfer and entropy production in unsteady ${\text{TiO}}_{2}/\text{EG}$ ${TiO}_{2} / EG$ nanofluid flow, taking into account nonlinear thermal radiation, Darcy–Forchheimer effects, and mass suction on a spinning sphere. This study examines aggregation and non-aggregation phenomena in terms of dynamic viscosity and thermal conductivity. Skin friction coefficient, heat transfer rate, entropy generation, velocity, and temperature-related nonlinear versions of classic mathematical problems may be solved using the bvp4c solver in MATLAB. Data selection, network creation, training, and performance evaluation using the mean square error metric are all part of the model's artificial neural network architecture. Tables and graphics demonstrate the impact of parameters on subjective profiles. The velocity profile in the x-direction increases with nanoparticle volume fraction $\phi$ $ϕ$ , unsteadiness $A$ $A$ , porous media permeability $K,$ $K,$ and magnetic parameter $M$ $M$ , but decreases with the Darcy–Forchheimer coefficient $\delta$ $δ$ parameter. The z-direction velocity profile declines with increasing $\phi , A, K, M$ $ϕ, A, K, M$ and $\delta$ $δ$ . As $A$ $A$ grows, the temperature profile lowers, but bigger values of the radiation parameter, Biot number, Eckert number, and temperature ratio parameter increase. Skin friction in the x-direction increases with higher ( $K, M, \phi$ $K, M, ϕ$ , and $S$ $S$ ) but decreases with $\delta$ $δ$ . Similarly, skin friction in the z-direction rises with higher values of $K, \phi , M, \delta .$ $K, ϕ, M, δ .$ As $Ec$ $Ec$ increases, the local Nusselt number decreases and rises with $Bi, \phi , Rd$ $B i, ϕ, R d$ , and ${\theta }_{w}.$ $θ_{w} .$ As Brinkmann numbers and radiation parameters grow, entropy production increases, showing dual behavior for the magnetic parameter.