Effects of surface roughness on nonlinear convective dissipative flow of micropolar nanofluids with dual activation energies and triple diffusion

doi:10.1007/s10483-025-3294-9

Abstract

Abstract:

This study explores the complex dynamics of unsteady convective flow in micropolar nanofluids over a rough conical surface, with a focus on the effects of triple diffusive transport and Arrhenius activation energy. The primary objective is to understand the interplay among nonlinear convection, micro-rotation effects, and species diffusion under the influence of thermal and electromagnetic forces. The analysis is motivated by practical applications of cryogenic fluids, specifically liquid hydrogen and liquid nitrogen, where precise control of heat and mass transport is critical. The conical surface roughness is mathematically modeled as a high-frequency, small-amplitude sinusoidal waveform. To address the non-similar nature of the boundary-layer equations, Mangler's transformations are employed, followed by the implementation of a finite difference scheme for numerical solutions. The methodology further integrates a machine learning-based neural network to predict the skin friction under the influence of roughness-induced perturbations, ensuring computational efficiency and improved generalization. The study yields several novel findings. Notably, the presence of surface roughness introduces the wave-like modulations in the local skin friction coefficient. It is also observed that nonlinear convective interactions, enhanced by temperature gradients and vortex viscosity parameters, significantly intensify near-wall velocity gradients. Moreover, key physical quantities are correlated with governing parameters using power-law relationships, providing generalized predictive models. The validation of the numerical results is achieved through consistency checks with the existing limiting solutions and convergence analysis, ensuring the reliability of the proposed computational framework.

Key words: rough-conical surface, micropolar nanoliquid, magnetohydrodynamics (MHD), artificial neural network (ANN), finite difference method (FDM), triple mass diffusion, nonlinear convection, activation energy

2010 MSC Number:

O373

Z. Z. RASHED, S. E. AHMED. Effects of surface roughness on nonlinear convective dissipative flow of micropolar nanofluids with dual activation energies and triple diffusion. Applied Mathematics and Mechanics (English Edition), 2025, 46(9): 1809-1828.

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Figures/Tables 23

Fig. 1

Table 1

Comparisons of −θ′(ξ, 0) with the results of Huang and Yin[33] at K=βT=βC1=βC2=NT=0"

$ξ$	Present result	Huang and Yin^[33]
0	0.443 50	0.443 7
0.5	0.528 70	0.528 6
1	0.580 00	0.580 8
2	0.633 50	0.637 3
6	0.713 70	0.712 3
10	0.731 14	0.733 0
20	0.749 34	0.750 0

Table 1

Table 2

ANN analyses of the skin friction for Ri"

Unite	Initial value	Stopped value	Target value
Epoch	0	13	1 000
Performance	0.854	$9.01 × 10 − 7$	$1 × 10 − 6$
Gradient	2.14	0.000 594	$1 × 10 − 7$
Damping factor	0.001	$1 × 10 − 8$	$1 × 1010$
Validation check	0	0	6

Table 2

Table 3

ANN analyses of the skin friction for K"

Unite	Initial value	Stopped value	Target value
Epoch	0	16	1 000
Performance	21.3	$6.17 × 10 − 7$	$1 × 10 − 6$
Gradient	24.5	0.002 75	$1 × 10 − 7$
Damping factor	0.001	$1 × 10 − 8$	$1 × 1010$
Validation check	0	0	6

Table 3

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References 33

[1]	PALLARES, J. and FABREGAT, A. Numerical simulation of the particle wall mass transfer rates on rough surfaces confining turbulent natural convection flows. International Journal of Thermal Sciences, 196, 108685 (2024)
[2]	PATIL, P. M., HIREMATH, P. S., and MOMONIAT, E. Impulsive motion causes time-dependent nonlinear convective Williamson nanofluid flow across a rough conical surface: semi-similar analysis. Alexandria Engineering Journal, 74, 171–185 (2023)
[3]	XU, F., ZHONG, J., SU, J., ZHAO, B., HE, Y., SUN, C., and WANG, J. Effects of rough surfaces on annular centrifugal Rayleigh-Bénard convection. International Journal of Heat and Mass Transfer, 232, 125929 (2024)
[4]	AXCELL, B. P. and THIANPONG, C. Convection to rotating disks with rough surfaces in the presence of an axial flow. Experimental Thermal and Fluid Science, 25(1), 3–11 (2001)
[5]	ZHAN, C., CHAI, Z., and SHI, B. A two-relaxation-time lattice Boltzmann study on the Soret and Dufour effects of double-diffusive convection over a rough surface. Applied Mathematical Modelling, 106, 1–29 (2022)
[6]	AKHTER, R., ALI, M. M., BILLAH, M. M., and UDDIN, M. N. Hybrid-nanofluid mixed convection in square cavity subjected to oriented magnetic field and multiple rotating rough cylinders. Results in Engineering, 18, 101100 (2023)
[7]	VAIDYA, H., PRASAD, K. V., CHOUDHARI, R., SHETTY, J., and SHIVALEELA. A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM. Results in Physics, 64, 107939 (2024)
[8]	PATIL, P. M., SHASHIKANT, A., and HIREMATH, P. S. Influence of liquid hydrogen and nitrogen on MHD triple diffusive mixed convection nanoliquid flow in presence of surface roughness. International Journal of Hydrogen Energy, 43, 20101–20117 (2018)
[9]	PATIL, P. M., SHASHIKANT, A., HIREMATH, P. S., and MOMONIAT, E. Influence of surface roughness on multidiffusive mixed convective nanofluid flow. Physica Scripta, 94, 055201 (2019)
[10]	PATIL, P. M., SHASHIKANT, A., and HIREMATH, P. S. Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion. International Journal of Hydrogen Energy, 44, 11121–11133 (2019)
[11]	PATIL, P. M., SHASHIKANT, A., and HIREMATH, P. S. Diffusion of liquid hydrogen and oxygen in nonlinear mixed convection nanofluid flow over vertical cone. International Journal of Hydrogen Energy, 44, 17061–17071 (2019)
[12]	PATIL, P. M., SHASHIKANT, A., HIREMATH, P. S., and ROY, S. Study of liquid oxygen and hydrogen diffusive flow past a sphere with rough surface. International Journal of Hydrogen Energy, 44, 26624–26636 (2019)
[13]	PATIL, P. M., KULKARNI, M., and TONANNAVAR, J. R. A computational study of the triple-diffusive nonlinear convective nanoliquid flow over a wedge under convective boundary constraints. International Communications in Heat and Mass Transfer, 128, 105561 (2021)
[14]	PATIL, P. M., BENAWADI, S., and SHEREMET, M. A. The unsteady nonlinear convective flow of a nanofluid due to impulsive motion: triple diffusion and magnetic effects. Thermal Science and Engineering Progress, 35, 101456 (2022)
[15]	PATIL, P. M. and GOUDAR, B. Influence of activation energy on triple diffusive entropy optimized time-dependent quadratic mixed convective magnetized flow. Journal of Taibah University for Science, 16, 689–702 (2022)
[16]	ZHANG, Y., ZHANG, M., and BAI, Y. Unsteady flow and heat transfer of power-law nanofluid thin film over a stretching sheet with variable magnetic field and power-law velocity slip effect. Journal of the Taiwan Institute of Chemical Engineers, 70, 104–110 (2017)
[17]	RAMZAN, M., BILAL, M., and CHUNG, J. D. Radiative Williamson nanofluid flow over a convectively heated Riga plate with chemical reaction — a numerical approach. Chinese Journal of Physics, 55(4), 1663–1673 (2017)
[18]	USMAN, M., SOOMRO, F. A., UL HAQ, R., WANG, W., and DEFTERLI, O. Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method. International Journal of Heat and Mass Transfer, 122, 1255–1263 (2018)
[19]	WAQAS, H., IMRAN, M., and BHATTI, M. M. Influence of bioconvection on Maxwell nanofluid flow with the swimming of motile microorganisms over a vertical rotating cylinder. Chinese Journal of Physics, 68, 558–577 (2020)
[20]	AHMED, S. E. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Applied Mathematics and Mechanics (English Edition), 38(8), 1171–1180 (2017) https://doi.org/10.1007/s10483-017-2231-9
[21]	ERINGEN, A. C. Theory of thermomicrofluids. Journal of Mathematical Analysis and Applications, 38, 480–496 (1972)
[22]	ERINGEN, A. C. Simple micropolar fluids. International Journal of Engineering Science, 2, 205–217 (1964)
[23]	LUKASZEWICZ, G. Micropolar Fluids: Theory and Applications, Birkhäuser, Boston (1999)
[24]	ABBAS, N., ALI, M., SHATANAWI, W., and HASAN, F. Unsteady micropolar nanofluid flow past a variable Riga stretchable surface with variable thermal conductivity. Heliyon, 10, e23590 (2024)
[25]	PATIL, P. M., GOUDAR, B., and MOMONIAT, E. Magnetized bioconvective micropolar nanofluid flow over a wedge in the presence of oxytactic microorganisms. Case Studies in Thermal Engineering, 49, 103284 (2023)
[26]	PATIL, P. M., HIREMATH, P. S., and MOMONIAT, E. Impulsive motion causes time-dependent nonlinear convective Williamson nanofluid flow across a rough conical surface: semi-similar analysis. Alexandria Engineering Journal, 74, 171–185 (2023)
[27]	PATIL, P. M., GOUDAR, B., and SHEREMET, M. A. Tangent hyperbolic ternary hybrid nanofluid flow over a rough-yawed cylinder due to impulsive motion. Journal of Taibah University for Science, 17, 2199664 (2023)
[28]	PATIL, P. M., ROY, M., SHASHIKANT, A., ROY, S., and MOMONIAT, E. Triple diffusive mixed convection from an exponentially decreasing mainstream velocity. International Journal of Heat and Mass Transfer, 124, 298–306 (2018)
[29]	PATIL, P. M. and GOUDAR, B. Entropy generation analysis from the time-dependent quadratic combined convective flow with multiple diffusions and nonlinear thermal radiation. Chinese Journal of Chemical Engineering, 53, 46–55 (2023)
[30]	PATIL, P. M., ROY, M., ROY, S., and MOMONIAT, E. Triple diffusive mixed convection along a vertically moving surface. International Journal of Heat and Mass Transfer, 117, 287–295 (2018)
[31]	AL-HANAYA, A., RASHED, Z. Z., and AHMED, S. E. Radiative flow of temperature-dependent viscosity power-law nanofluids over a truncated cone saturated heat generating, porous media: impacts of Arrhenius energy. Case Studies in Thermal Engineering, 53, 103874 (2024)
[32]	AHMED, S. E. and ALQARNI, M. Z. Blottner finite difference analysis for non-Darcy flow of variable viscosity power-law nanofluids over a truncated cone with Arrhenius activation energy. Alexandria Engineering Journal, 86, 537–546 (2024)
[33]	HUANG, C. J. and YIH, K. A. Nonlinear radiation and variable viscosity effects on free convection of a power-law nanofluid over a truncated cone in porous media with zero nanoparticles flux and internal heat generation. Journal of Thermal Science and Engineering Applications, 13, 031020 (2021)