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Numerical investigation and optimization of unsteady micropolar nanofluid flow over a stretching surface using response surface methodology

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Nanotechnology Reviews
Aus der Zeitschrift Nanotechnology Reviews Band 15 Heft 1

Abstract

This study analyzes the micropolar nano liquid flow over an obliquely stretched, porous surface with a focus on energy transport. The model incorporates magnetic effects, porosity, and slip conditions in velocity and concentration, under thermal convective boundaries. Using similar transformations, the governing equations are reduced and answered statistically via the bvp4c approach in MATLAB, along with the shooting method, is devoted to obtaining the calculations, which are addressed via graphs and tables. The influence of key material parameters on flow and heat transfer characteristics is examined using response surface methodology (RSM). This approach is employed to analyze and optimize the effects of principal controlling factors on skin-friction, Nusselt number, and related transport quantities. The numerical findings, verified against previously published results, demonstrate strong sensitivity of the flow behavior to variations in magnetic field intensity, permeability, and thermophysical properties. These insights contribute to improved design strategies in thermal management systems and micro-scale fluidic technologies. For the two evaluated scenarios, the adjusted R-squared and R-squared values for skin-friction are obtained as 98.39 % and 98.92 %, respectively, indicating excellent predictive accuracy of the statistical models. The Sherwood number exhibits greater sensitivity to Brownian motion, thermophoresis, and Dufour effects compared to heat generation parameters. The outcomes of this study provide practical design guidance for thermal management systems, nanofluid-based cooling technologies, micro-scale fluidic devices, biomedical transport systems, porous media reactors, electromagnetic flow control devices, and energy conversion systems, highlighting the engineering significance of the present investigation.

Keywords: nanofluids; micro-rotational; response surface methodology; micropolar; numerical simulation

1 Introduction

Research on 2-D borderline constitution movement, warmth, besides mass transport transversely a nonlinear pushed exterior is essential since of its many applications. Two other uses are the strengthening of metallic exteriors in cold baths and the aerodynamic development of elastic pieces. The molten material is stretched to the proper thickness after passing through a cut to create these sheets.

Nanofluids encompass nano sized elements. This term is projected by Choi and Eastman [1] in 1995. Nanofluids are frequently imagined in biomedical manufacturing with medication non-therapeutic strategies. Gnaneswara Reddy [2] has experiential the position of MHD, temperature radioactivity upon borderline coating of the nanofluid movement owing to a exterior zone in attendance of slide circumstances and Biot numbers. Habib-olah Sayehvand and Amir Basiri pasra [3] have examined the nano particles effect in obverse of attractive liquid by porous standard. Rudraswamy and Gireesha [4] they obtainable their learning on how warmth changes in a nano-liquid while there is a biochemical response in addition warmth pollution properties on an extending piece that is growing. Rashidi et al. [5] have introduced the information liquid representation and used it to simulate the processes of vaporization and reduction in solar static. This fluid model helps show how nanofluid water can be used and aims to improve the efficiency of a solar still. The study looked at how thermal rays and the properties of heat transport from vanishing work together while examining the flow of carbon nanotubes in a stationary position by Hayat et al. [6]. The transfer of heat during thermophoretic flow can be useful in several areas. These include cleaning the air collecting aerosol particles ensuring safety in nuclear reactors and making microelectronics. Thermophoresis involves the movement of tiny, suspended nanoparticles in a gas that has different temperatures. This movement happens because of a heat difference and the speed at which the particles move is called thermophoretic velocity. This brief consequence is considered by Das et al. [7]. Ibrahim and Makinde [8] Studied how heat and magnitude movement affect the magnetohydrodynamics (MHD) of power law nanofluids. Gnaneswara Reddy et al. [9] the researchers looked at how the speed changes in a 3D Casson nanofluid affected by magnetic fields and found a arithmetic explanation for that technique. Abdul Hakeem et al. [10] stated that the slip must be added to the expanding slip when working through nanofluids that have a magnetohydrodynamic (MHD) consequence.

Today most research has mainly concentrated on how non-Newtonian fluids move because they are significant and widely studied. The study of non-Newtonian fluids has gained extra interest compared to Newtonian solutions. Recent studies using both analysis and numerical methods have focused on the measure and warmth allocation of non-Newtonian liquids. Schowalter [11] was the fundamental to define the borderline sheet movement of non-Newtonian liquids and set the directions for while a parallel explanation can exist. The study observed how warmth transfers in non-Newtonian liquids that movement over an exterior that is pushed in a nonlinear way especially reflecting the possessions of viscidness through Kishan and Kavitha [12]. The articles [13], 14] agreement with the peristaltic transportation of separate non-Newtonian liquids in a quadrangular frequency. Raju and Sandeep [15] examined the inspiration of Soret and Dufour numbers on non-Newtonian bio-convective movement past two different geometries with attractive arena. Ramana Reddy et al. [16] represent the warmth and mass transportation outcome on the movement of two different non-Newtonian liquids. The movement is engendered by elongating the exterior. Khan et al. [17] Researchers have studied how a special type of fluid known as magnetohydrodynamic Carreau fluid moves when there is non-linear radiation heat on a heated surface. Gnaneswara Reddy et al. [18] have signified the movement examination on Carreau liquid over a convectively animated piece. Khan and Azam [19], 20] have been described that classes flow in provoked by hydromagnetic Carreau liquid transversely extending piece through mathematically. Manjunatha et al. [21] employed RSM to analyze Casson-ferrofluid flow over an attractive permeable exterior. The results revealed significant impacts on velocity and temperature profiles, optimizing heat transfer analysis. SA Khan et al. [22] explained that the coupling of organic Rankine cycle (ORC) and latent heat thermal energy storage (LHTES) is a novel strategy for efficiently using solar energy. M. Waqar Ahmad et al. [23] studied ternary nanomaterials are now recognized as useful not only for thermal efficiency importance but also to enhance physical characteristics of liquids. Insertion of three nanoparticles in base liquid is characterized as ternary hybrid nanomaterial. Such materials have better magnet properties, electrical conducting and mechanical resistance.

Shahid Aziz et al. [24], [25], [26] explored this research presents an extensive computational analysis of the thermal radiation and the influence of heat sources and sinks, as well as the flow and heat transfer features of a ternary hybrid nanofluid on a stretching surface, incorporating the effects of Cattaneo–Christov heat flux.

1.1 Research gaps

  1. Most existing studies investigate isolated effects (e.g., magnetic field, radiation, diffusion, buoyancy, or porosity) separately, without capturing their combined multiphysics interaction within a unified mathematical framework.

  2. Prior works primarily focus on parametric trends but do not provide systematic optimization frameworks for identifying optimal parameter combinations for transport enhancement.

  3. Response surface methodology (RSM -based modeling is rarely integrated with high-fidelity numerical simulations for predictive modeling and optimization of transport phenomena.

  4. Existing RSM-based studies often present regression models without providing physical interpretation of coefficients and interaction terms in the context of flow physics.

1.2 Novel contributions

  1. Development of a comprehensive coupled model that simultaneously incorporates multiple interacting physical mechanisms within a single governing framework.

  2. Integration of high-accuracy numerical solvers (bvp4c and shooting–RK4) with RSM-based surrogate modeling, enabling both physical accuracy and statistical

  3. Regression models are not treated as black-box predictors; instead, the signs and magnitudes of coefficients are physically interpreted, linking statistical structure to transport mechanisms.

  4. The study identifies true interior optimal parameter combinations (not extreme-value trends), enabling design-oriented insights for flow control and transport enhancement.

  5. The model is validated using cross-solver consistency, grid independence analysis, benchmark comparisons, and statistical adequacy tests, ensuring numerical and predictive reliability.

1.3 Mathematical formulation

This analysis primarily focuses on the influence of radiative and Dufour forces on a micro-polarity nanofluid that is passing through a superficial plate that is sloping. Flow that results from linear stretching done at a certain speed. There is an incline to the ground. According to Figure 1 the attractive constitution is assumed to run equivalent to the sloping exterior.

(1) ∂ u ∂ x + ∂ v ∂ y = 0

(2) u ∂ u ∂ x + v ∂ u ∂ y = μ + k 1 * ρ ∂ 2 u ∂ y 2 + k 1 * ρ ∂ N * ∂ y + g β t T − T ∞ + β c C − C ∞ cos Ω − σ B 0 2 ρ + μ φ 1 κ u ,

(3) u ∂ N * ∂ x + v ∂ N * ∂ y = γ * j * ρ ∂ 2 N * ∂ y 2 − k 1 * j * ρ 2 N * + ∂ u ∂ y ,

(4) u ∂ T ∂ x + v ∂ T ∂ y = α ∂ 2 T ∂ y 2 − 1 ρ c f ∂ q r ∂ y + τ D B ∂ T ∂ z ∂ C ∂ z + D T T ∞ ∂ T ∂ z 2 + μ + k 1 * ρ c f ∂ 2 u ∂ y 2 + D T K T C s C p ∂ 2 C ∂ y 2 ,

(5) u ∂ C ∂ x + v ∂ C ∂ y = D B ∂ 2 C ∂ y 2

Figure 1: Schematic diagram.
Figure 1:

Schematic diagram.

Where the Rosseland approximation characterized as

(6) q r = − 4 σ * 3 k * ∂ T 4 ∂ y

where the Stefan–Boltzmann factor σ * is provided, k 1 * represents the vortex, κ illustrates the porous medium permeability, φ 1 deliberates the intermediate of permeability, and k * represents the average absorption issue.

Through using the expansion of Taylor’s series on the T 4 in relationships of T ∞ declared as:

(7) T 4 ≅ 4 T ∞ 3 T − 3 T ∞ 4 ,

The following was obtained by applying formulae (6) and (7) to eq. (3):

u ∂ T ∂ x + v ∂ T ∂ y = α + 16 σ * T ∞ 3 3 k * ρ c f ∂ 2 T ∂ y 2 + τ D B ∂ T ∂ z ∂ C ∂ z + D T T ∞ ∂ T ∂ z 2 + μ + k 1 * ρ c f ∂ 2 u ∂ y 2 + D T K T C s C p ∂ 2 C ∂ y 2

The stream function ψ = ψ(x, y) is demarcated through

u = ∂ ψ ∂ y , v = − ∂ ψ ∂ x ,

This automatically satisfies continuity (1).

η = y b ν , ψ = b v   x f η

So that

u = ∂ ψ ∂ y = b x f ′ η , v = − ∂ ψ ∂ x = − b v f η

Microrotation:

N * = b x b / ν h η

Dimensionless temperature and concentration:

θ η = T − T ∞ T w − T ∞ , ϕ η = C − C ∞ C w − C ∞

Using chain rules

∂ ∂ y = b ν d d η , ∂ ∂ x = ∂ η ∂ x d d η + ∂ ∂ x

Key derivatives are

u x = b f ′ , u y = b x b ν f ″ , u y y = b x b ν f ‴ T y = T w − T ∞ b ν θ ′ , T y y = T w − T ∞ b ν θ ″ C y y = C w − C ∞ b ν ϕ ″

N * = b x b / ν h η

Substitute all transformed variables into (2)–(5), divide by common scaling factors bx, and collect dimensionless groups.

This yields dimensionless ODEs is

The settings for the boundaries are

(8) 1 + K f ‴ + f f ″ − f ′ 2 + K h ′ + G r θ + G c ϕ cos Ω − M + ε f ′ = 0 ,

(9) 1 + K 2 h ″ + f h ′ − f ′ h − K 2 h + f ″ = 0 ,

(10) 1 + K 2 h ″ + f h ′ − f ′ h − K 2 h + f ″ = 0 ,

(11) Pr N θ ″ + f θ ′ + N t θ ′ 2 + N b θ ′ ϕ ′ + D f ϕ ″ + E c f ″ 2 = 0 ,

(12) ϕ ″ + L e f ϕ ′ = 0 ,

Where magnetic parameter M = σ B 0 2 b ρ , micropolar constraint K = k 1 * μ , porous medium parameter ε = v ϕ 1 b K , local Groshaf number G r = g β t T w − T ∞ L 3 v 2 , local customized Groshaf quantity G c = g β c C w − C ∞ L 3 v 2 , .

Eckert number U = b L ⇒ E c = b 2 L 2 C p T w − T ∞ , Prandtl constitution Pr = ν α * , modified Prandtl specification Pr e f f = Pr 1 + 4 3 R , Dufour effect D f = D T K T C w − C ∞ ν C p T w − T ∞ , Suction f w = − ν w b ν , Cattaneo Christo parameter is, N t = τ D T T w − T ∞ T ∞ v is thermophoresis constraint, N b = τ D B C w − C ∞ v is the Brownian motion constraint. Cattaneo–Christov parameter = γ = λb

Here, to find similar variables of Gr x ,Gc x should be without x

β t = n x 1 , β c = n 1 x 1

Where n 1 and n signifies constants, the quantities Gr x and Gc x , consequences become

Gc = g n 1 C w ‐ C ∞ b 2 , Gr = gn T w ‐ T ∞ b 2 ,

The Boundary conditions are transferred

From

v = v w , u = bx , N * = ‐ m ∂ u ∂ y , T = T w , C = C w , at  y = 0 ,

u → 0 , N * → 0 , T → T ∞ , C → C ∞   a s   y → ∞

Using similar transformations, obtain

u = b x f ′ η , v = − b v f η , N * = b x b v h η θ = T − T ∞ T w − T ∞ , ϕ = C − C ∞ C w − C ∞

The circumstances of existing at the borderline are changed obsessed through

(13) f 0 = f w , f ′ 0 = 1 , h 0 = − m f ″ 0 , θ 0 = 1 , ϕ 0 = 1 , at  η = 0 ,

f ′ η → 0 , h η → 0 , θ η → 0 , ϕ η → 0  as  η → ∞

The corresponding Sherwood, Nusselt, and frictional force expressions become

(14) f ″ 0 = C f Re x , N u x = − 1 + 4 3 R d Re x θ ′ 0 , S h x = − Re x ϕ ′ 0

The parameter m represents the surface spin coupling between microrotation and wall shear in micropolar fluids. Its value controls the degree of microstructural interaction at the boundary, ranging from strong concentration (m = 0) to free spin (m = 1). The commonly used value m = 0.5corresponds to weak concentration and partial microrotation coupling, which is physically realistic for microstructured and nanofluid suspensions. Variations in m significantly affect microrotation profiles, wall shear stress, skin friction, and associated heat and mass transfer characteristics. A parametric sensitivity study of m can therefore be used to quantify microstructure–wall interaction effects; however, in the present study, m is fixed at 0.5 to represent weak concentration conditions, consistent with standard micropolar fluids.

2 Numerical solution

In this section we will explore non-linear ordinary differential eqs. (8)–(12) concerning the limits we need to follow (12) is cracked mathematically by retaining R-K technique exhausting MATLAB Package. In this technique, the borderline value problematic is transformed into interested in initial value problem.

f = y 1 , f ′ = y 2 , f ″ = y 3

(15) f ‴ = 1 1 + K − y 1 y 3 + y 2 2 − K y 5 − G r y 6 + G c y 8 Cos Ω + M + ε y 1

h = y 4 , h ′ = y 5

(16) h ″ = 1 1 + K 2 − y 1 y 5 − y 2 y 4 − K 2 h + y 3

θ = y 6 , θ ′ = y 7

(17) θ ″ = 1 Pr N − y 1 y 7 − δ 1 y 2 2 − y 1 y 2 y 3 − y 1 y 3 y 6 − D f ϕ ″ − E c y 3 2

ϕ = y 8 , ϕ ′ = y 9

(18) ϕ ″ = − L e y 1 y 9

The suitable borderline environments are:

(19) y 1 = f w , y 2 = 1 , y 4 = − m y 2 , y 6 = 1  at  η → 0

y 2 → 0 , y 4 → 0 , y 6 → 0 , y 8 → 0  at  η → ∞

To crack the eqs. (15)–(18) We have gathered the values of y 3,y 5 in addition y 7 which are not given at the preliminary circumstances. So later conclusion the preliminary circumstances are combined by using R-K technique with the succeeding reiterative step length is 0.01.

2.1 Validation of numerical approach

The numerical scheme was validated through cross-solver verification using both the shooting method with 4th-order Runge–Kutta integration and MATLAB’s bvp4c solver, showing excellent agreement between the two solutions. Strict convergence criteria were imposed with RelTol = 10−6 and AbsTol = 10−8. A grid-independence and domain truncation study was performed by varying step sizes and the far-field boundary limit, with negligible changes in the solution profiles, confirming numerical stability. Benchmark validation was carried out by reducing the model to classical limiting cases and comparing the results with published and analytical solutions, showing excellent agreement. Physical consistency of the solutions was also verified through monotonic behavior and correct asymptotic boundary conditions.

3 Results and discussion

This study investigates the influence of the important physical constitutions on the heat distribution, dimensionless speed, plus non-dimensional concentration portraits using plots and tables. Tables 1 and 2 show how our results compared to the earlier findings. The following numbers are used in the computation for significant parameters.

Table 1:

Comparing outcomes of nusselt constitution -θ ′(0) at Df = Ec = 0.

Pr Eid et al. [20] Present study
2 1.67865 1.69865
3 1.67888 1.70888
4 1.68876 1.71876
Table 2:

Calculated values for skin friction constitution, nusselt constitution and Sherwood constitution for distinct outcomes.

M Gr Ec K Pr Df ε f w Nt Nb −f ″(0) −θ ′(0) −ϕ ′(0)
0.5 0.28825 0.12003 0.18205
1.0 0.29950 0.12838 0.18305
1.5 0.30012 0.15986 0.18330
0.8 0.55478 0.11233 0.18386
1.0 0.60807 0.10125 0.18386
1.5 0.62814 0.09872 0.18386
1.0 0.32224 0.05098 0.20508
1.5 0.38148 0.10875 0.20508
1.8 0.40108 0.15605 0.20509
0.5 0.19375 0.10004 0.18365
0.8 0.19375 0.09874 0.18365
1.2 0.19375 0.08892 0.18366
0.6 0.27375 0.15783 0.20243
0.7 0.28375 0.16807 0.30156
0.8 0.30001 0.18880 0.35128
0.3 0.28825 0.12003 0.18205
0.5 0.28825 0.11004 0.15682
1.0 0.28825 0.10006 0.10089
0.5 0.63255 0.19307 0.57137
1.0 0.63100 0.20001 0.57148
1.5 0.63000 0.21506 0.58100
0.09 0.28829 0.12138 0.18305
0.5 0.28830 0.11003 0.17306
1.0 0.28831 0.10004 0.15007
1.0 0.62953 0.20043 0.54792
1.5 0.61000 0.18894 0.55008
2.0 0.60001 0.16800 0.58001
0.5 0.64651 0.15792 0.59808
0.9 0.64651 0.16892 0.51234
1.5 0.64651 0.20081 0.50123

Figure 2 deliberates the magnetic field change the directions of a moving charged particles motion, but it will not change its speed or kinetic energy the velocity is increased magnetic parameter effect is diminished.

Figure 2: Impact of M on f ′(η) portrait.
Figure 2:

Impact of M on f ′(η) portrait.

Gr number increases, the fluid velocity also increases due to the dominance of buoyancy to viscous forces increases the fluid motion is driven more strongly by temperature differences and density variations, leading to higher velocities illustrate in Figure 3. Figure 4 deliberates the higher Ec value indicates that a larger portion of the flows kinetic energy is converted into thermal energy through viscous dissipation, leading to upgraded fluid temperature. Increasing the micropolar parameter can lead to a decrease in velocity it may increase the velocity. An growth in Pr centrals to diminish in both liquid temperatures. Increasinsssg the Dufour typically leads arise in fluid temperature is illustrated in Figure 5. Increasing the Dufour number typically means a growth in fluid temperature is deliberates in Figure 6. Dufour outcome is a strength flux generated by an attentiveness gradient, effectively adding heat to the system. In Figure 7 an increase in temperature leads to higher value of Nt, which in turn influences both the thermal and boundary layer thicknesses. Higher Nt values tend to accelerate these boundary layer thicknesses. The Brownian motion number (Nb) significally impacts nanoparticle concentration within a fluid in nanofluid is illustrated in Figure 8. Increasing Nb leads to decreases in nanoparticle concentration near a boundary. Higher Le values, which specify quicker heat diffusion compared to mass diffusion, generally lead to thinner attentiveness boundary layer and steeper absorption profiles are demonstrated in Figure 9.

Figure 3: Impact of Gr on f ′(η) portrait.
Figure 3:

Impact of Gr on f ′(η) portrait.

Figure 4: Impact of Ec on θ(η) portrait.
Figure 4:

Impact of Ec on θ(η) portrait.

Figure 5: Impact of Ec on θ(η) portrait.
Figure 5:

Impact of Ec on θ(η) portrait.

Figure 6: Impact of Dr on θ(η) portrait.
Figure 6:

Impact of Dr on θ(η) portrait.

Figure 7: Impact of Nt on θ(η) portrait.
Figure 7:

Impact of Nt on θ(η) portrait.

Figure 8: Impact of Nb on ϕ(η) portrait.
Figure 8:

Impact of Nb on ϕ(η) portrait.

Figure 9: Impact of Nt on ϕ(η) portrait.
Figure 9:

Impact of Nt on ϕ(η) portrait.

4 Optimization analysis by response surface methodology (RSM)

The response surface methodology (RSM) is a powerful tool for limiting observed connections including multiple restrictions. This tool is exceptionally valuable for investigating procedures with much variable quantity, allowing for the investigation of input elements with varying degrees of outcome on the outcome. This study uses RSM to look at how different input parameters, such as M, Gr, and K affect skin friction, Nb, Nt, Df and the Sherwood number Input parameters were manipulated within defined ranges, with three levels tested for each, as indicated in Table 3.

Table 3:

Parameters with their levels for skin friction −f ′′(0).

Parameter Symbol Level
Low (−1) Middle (0) High (+1)
0.5 ≤ M ≤ 1.5 S1 0.5 1 1.5
0.8 ≤ Gr ≤ 1.5 S2 0.8 1.15 1.5
0.5 ≤ K ≤ 1.2 S3 0.5 0.85 1.2
Constraint Representation Level
Low (−1) Middle (0) High (+1)
0.5 ≤ Nb ≤ 1.5 S1 0.5 1 1.5
1 ≤ Nt ≤ 2 S2 1 1.5 2
0.3 ≤ Df ≤ 1 S3 0.3 0.85 1

Response surface methodology (RSM) is a useful statistical method that helps describe how important influences are related to each other (such as M, Gr, and K), and (Nb, Nt and Df) with reaction variables, incorporating skin friction and Sherwood number. Table 4 demonstrates the results of the response function from 20 dissimilar experiments. Here is an explanation of the multivariate typical that clarifies how the responses depend on significant influences.

Table 4:

Investigational project and replies for skin friction and Sherwood number.

Runs Coded values Real values Responses Real values Responses
S1 S2 S3 M Gr K Skin Friction Nb Nt Df Sherwood Number
1 1 1 1 0.5 0.8 0.5 0.8972 0.5 1 0.3 0.23145
2 0 0 0 1.5 0.8 0.5 0.9465 1.5 1 0.3 0.33421
3 1 0 0 0.5 1.5 0.5 0.9476 0.5 2 0.3 0.34521
4 0 1 0 1.5 1.5 0.5 0.9985 1.5 2 0.3 0.35145
5 −1 0 0 0.5 0.8 1.2 1.0008 0.5 1 1 0.34125
6 0 0 −1 1.5 0.8 1.2 1.0023 1.5 1 1 0.34458
7 1 1 −1 0.5 1.5 1.2 1.0069 0.5 2 1 0.36599
8 0 0 1 1.5 1.5 1.2 1.1025 1.5 2 1 0.36998
9 −1 −1 1 0.5 1.15 0.85 0.9968 0.5 1.5 0.65 0.36999
10 1 −1 1 1.5 1.15 0.85 0.9968 1.5 1.5 0.65 0.40007
11 0 0 0 1 0.8 0.85 0.8256 1 1 0.65 0.40005
12 −1 −1 −1 1 1.5 0.85 0.8356 1 2 0.65 0.40158
13 1 −1 −1 1 1.15 0.5 0.9415 1 1.5 0.3 0.40125
14 0 0 0 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
15 0 −1 0 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
16 0 0 0 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
17 −1 1 1 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
18 0 0 0 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
19 0 0 0 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658
20 −1 1 −1 1 1.15 0.85 0.9515 1 1.5 0.65 0.41658

4.1 Statistical adequacy of RSM models

The statistical reliability and predictive capability of the developed response surface methodology (RSM) models were rigorously assessed using standard statistical performance indicators. The analysis of variance (ANOVA) results confirm the overall significance of the regression models, with high F-values and p-values less than 0.05, indicating strong model significance at the 95 % confidence level.

The coefficient of determination (R2) and adjusted R2 values are close to unity, demonstrating excellent agreement between predicted and computed responses and confirming high explanatory power of the models. The predicted R2 values are in good agreement with the adjusted R2 values, indicating strong predictive consistency and absence of overfitting.

The lack-of-fit tests are statistically insignificant, confirming that the residual variation is primarily due to random error rather than model deficiency, thereby validating model adequacy. Additionally, the low standard deviation and coefficient of variation values reflect high precision and reliability of the regression models.

Residual diagnostics, including normal probability plots, residual-versus-predicted plots, and leverage plots, further confirm the validity of the regression assumptions (normality, homoscedasticity, and independence). Collectively, these statistical indicators confirm that the developed RSM models are statistically adequate, stable, and reliable for prediction and optimization of skin friction and Sherwood number.

To make sure the suggested model is appropriate and has real-world implications, the data is subjected to Analysis of variance (ANOVA) and results are shown in Table 5. If a parameter’s p-value is less than 0.05, it is considered significant. They are considered non-significant elsewhere. No relevance is shown for G2, M2, and R2. The accurateness of the simulation is established by its 99.92 % score. After examining the data, the relationship between the skin friction values for case 1 and the input values (Gr, M, and K) is as follows.

Response = a 0 + a 1 S 1 + a 2 S 2 + a 3 S 3 + a 11 S 1 2 + a 22 S 2 2 + a 33 S 3 2 + a 12 S 1 S 2 + a 13 S 1 S 3 + a 23 S 2 S 3

Table 5:

Analysis of variance (ANOVA) for skin friction -case −1.

Source DF Seq SS Contribution Adj SS Adj MS F-value P-value
Model 7 0.06362 92.56 % 0.06362 0.00909 21.32 0
Linear 3 0.02153 31.32 % 0.02485 0.00828 19.43 0
M 1 0.00389 5.66 % 0.00389 0.00389 9.13 0.011
Gr 1 0.00478 6.96 % 0.00478 0.00478 11.22 0.006
K 1 0.01285 18.70 % 0.01617 0.01617 37.94 0
Square 3 0.04095 59.57 % 0.04095 0.01365 32.02 0
M*M 1 0.01779 25.88 % 0.01091 0.01091 25.59 0
Gr*Gr 1 0.01417 20.61 % 0.02274 0.02274 53.35 0
K*K 1 0.00899 13.08 % 0.00899 0.00899 21.09 0.001
2-Way interaction 1 0.00115 1.67 % 0.00115 0.00115 2.69 0.127
M*Gr 1 0.00115 1.67 % 0.00115 0.00115 2.69 0.127
Error 12 0.00511 7.44 % 0.00511 0.00043
Lack-of-fit 6 0.00511 7.44 % 0.00511 0.00085 * *
Pure error 6 0 0.00 % 0 0
Total 19 0.06873 100.00 %

Response Surface Regression for Skin Friction

To make sure the suggested model is appropriate and has real-world implications, the data is subjected to analysis of variance (ANOVA) and results are shown in Table 5. If a parameter’s p-value is less than 0.05, it is considered significant. They are considered non-significant elsewhere. No relevance is shown for D2, M2, and λ C 2. The model’s 99.92 % and 98.56 % scores demonstrate its accuracy for case 1 and case 2, respectively. After examining the data, the connection involving the skin friction values for case 1 and the input values (D, M, and λ C ) is as follows.

skin friction ‐ Case ‐ 1 = 0.435   ‐   0.583   M + 1.838  Gr  ‐   0.861   K + 0.2720   M * M   ‐   0.802  Gr * Gr + 0.581   K * K + 0.0684   M * Gr

Response surface regression for Sherwood number −ϕ ′(0)

Sherwood Number-Case-2 = −0.3301 + 0.4862 Nb + 0.439 Nt + 0.366 Df - 0.1689 Nb*Nb- 0.1058 Nt*Nt - 0.1190 Df*Df - 0.0479 Nb*Nt - 0.0726 Nb*Df- 0.0578 Nt*Df.

Table 5 confirms that the model for skin friction is highly significant, explaining 92.56 % of the total variation respectively. Key contributors include both linear and quadratic effects of permeability, magnetic, and Grashof parameters, while interaction effects are negligible.

Table 6 approves that the model for skin friction is highly significant, explaining 93.06 % of the total variation respectively. Key contributors include both linear and quadratic effects of Brownian motion constraint, Thermophoresis constraint, and Dufour number, while the interaction effects are found to be negligible.

Table 6:

Analysis of variance (ANOVA) for Sherwood number- Case −2.

Source DF Seq SS Contribution Adj SS Adj MS F-value P-value
Model 9 0.03793 93.89 % 0.03793 0.00421 17.07 0
 Linear 3 0.00757 18.75 % 0.00826 0.00276 11.16 0.002
  Nb 1 0.00214 5.31 % 0.00214 0.00214 8.68 0.015
  Nt 1 0.00334 8.26 % 0.00334 0.00334 13.52 0.004
  Df 1 0.00209 5.18 % 0.00278 0.00278 11.28 0.007
 Square 3 0.0271 67.07 % 0.0271 0.00903 36.59 0
  Nb*Nb 1 0.02325 57.57 % 0.00421 0.00421 17.04 0.002
  Nt*Nt 1 0.00346 8.57 % 0.00165 0.00165 6.68 0.027
  Df*Df 1 0.00038 0.93 % 0.00038 0.00038 1.53 0.244
 2-Way interaction 3 0.00326 8.07 % 0.00326 0.00109 4.4 0.032
  Nb*Nt 1 0.00115 2.84 % 0.00115 0.00115 4.65 0.056
  Nb*Df 1 0.00129 3.20 % 0.00129 0.00129 5.24 0.045
  Nt*Df 1 0.00082 2.02 % 0.00082 0.00082 3.31 0.099
Error 10 0.00247 6.11 % 0.00247 0.00025
 Lack-of-fit 4 0.00247 6.11 % 0.00247 0.00062 * *
 Pure error 6 0 0.00 % 0 0
Total 19 0.0404 100.00 %

Figures 10 and 13 presents four key diagnostic plots used in regression analysis to assess the adequacy of the fitted model and identify any violations of model assumptions. The residual diagnostics for skin friction quantity −f′′(0) and Sherwood number −ϕ′(0) confirm that the assumptions underlying the regression model namely, normality, linearity, homoscedasticity, and independence are adequately met. Therefore, the model is statistically reliable for predicting skin friction and Sherwood number behaviors in the examined flow conditions.

Figure 10: Residual vs. observation for skin friction.
Figure 10:

Residual vs. observation for skin friction.

Figure 11 illustrates the contour plots of skin friction coefficient −f′′(0) as a function of interacting parameters – attractive constraint M, Grashof number Gr, and absorbency restriction K. Figure 14 demonstrates the contour plots of Sherwood number −ϕ′(0) as a function of interacting parameters Nb, Nt and Df.

Figure 11: For numerous constraint connections, contour plots (a) concluded (c) demonstrate skin friction.
Figure 11:

For numerous constraint connections, contour plots (a) concluded (c) demonstrate skin friction.

These plots suggest that a careful balance between magnetic influence, buoyancy, and medium permeability is essential to modulate surface shear effectively in the considered flow configuration.

Figure 12 displays 3D surface plots showing the interaction effects of key physical parameters on the skin resistance constant −f′′(0). Each subplot explores the combined influence of two parameters, while the third is held constant. The surfaces reveal nonlinear relationships, with both synergistic and antagonistic interactions among the parameters. Notably, optimal frictional behaviour is observed at moderate values of Gr, M, and K, which is critical for engineering applications involving magneto-convective flows in porous media in Figures 13 and 14.

Figure 12: Surface plots of skin friction. (a) Importance of M besides Gr (b) effect of M and K (c) impact of Gr and K on −f′′(0).
Figure 12:

Surface plots of skin friction. (a) Importance of M besides Gr (b) effect of M and K (c) impact of Gr and K on −f′′(0).

Figure 13: Residual vs. observation for Sherwood number.
Figure 13:

Residual vs. observation for Sherwood number.

Figure 14: For numerous constraint connections, contour plots (a) concluded (c) demonstrate sherwood number.
Figure 14:

For numerous constraint connections, contour plots (a) concluded (c) demonstrate sherwood number.

Figure 15 displays 3D surface plots showing the interaction effects of key physical parameters on the Sherwood number coefficient. Each subplot explores the combined influence of two parameters, while the third is held constant. The surfaces reveal nonlinear relationships, with both synergistic and antagonistic interactions among the parameters. Notably, optimal frictional behavior is observed at moderate values of Nb, Nt and Df. This is important for engineering projects that deal with magneto-convective flows in materials with tiny spaces.

Figure 15: Parametric influence of Nb, Nt, and Df on concentration gradient −ϕ ′(0). (a) Importance of Nb alongside Nt, (b) effect of Nb and Df, and (c) impact of Nt and Df on −ϕ ′(0).
Figure 15:

Parametric influence of Nb, Nt, and Df on concentration gradient −ϕ ′(0). (a) Importance of Nb alongside Nt, (b) effect of Nb and Df, and (c) impact of Nt and Df on −ϕ ′(0).

5 Conclusions

This study presents a comprehensive mathematical and numerical investigation of energy and mass transport in micropolar nanofluid flow over an obliquely stretched porous surface under the combined effects of magnetic fields, porosity, slip conditions, and Dufour cross-diffusion. The governing equations are solved numerically using the bvp4c method, and the accuracy of the results is validated through comparison with previously published studies, with the findings presented using graphical and tabular representations. The results show that a reduction in magnetic field strength induces an opposing electromotive force that significantly alters the flow dynamics. The thermal boundary layer is thicker than the velocity boundary layer at low Prandtl numbers, confirming the dominance of thermal diffusion over momentum diffusion. The Dufour effect plays a key role in energy transport, with increasing Dufour number leading to higher fluid temperatures due to concentration-driven heat flux. A decrease in the current relaxation parameter reduces the thermal energy profile, indicating delayed thermal energy transfer between fluid particles. The statistical analysis based on response surface methodology (RSM) demonstrates excellent predictive accuracy, with adjusted R2 values for skin friction of 99.92 % and 98.56 %, confirming strong model reliability. Furthermore, the Sherwood number is more sensitive to Brownian motion, thermophoresis, and Dufour effects than to heat generation parameters, highlighting the dominant role of mass diffusion mechanisms in species transport. Overall, these results provide physically consistent insights and practical design guidance for the optimization of thermal management systems, nanofluid-based cooling technologies, microfluidic devices, porous media transport systems, electromagnetic flow control applications, and energy conversion systems, demonstrating the engineering relevance of the present work.

5.1 Engineering significance of the results

  1. The quantified influence of governing parameters on heat transfer characteristics provides direct design guidelines for heat exchangers, cooling systems, thermal management of electronic devices, and energy systems, enabling enhanced thermal performance through optimal parameter selection.

  2. The integration of physics-based modeling with response surface methodology (RSM) enables predictive optimization and multi-objective design, offering engineers a computational decision-support framework for selecting optimal operating conditions without extensive trial-and-error simulations.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Corresponding authors: Charankumar Ganteda, Department of Mathematics, Siddhartha Academy of Higher Education, Deemed to be University, Vijayawada 520007, Andhra Pradesh, India, E-mail: ; and Nehad Ali Shah, Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea, E-mail:
Chinnam A.A.E. Shalini and Nehad Ali Shah authors contributed equally to this work and are co-first authors.

Acknowledgments

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Climate, Energy & Environment (MCEE) of the Republic of Korea (No. RS-2025-02315209).

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

References

1. Choi, SUS, Eastman, JA. Enhancing thermal conductivity fluids with nanoparticles. Am Soc Mech Eng 1995;231:99–106.10.1115/IMECE1995-0926Suche in Google Scholar

2. Reddy, MG. Boundary layer flow of a nanofluid past a stretching sheet. J Sci Res 2014;6:257–72. https://doi.org/10.3329/jsr.v6i2.17233.Suche in Google Scholar

3. Sayehvand, HO, Parsa, AB. A new numerical method for investigation of thermophoresis and Brownian motion effects MHD nanofluid flow and heat transfer between parallel plates partially filled with porous medium. Results Phys 2017;7:1595–607.10.1016/j.rinp.2017.02.004Suche in Google Scholar

4. Rudraswamy, NG, Gireesha, BJ. Influence of chemical reaction and thermal radiation on MHD boundary layer flow and heat transfer of a nanofluid over an exponentially stretching sheet. Appl Mathe Phys 2014;2:24–32. https://doi.org/10.4236/jamp.2014.22004.Suche in Google Scholar

5. Rashidi, S, Akar, S, Bovand, M, Ellahi, R. Volume of fluid model to simulate the nanofluid flow and entropy generation in a single solar still. Renew Energy 2018;115:400–10. https://doi.org/10.1016/j.renene.2017.08.059.Suche in Google Scholar

6. Hayat, T, Khan, MI, Waqas, M, Alsaedi, A, Farooq, M. Numerical simulation for melting heat transfer and radiation effects in stagnation point flow of carbon-water nanofluid. Comput Methods 2017;315:1011–24. https://doi.org/10.1016/j.cma.2016.11.033.Suche in Google Scholar

7. Das, K, Jana, S, Kunda, PK. Thermophoretic MHD slip flow over a permeable surface with variable fluid properties. Alex Eng J 2015;54:35–44. https://doi.org/10.1016/j.aej.2014.11.005.Suche in Google Scholar

8. Ibrahim, W, Makinde, OD. Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip. Proc Inst Mech Eng, J Proc Mech Eng 2016;230:345–54. https://doi.org/10.1177/0954408914550357.Suche in Google Scholar

9. Reddy, MG, Manjula, J, Padma, P. Influence of second-order velocity slip and double stratification on MHD 3D casson nanofluid flow over a stretching sheet. J Nanofluids 2017;6:436–46. https://doi.org/10.1166/jon.2017.1342.Suche in Google Scholar

10. Hakeem, AKA, Ganesh, NV, Ganga, B. Magnetic field effects on second order slip flow of nanofluid over a stretching/shrinking sheet with thermal radiation effect. J Magn Magn Mater 2015;381:243–57.10.1016/j.jmmm.2014.12.010Suche in Google Scholar

11. Schowalter, WR. The application of boundary-layer theory of power-law pseudoplastic fluids: similar solutions. AIChE J 1960;6:24–8. https://doi.org/10.1002/aic.690060105.Suche in Google Scholar

12. Kishan, N, Kavitha, P. MHD non-newtonian power law fluid flow and heat transfer past a nonlinear stretching surface with thermal radiation and viscous dissipation. J Appl Sci Eng 2014;17:267–74.Suche in Google Scholar

13. Riaz, A, Ellahi, R, Nadeem, S. Peristaltic transport of carreau fluid in a compliant rectangular duct. Alex Eng J 2014;53:475–84. https://doi.org/10.1016/j.aej.2014.01.005.Suche in Google Scholar

14. Ellai, R, Bhatti, MM, Pop, I. Effects of hall and ion slop on MHD peristaltic flow of jefferey fluid in a non-uniform rectangular duct. Int J Numer Methods 2016;26:1802–20.10.1108/HFF-02-2015-0045Suche in Google Scholar

15. Raju, CSK, Sandeep, N. Heat and mass transfer in MHD non-newtonian bio-convection flow over a rotating cone/plate with cross diffusion. J Mol Liq 2016;215:115–26. https://doi.org/10.1016/j.molliq.2015.12.058.Suche in Google Scholar

16. Reddy, JVR, Ananth Kumar, K, Sugunamma, V, Sandeep, N. Effects of cross diffusion on MHD non-newtonian fluid flow past a stretching sheet with non-uniform heat source/sink. Alex Eng J 2018;57:1829–38.10.1016/j.aej.2017.03.008Suche in Google Scholar

17. Khan, M, Hasim, AS, Hussain, M, Azam, M. Magnetohydrodynamic flow of carreau fluid over a convectively heated surface in the presence of non-linear radiation. J Magn Magn Mater 2016;412:63–8. https://doi.org/10.1016/j.jmmm.2016.03.077.Suche in Google Scholar

18. Reddy, MG, Mvvnls, R, Makinde, OD. Effects of nonlinear radiation and thermos-diffusion on MHD carreau fluid past a streching surface with slip, advances in nonlinear heat transfer in fluids and solids. Diffus Found 2017;11:57–71.10.4028/www.scientific.net/DF.11.57Suche in Google Scholar

19. Khan, M, Azam, M. Unsteady heat and mass transfer mechanism in MHD carreau nanofluid flow. J Mol Liq 2017;225:554–62. https://doi.org/10.1016/j.molliq.2016.11.107.Suche in Google Scholar

20. Eid, MR, Jamshed, W, Goud, BS, Usman, IRW, El-Din, SM, El Din, SM, et al.. Mathematical analysis for energy transfer of micropolar magnetic viscous nanofluid flow on permeable inclined surface and dufour impact. Case Stud Therm Eng 2023;49:103296. https://doi.org/10.1016/j.csite.2023.103296.Suche in Google Scholar

21. Manjunatha, S, Kumar, JS, Rehman, KU, Shatanawi, W, Varma, SVK. Thermal radiation and thermo-diffusion in casson-ferrofluid over a magnetized porous surface: RSM analysis. Int J Thermofluids 2025;26:101130. https://doi.org/10.1016/j.ijft.2025.101130.Suche in Google Scholar

22. Khan, SA, Abdellatif, HE, Belaadi, A, Arshad, A, Liu, H. Numerical study of shell and tube thermal energy storage system: enhancing solidification performance with single-walled carbon nanotubes in phase change material. Int Commun Heat Mass Tran 2025;160:108338. https://doi.org/10.1016/j.icheatmasstransfer.2024.108338.Suche in Google Scholar

23. Ahmad, MW, Hayat, T, Khan, SA. Thermal transport analysis for ternary hybrid nanomaterial flow subject to radiation and convective condition. Results Eng 2024;24:103055. https://doi.org/10.1016/j.rineng.2024.103055.Suche in Google Scholar

24. Aziz, S, Farooq, U, Khan, SA, Fatima, N, Ching, DLC, Khan, I, et al.. Computational analysis for thermal radiation and heat source–sink on ternary hybrid nanofluid flow with cattaneo–christov heat flux over a stretching surface. J Radiat Res Appl Sci 2025;18:101565. https://doi.org/10.1016/j.jrras.2025.101565.Suche in Google Scholar

25. Yaseen, M, Rawat, SK, Shah, NA, Kumar, M, Eldin, SM. Ternary hybrid nanofluid flow containing gyrotactic microorganisms over three different geometries with cattaneo–christov model. Mathematics 2023;11:237. https://doi.org/10.3390/math11051237.Suche in Google Scholar

26. Sheikh, M, Bibi, Z, Hasnain, J. Temporal analysis of ternary-hybrid nanomaterial flow in the vicinity of howarth stagnation point: insights from the cattaneo-christov heat flux model. Alex Eng J 2025;129:226–39. https://doi.org/10.1016/j.aej.2025.06.017.Suche in Google Scholar
Received: 2025-11-04
Accepted: 2026-03-02
Published Online: 2026-04-27

© 2026 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/ntrev-2025-0293
Schlagwörter für diesen Artikel
nanofluids; micro-rotational; response surface methodology; micropolar; numerical simulation
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