Abstract
Nanofluids have potential role in the heat transfer enhancement for engineering applications. These fluids together with physical controls change the dynamics of flow inside oblique channel. Thus, this work focuses on the organization of hybrid model using dissipation function and enhanced properties nanoparticles (NiZnFe2O4, and MnZnFe2O4). The similarity transforms used in the governing model and obtain a new model for hybrid nanofluids. The output estimated in the form of graphical results using Levenberg Marquardt Back Propagation scheme under multiple variations. It is noticed that the velocity is maximum towards the middle line of the channel and backflow observed in the surrounding of walls. Higher concentration declines the velocity due to improved density while Reynolds number enhances it. Further, the temperature is also scrutinized optimum about 
for Eckert and Reynolds number, which represents the central part of the physical domain. The skin friction improves from 3.87182 to 3.88703, 0.76311 to 0.77658 against 
to 
. The significant increase (7.63195 to 8.09306, and 4.68020 to 4.96782) in the heat transfer gradient is observed for 1.0% to 4.0% concentration factor. The convergence of the model achieved excellently in the form of error histogram (
), MSE from 
to 
, best validation performance from 
to 
(velocity case), 
to 
(temperature case) at epochs 1000. The heat transport through such configuration has potential relevance to the thermal transport in cooling of drilling, mining machinery, and mines equipment. Such problems can also be useful for heat transport systems associated with deep mine energy and waste heat recovery which required effective heat removal.
Keywords: Neural Networking, Heat transfer, Mining technology, Hybrid Nanofluids, Dissipation energy Channel flow
Introduction
The characteristics of fluids saturated by bi-hybrid nanomaterials [1] in channel made by walls with uniform slope is of broaden significance from applications point of view. Such setup is beneficial for thermal dynamics of heat exchanging devices, micro and nano-leveled systems. The oblique flow geometry attracted the researcher’s attention because of their configuration and forces exerted by the walls. Extending nanofluid’s study in oblique channel also enhances the applicability of flow transport regarding thermal applications. These fluids are much better for cooling and heating applications than common fluid classes. The reason of enriched thermal conductivity provided by the inclusion of nanoparticles [2] in fluid make the traditional classes more effective for thermal applications. This class also helpful to maintain the temperature at desired level due to the control of nanoparticles addition. Thus, these tinny nanomaterials can be considered as catalytic agent to control the model performance. Analysis of nanofluid problems is slanted walls channel is of wider interest for optimizing the engineering and industrial applications.
Implication of magnetic field on the physical models comprising the study of nanofluids affects the performance by producing extra forces in the system which alter the dynamics of heat transfer. This is due to nanoparticles [3] and fluid motion in the fluidic setup. Magnetic field from multiple orientation along with nanofluids is a potential motive for heat optimization in new cooling devices. Production of Lorentz forces according to the applied strength provides resistive force factor which is good for flow control and also influenced in the heat gradient. The geometric shape associated to magnetic field explores more fascinating applications of nanofluids in which flow through convergent/divergent channel is one of configuration. Orientation of applied field can behave contrarily on the fluid flow; thus, direction of acting magnetic field on the system is important. Transversely oriented magnetic field is a helping tool which produces eddy phenomena in the fluids, causes reduction in the energy consumption in industrial processes. Power generation and reactors section cooling working on this process to acquire the heat at different levels by applying multiple strength magnetic field.
The heating source and natural radiations [4] are potential ways to augment the functionality of nanofluids. The radiative thermal transmission is good for combustion processes and cope the heat problem in aircrafts, where the surfaces exhibiting dominant temperature. Modifying the energy model with these constraints are beneficial for heat dissipation from the surface. Impacts of radiations and heating parameters further enhances the proficiency of nanofluids in which the absorption of heat by the nanoparticles has critical role. Interaction of these quantities with nanoparticles provides excellent heat mechanism in nanofluids. Thus, exploration of nanofluids inclined walls channel is imperative from applications perspectives. Sari et al. [5], made efforts for heat transfer models with addition of magnetic forces. The unique configuration of oblique walls attracted the researchers and they show that MHD control the flow and weak effects reduces the backflow separation from the walls.
Dogonchi and Ganji [6], reported an approximate analytical investigation has been undertaken to examine the effects of key governing parameters, including the stretching/shrinking rate, thermal radiation, Reynolds number, Hartmann number, channel divergence angle, and nanoparticle solid volume fraction. The analysis demonstrates that both velocity and thermal distributions increase with a rise in the stretching parameter. Vinutha et al. [7] further examined that enhancement of local and external pollutant sources promotes concentration within divergent channels, whereas a decline is observed for convergent configurations. The inclusion of nanoparticles intensifies the surface drag force, suggesting significant implications for thermal regulation, mitigation of pollutant dispersion, and improved circulation in nanofluid systems. Further investigations have been made by various researchers (see Refs [8–11]). for the applications of nanofluids [12, 13] applications in engineering regarding the heat mechanism problems. The findings of Akinshilo et al. [14] indicate that an increase in the Reynolds number elevates the effective viscosity while reducing the velocity field. Similarly, heat transfer is suppressed at higher Darcy numbers due to reduced flow intensity, thereby diminishing internal friction. Comparison with previously published studies confirms the consistency and accuracy of the present results. Bég et al. [15] analyzed that in divergent channels, larger opening angles combined with higher Reynolds numbers induce a pronounced reduction in temperature, while the inverse trend is recorded for convergent channels.
Saadoon et al. [16] conducted numerical investigation and reveal that the integration of nanofluids in converge-diverge mini-channels markedly enhances the hydrothermal performance of heat sinks. Among the tested working fluids, Ag-H2O nanofluid demonstrates superior heat transfer efficiency over Fe3O4-H2O, achieving up to a 43.27% improvement in the Nusselt number at a nanoparticle volume concentration of 0.075%. The recent trends in the field of nanofluids explored potential results for heat transfer using multiple schemes (see the Refs [17–20]., and [21]). These studies highlighted different aspects of heat transport using nanofluids and their applications in industrial areas. Moreover, Ashraf [22] studied combined influence of absorption and Joule heating and shown that it plays a constructive role in controlling thermal transport, with ternary nanofluids containing blade-shaped nanoparticles exhibiting a significant enhancement in heat transfer performance. Jan et al. [23] observed that at increased solid volume fractions, distinct flow characteristics are observed: velocity diminishes in divergent channels while it intensifies in convergent channels. The influence of the Eckert number and porosity parameter is evident in the skin friction behavior, where an increase is recorded for divergent geometries and a reduction for convergent configurations, applicable to both nanofluids and hybrid nanofluids. Notably, hybrid nanocomposites exhibit more dominant thermophysical effects compared to conventional nanocomposites in both expanding and contracting channels.
Ullah et al. [24] shown that an increase in the couple stress parameter enhances resistance to wall shear stress and simultaneously promotes the transport of hybrid nanofluids, thereby improving the overall stability of the base fluid (blood). Moreover, numerical analysis confirms that variations in nanoparticle volume fraction yield a significant percentage rise in heat transfer capability. The study of Kurtulmuş et al. [25] reveals a substantial enhancement in thermal transport, albeit accompanied by a marked pressure drop. The maximum thermal performance factor (TPF) is achieved as 1.46 for M=0.5. Numerical simulations, conducted under identical parametric conditions, are in strong agreement with experimental findings, thereby validating the model predictions. Ramesh et al. [26] exercised the Runge-Kutta-Fehlberg (RKF) fourth-fifth order integration technique, and the obtained solutions are benchmarked against previously reported results. The physical implications of the governing constraints are illustrated through graphical interpretations, demonstrating a reduction in velocity within divergent channels and an enhancement within convergent channels at higher particle concentration. Furthermore, the porosity parameter and inertia coefficient are shown to amplify velocity near the channel walls, underscoring their critical role in regulating flow behavior.
Research gap
Despite extensive progress in heat transfer using nanofluids, the Jeffery Hamel flow (flow through converging/diverging channel) for ferrite nanomaterials (NiZnFe2O4-MnZnFe2O4)/C2H6O2 hybrid nanofluid insufficiently discussed, specifically by implementing data driven scheme. The previous attempts made using numerical approaches and provide limited insights into whether the ANN approach can precisely learn the combined framework for the parameters, thermal transport properties and the channel configuration. The function of adding NiZnFe2O4-MnZnFe2O4 in C2H6O2 with artificial intelligence based scheme provides a potential gap that has gained limited attention in converging diverging channel flows. Addressing this significant gap offers a systematic model for quantifying thermal response and assessing the ANN predictive ability rather than extending the traditional nanofluids simulation
Novelty
The novelty of this attempt is to develop integrated computational model for Jeffery Hamel and the contribution of NiZnFe2O4-MnZnFe2O4 in the heat mechanism of C2H6O2 by combining the distinct thermophysical characteristics of ferrite nanomaterial. The investigation prolongs the traditional Jeffery Hamel analysis by examining the influence of driving parameters like Reynolds, Eckert, hybrid nanomaterial concentration, and converging diverging parameter on the dynamics and associated heat transport in hybrid (NiZnFe2O4-MnZnFe2O4)/C2H6O2. Further, the methodological novelty falls in the addition of an ANN as a data driven model that trained using bvp4c to achieve the effective results between the varying parameters and the model thermal response. The proposed study develops an integrated approach in which physics based model and ANN used together to describe thermal transport in Jeffery Hamel flow of hybrid nanofluid. Thus, the framework adds new computational insights into the heat transport response to controlling governing parameters while allowing an effective framework for predicting output in investigated parametric domain
Model configuration
Figure 1 depicts the laminar movement of a viscous, incompressible fluid bounded by two inclined plane surfaces forming an angle of 
. The flow is initiated by a source or sink located at the cusp and is assumed to be two-dimensional, unidirectional, and symmetric with respect to the central axis (
). Under these assumptions, the velocity components reduce to 
, while 
, becomes zero. The channel’s polar angle is 
, while the flow is in the radial direction r. The present analysis is devoted to examining the combined effects of nanoparticles, and dissipation heat interactions, in nanofluidic system inside the channel and often called it Jeffery Hamel flow (JHF). The channel sides are rigid and unable to expand or contract.
Fig. 1.
Geometry of the problem
Under the steady, radial, 2D laminar and incompressible assumptions for converging diverging channel flow, the continuity equation is expressed in Eq. (1), as the transverse component of the velocity is zero, therefore the conservation of mass is defined as in Eq. (1).
 |
1 |
 |
2 |
 |
3 |
 |
4 |
The continuity equation yields 
. The boundary conditions for the problem obey the symmetry and rigid walls assumptions. Due to symmetry about the centerline 
, the velocity and temperature gradients should be zero as given in Eq. (5). Further, Eq. (6) represents the conditions at the walls 
, in the absence of no slip effects.
 |
5 |
 |
6 |
Physically, the flow is symmetric around the centerline 
, thus the radial velocity has no angular changes locally across the center line which gives 
. The condition 
shows the radial velocity and gives the reference value used to normalize the velocity function. Similarly, the condition 
, physically represents the temperature symmetry about the centerline. This means that there is no change in temperature gradient in angular direction at the symmetry plane. The condition 
, physically describes no slip condition. The hybrid nanofluid has zero radial velocity at the fixed walls because these are non-stretching and fixed. Finally, the condition 
, signifies the walls temperature considered in the model consistent with the similarity transformations.
The transformative functions which are advantageous to the problem formulation are elaborated in Eq. (7) for the momentum and energy model, respectively.
 |
7 |
The mass conservation equation reduces in 
, where u denotes the function of 
, and r.
For the present investigation, the hybrid nanofluid which is composition of NiZnFe2O4 (Nickle zinc ferrite) and MnZnFe2O4 (manganese zinc ferrite) [27] with C2H6O2 is taken. The formulas which describe the augmented characteristics are given Table 1. While the corresponding values of individual components [28] are enlisted in Table 2.
Table 1.
Effective formulas for hybrid nanofluid case
| Properties | Effective formulas |
|---|---|
| Thermal conductivity |
|
| Density |
|
| Heat capacity |
|
| Dynamic viscosity |
|
Table 2.
Individuals properties of the components
| Characteristics |
|
|
|
|---|---|---|---|
|
1116.6 | 4800 | 4700 |
|
2382 | 710 | 1050 |
| k | 0.249 | 6.3 | 3.9 |
The appropriate simplified form of the problem is achieved after exercising the transformative variables and enhanced hybrid nanofluid properties in the basic physical laws.
 |
8 |
 |
9 |
The quantities appeared in Eqs. (8–9), are 
, 
, 
, and 
is converging/diverging factor. The positive and negative 
corresponds to diverging and converging cases, respectively. The shortened conditions on the boundaries and center line are achieved in Eq. (10).
 |
10 |
 |
11 |
A detailed examination of heat transfer behavior within the wall region, quantified by the local Nusselt number, along with the evaluation of shear stresses, is of paramount importance in engineering analysis and design. These parameters not only characterize thermal performance but also influence structural validation, fluid-surface interactions, and overall system efficiency across a wide range of engineering applications. In the framework of the present study, their definitions are provided as follows.
 |
12 |
The mathematical execution of Eq. (12), yields the final form as below.
 |
13 |
 |
14 |
ANN architecture and execution
The machine learning schemes for the execution of the problem become famous for better estimation of the results. Thus, the current analysis has done through ANN [29] scheme using LMBP [30]. The scheme is together with bvp4c for execution of the data to drive the ANN algorithm. The whole procedure involves the preceding steps for successful implementation.
Introduce the transformed functions for the governing model.
Incorporate these functions in the problem equations after rearranging in suitable version.
Step 2 produces reduced form of the higher order problem.
The conditions which control the nanofluid flow in the channel also transformed accordingly.
Implement the bvp4c successfully and obtained the data for the energy and velocity equations.
Using LMBPS data driven algorithm, the further processing carried out and furnished the output results. The whole data divided into 15%, 15%, and 70% for the execution of training, testing and validation purposes.
By following the above steps, the energy and velocity equations are supported by the following functions.
 |
15 |
 |
16 |
Now it is indispensable to arrange the problem in feasible form as below.
 |
17 |
 |
18 |
Incorporation of functions from Eqs. (14–15) in Eqs. (16–17), yields the below model.
 |
19 |
 |
20 |
To proceed the process of computation, the appropriate reduced equations are as follows.
 |
21 |
 |
22 |
The accuracy fixed up to the mark and the algorithm LMBPs successfully applied according to the architecture designed in Fig. 2 by engaging the purelin and tansig functions in the output and hidden layers, respectively. Further execution performed using the parameters and decorated the results in the preceding section.
Fig. 2.
The ANN structure and machine learning operation
Results and discussion
The characteristics of nanofluid laminar flow in the channel greatly changes when the parameters vary over certain ranges. This decides that how the flow control or thermal efficiency of the functional fluid can be maintained. Thus, this section decorates the physical results of the model for both convergent and divergent cases.
Figures 3 and 4 elaborate the physical scenarios of the velocity and temperature inside convergent and divergent channel. Increase in the concentration 
enhances the velocity in convergent while it reduces in divergent channel. However, the fluid attains optimum velocity about the center line 
. In divergent case, the decrement is examined as the concentration increases. Physically, the opening channel prolong the flow area as a moment the fluid layers flow towards the space provided due to the walls opening. Thus, it reduces the velocity. In contrast, the convergent channel enhances the velocity due to increase in the pressure because the force per unit area becomes stronger. This physical situation leads to the velocity enhancement. At high concentration 
, the fluid layers move back and hence produces backflow to some extent. Similarly, for stronger Re the velocity declines and more back movement of the layers is examined. Figure 4 highlights the temperature versus the parameters. Under this model, the efficiency drops for Eckert and it prominently increases for Re. For convergent case, the optimum changes in the temperature are noticed. At the walls, the temperature vanishes as per the implemented conditions and the fluid near the center attains maximum temperature.
Fig. 3.
The velocity response for the parameters
Fig. 4.
The temperature response for the parameters
The training state and performance for the model dynamics under convergent and divergent walls are demonstrated in Figs. 5, 6, 7 and 8, respectively. The training state help to monitor the parametric optimization, enable to check the convergence, notice the issues like overfitting, and vanishing gradients. This also helpful to predict that when the training should stop or to adjust the training quantities for excellent convergence. On the other hand, the performance state gives the effectiveness of the model factors. From the results, remarkable states of the performance and training stages are achieved. Under varying the quantities, excellent convergence of gradients, Mu, validation, and training performance is estimated.
Fig. 5.
The state of training for the velocity case (convergent (a-b) and divergent (c-d) cases)
Fig. 6.
The state of training for the temperature case (convergent (a-b) and divergent (c-d) cases)
Fig. 7.
The Performance state for the velocity case (convergent and divergent cases)
Fig. 8.
The Performance state for the temperature case (convergent and divergent cases)
The error estimation through histogram by considering the convergent and divergent situations is furnished in Figs. 9 and 10. The error is up to the mark in response of the problem parameters. However, for divergent case, the convergence is rapid than convergent case. Overall, convergence in all the cases is remarkable. To get the rapid convergence of the results, it is essential to change the parameter 
for divergent case. Further, the temperature convergence is also very good in both the cases in Fig. 10. This convergence achieved at 20 bins in all the cases.
Fig. 9.
Trends of Error Histogram for the velocity (both convergent (a-b) and divergent (c-d) cases)
Fig. 10.
Trends of Error Histogram for the velocity (both convergent (a-b) and divergent (c-d) cases)
The regression and functions fitting curves for the velocity and temperature behaviour in convergent and divergent channels is illustrated in Figs. 11, 12, 13 and 14, respectively. It is pointed that the regressions are well aligned with linear behaviour and R=1.0 in both the cases which shows excellent validity. However, both the scenarios depict that under the ranges of 
and Re, the regression fitting is excellent. Similarly, the functions fitting curves also observed good for the model parameters and well ranged with validation output, targets, and training targets, respectively. These fitting trends are furnished in Fig. 13, and Fig. 14, respectively.
Fig. 11.
Trends of regression for the velocity (both convergent and divergent cases)
Fig. 12.
Trends of regression for the temperature (both convergent and divergent cases)
Fig. 13.
Trends of fitting functions for the velocity (both convergent and divergent cases)
Fig. 14.
Trends of fitting functions for the temperature (both convergent and divergent cases)
The changes in shear drag and transfer of heat with changing parameters inside the channel are presented in Tables 3 and 4 through numerical means. The shear drag can be enhanced with strengthening nanoparticles. However, the diverging channel shows less trends than convergent case. The Reynolds number provided that the drag can be further improved by applying higher values. From Table 4, the dominant increase in heat transport rate is obvious for concentration factor by improving the thermal conductivity of the model. Improved thermal conductivity allows the fluid to transfer heat quickly. Further, the dissipation energy is observed highly effective for the heat phenomena because it enhances the internal capability of the fluid to produce heat. Converging scenarios transmits quick heat than diverging once.
Table 3.
Changes in the shear drag with parameters
| Parameters | Skin Friction | |||
|---|---|---|---|---|
|
|
Re | |Converging Flow| | Diverging Flow |
| 0.01 | 0.02 | 14 | 3.87182 | 0.76311 |
| 0.02 | 3.87896 | 0.76944 | ||
| 0.03 | 3.88401 | 0.77391 | ||
| 0.04 | 3.88703 | 0.77658 | ||
| 0.01 | 0.01 | 3.76749 | 0.66932 | |
| 0.02 | 3.87182 | 0.75311 | ||
| 0.03 | 3.97885 | 0.85683 | ||
| 0.04 | 4.08864 | 0.95028 | ||
| 0.02 | 13 | 3.73158 | 0.63650 | |
| 26 | 5.33345 | 1.82806 | ||
| 39 | 6.59999 | 2.46688 | ||
| 52 | 7.66892 | 3.45231 | ||
Table 4.
Changes in the Nusselt number with parameters
| Parameters | Nusselt Number | ||||
|---|---|---|---|---|---|
|
|
Re | Ec | Converging Flow | Diverging Flow |
| 0.01 | 0.02 | 14 | 0.3 | 7.63195 | 4.68020 |
| 0.02 | 7.78860 | 4.77843 | |||
| 0.03 | 7.94227 | 4.87430 | |||
| 0.04 | 8.09306 | 4.96782 | |||
| 0.01 | 0.01 | 7.62278 | 4.64878 | ||
| 0.02 | 7.63192 | 4.68021 | |||
| 0.03 | 7.63437 | 4.71786 | |||
| 0.04 | 7.63021 | 4.76124 | |||
| 0.02 | 13 | 7.45261 | 4.53862 | ||
| 26 | 9.48437 | 6.91848 | |||
| 39 | 11.0368 | 9.09935 | |||
| 52 | 12.3087 | 11.0352 | |||
| 15 | 0.1 | 2.60236 | 1.61218 | ||
| 0.3 | 7.80709 | 4.83654 | |||
| 0.5 | 13.0118 | 8.06091 | |||
| 0.7 | 18.2165 | 11.2853 | |||
Conclusion
This study reports a detailed investigation of flow and heat transport behaviour in hybrid nanofluids for convergent and divergent scenarios. The following are the study’s findings.
The velocity reduces for higher concentration in divergent channel while the convergent channel improves it.
Backflow of nanofluids examined near the walls at high Re ( Re=10 to Re=25) values and the optimum velocity achieved about the center portion of the channel.
The maximum thermal changes observed near
, while these changes gradually slowdown towards the walls.The training states, performance, regression, histogram and functions fitting are obtained up to remarkable accuracy using NN scheme.
Hybrid nanofluids provide better transport characteristics with varying physical quantities.
The skin friction improves from 3.87182 to 3.88703, 0.76311 to 0.77658 against
to 
. The significant increase (7.63195 to 8.09306, and 4.68020 to 4.96782) in the heat transfer gradient is observed for 1.0% to 4.0% concentration factor.The convergence of the model achieved excellently in the form of error histogram (
), MSE from 
to 
, best validation performance from 
to 
(velocity case), 
to 
(temperature case) at epochs 1000.
Limitations and future work
The present research is limited to viscous incompressible model for hybrid nanofluid flow in Jeffery Hamel configuration in the absence of chemical reaction and hybrid nanomaterial and primary solvent are homogenous mixture. The results obtained under laminar flow regimes with specified ranges of the parameters. The future work on this topic could be extended for non-Newtonian, cross fluid, combining mass and bioconvective models, perpendicular and inclined influence of magnetic field, and advanced nanofluids. Further, extension could be made by using machine learning approaches for their effectiveness for Jeffery Hamel problems
Possible applications
The current research on theoretical heat transfer investigation in Jeffery Hamel flow provides essential into thermal transport in convergent divergent flows and the hybrid nanomaterial improved the fluid characteristics. These findings may be relevant to mining technology linking the heat exchangers, thermal management of machinery, mineral equipment processing and cooling where flow area is of converging diverging channel form. However, the potential uses should be viewed as potential engineering relevance, since the research model is theoretical instead of experimental
Acknowledgements
This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. KFU265984].
The authors extend their appreciation to Northern Border University, Saudi Arabia, for supporting this work through project number (NBU-CRP-2026-2225).
Nomenclature
- u
velocity component (m/s)
- θ
polar angle
- r
radial component (m)
- T
temperature (K)
- p
pressure (Pa)
- μhnanofl
dynamic viscosity (Pa.s)
- ρhnanofl
density (kg/m3)
- khnanofl
thermal conductivity (W/mK)
- (ρcp )hnanofl
heat capacity (J/K)
- U
mainstream velocity (m/s)
- Tw
walls temperature (K)
- ϕNiZnFe2O4
nanoparticles concentration
- ϕMnZnFe2O4
nanoparticles concentration
- η
dimensionless variable
- F
dimensionless velocity
- β
dimensionless temperature
- α
converging/diverging angle
- Re
Reynolds number
- Pr
Prandtl number
- Ec
Eckert number
- ϕ1,ϕ2
nanoparticles concentration
Author contributions
Adnan and A.K.: Conceptualization, Formulation, Software. Adnan: Writing original draft. M.A.K., A.N.A., A.T., T.S., M.N.B., and S.U.S.: Methodology, software, Formal Analysis, Investigation, validation, visualization, writing review and editing.
Funding
This work was supported by the Deanship of Scientific Research, Vice Presidency for GraduateStudies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. KFU265984].
Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Declarations
Ethical Approval
Not Applicable.
Consent to Participate
Not Applicable.
Consent to Publish
Not Applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Contributor Information
Adnan, Email: adnan_abbasi89@yahoo.com.
Ayele Tulu, Email: ayeletulu@gmail.com.
Taoufik Saidani, Email: taoufik.saidan@nbu.edu.sa.
Muhammad Nasir Bashir, Email: mnasir@kfu.edu.sa.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.