Irregular Heat Research Articles

Deep learning multilayer stochastic intelligent computing for the analysis of irregular heat source of Carreau nanofluid within the vicinity of an exponentially expanding cylinder

Deep learning multilayer stochastic intelligent computing for the analysis of irregular heat source of Carreau nanofluid within the vicinity of an exponentially expanding cylinder

Impact of Brownian motion and thermophoresis in magnetohydrodynamic dissipative: Radiative flow of chemically reactive nanoliquid thin films on an unsteady expandable sheet in a composite media

AbstractThis study comprehensively examines magnetohydrodynamic heat transport characteristics within a thin nanofluid film on a stretchable sheet embedded in a composite medium. By considering factors such as the unsteady nature of sheet velocity, Brownian motion, thermophoresis, thermally radiative heat, irregular heat generation/sink, chemical reactions, and dissipation due to viscous fluid, the research provides valuable insights into the variations in fluid velocity, temperature, and nanoparticles concentration. The computational solution utilizes the efficient numerical method that enables accurate predictions of system behavior under varying conditions. Notable findings include the influence of Schmidt numbers on nanoparticle concentration distribution, the opposing impact of thermophoresis parameter values, and the influence of Brownian motion and heat source/sink on temperature profiles in thin nanofluid film. Also, nanoliquid film thickness is reduced by enhancing the porous parameter values and Hartmann number values. The nanoliquid film becomes thinner when the space‐dependent heat source/sink parameter is considered compared to the temperature‐dependent heat source/sink coefficient. In space‐dependent and temperature‐dependent cases, the increase in these parameters leads to a decrease in the temperature gradient. Furthermore, it is observed that higher thermophoresis values correspond to reduced nanoparticle concentration gradient profiles. Also, enhancement in the chemical reaction values leads to an expansion in the solutal boundary region surrounding nanoparticles, and as a consequence, the concentration gradient of nanoparticles is enhanced. This research has significant potential for optimizing heat performance and advancing innovation in industrial and engineering processes.

Effects of time-dependent and radiation on a tri-hybrid nanofluid flowing on stretchable/shrinkable cylinders with irregular heat generation/absorption using Ohmic heating

This work focuses on the non-linear dynamics of unsteady tri-hybrid nanofluids inside a thermally radiative, expandable or contractible cylinder, which has been a consistent subject of interest for contemporary researchers. An advanced model is formulated to address the unsteady external flowing of a conductive 50 %:50 % by volume aqueous solution of ethylene glycol-based ternary hybrid nanofluid (THNF) over a linearly stretched cylindrical structure, considering the significant applications of an anti-freeze agent in industrial, construction, nuclear, and mechanical domains. The proposed tri-hybrid nanomaterials consist of cobalt magnetite, titania, and magnesium oxide nanoparticles. The heat transfer rate is analyzed concerning viscous dissipation, Ohmic heating, and convective boundary conditions. This research examines the effects of magnetic and induced electric fields. The non-dimensional similarity model for the controlling partial differential system is derived using appropriate transformations and solved by the homotopy analysis technique (HAM) to get series solutions. In contrast to porosity and magnetic characteristics, the flow rate increases with increasing unsteadiness and electric factors. Close to the surface, the Nusselt number rises with an increasing unsteadiness parameter, but skin frictions diminishes. THNF has been shown to significantly enhance the cooling of cylindrical conduits and mechanical antifreeze agents.

Numerical study of fluid flow and entropy optimization subject to second order slip condition across a permeable curved surface

The entropy generation analysis has great significance in the industrial sectors with heat transmission and fluid flows, for evaluating the irreversibility aspect of a system in heat transfer operations. The numerical simulation of entropy generation and the nanofluid flow across a permeable curved surface subject to cross-diffusion and irregular heat source/sink is reported in the current investigation. The thermodynamics 2nd law is used to simulate the entropy optimization. The flow phenomena are mathematically described by partial differential equations (PDEs), which are derived in a curvilinear coordinate system. The system of ODEs (ordinary differential equations) is derived by using the similarity conversion, which is further numerically calculated through the parametric continuation method (PCM) using MATLAB software. The results reveal that the velocity slip and curvature parameters improve the velocity profile whereas the inverse effect is observed against the surface permeability parameter. It can also be noticed that the entropy optimization enhances with the variation in Brinkman number and temperature ratio parameter. The impact of Schmidt number and chemical reaction decline the mass transmission ratio.

Neuro-computing analysis of model-based Casson hybrid nanofluid flow via three-dimensional radiative Riga plate with irregular heat source/sink

In this study, an analysis is conducted on a hybrid nanofluid using the Yamada-Ota and Hamilton-Crosser model in combination with the Casson fluid model. The hybrid nanofluid is analyzed in the context of a three-dimensional radiative Riga plate, which incorporates non-uniform heat source/sink effects. The thermal features and their behavior of the hybridized nanofluid is explored in the current investigation considering the flow over a radiative Riga plate with the impact of space and temperature dependent heat source/sink. The flow and thermal characteristics of the hybridized nanomaterial are presented for the consideration of Yamada-Ota & Hamilton Crosser models. Additionally, the analysis is enhanced by the implementation of Artificial neural network. Further the machine learning approach, a neuro-computing intelligent network is adopted for the computational techniques. The neural networks, which effectively uses the data and make predictions based on their acquired knowledge. The outcomes of the proposed analysis provide the flow behavior of the hybrid nanofluid. The effect of non-uniform heat source/sink of the Casson fluid model contributes to a greater hike in the fluid temperature. Moreover, the neuro-computing intelligent network shows efficient predictions of the involved thermal parameters.

An empirical analysis of hybrid MHD ferrofluid unsteady flow of two-dimensional heat transfer across a porous channel

This research investigates the heat transfer dynamics of a two-dimensional, incompressible, laminar, magnetohydrodynamics, time-dependent flow of a hybrid ferromagnetic fluid with radiation and irregular heat source/sink conditions through two porous channels. The study investigates the unique capability of ferromagnetic solid nanoparticles to improve the thermal efficiency of the host fluid, with potential applications in medicine such as drug targeting, cell separation, and magnetic resonance imaging. A mathematical model is developed as a nonlinear partial differential equation (PDE), which is subsequently converted into a nonlinear ordinary differential equation (ODE) using similarity transformations. The numerical solution is obtained using the 4th-order Runge-Kutta method implemented in Mathematica software. We analyze the impact of various nondimensional factors on the numerical results, including skin friction coefficient and Nusselt number, as well as graphical results depicting the velocity and temperature profiles of the hybrid ferrofluid. Boosting the film thickness parameter (λ) improves the heat transfer rate at the bottom of the porous channel. Raising the irregular heat source/sink parameters ( A * and B * ) and causing opposite impacts on the heat transfer rate at the bottom porous channel. Higher the radiation (R) values, the temperature profile behaves oppositely in both porous channels. The analysis reveals that the hybrid ferrofluid exhibits a higher rate of heat transfer compared to the ferrofluid.

Numerical analysis for Cattaneo-Christov heat flux on convective viscous non-Newtonian fluid flow through porous medium with nonuniform heat source

This work investigates the Ohmic heating, nonuniform heat generation, and Hall effects with Cattaneo-Christov model (CCM) on flow and heat transfer of power-low non-Newtonian fluids (NNFs) past stretching surface embedded in a porous medium. Runge-Kutta method is used to solve non-linear ODEs numerically using a shooting procedure. We study non-Newtonian fluids for power law values of 0.7 and 1.2, respectively. Innovation of this work lies in studying the effect of Hall currents in presence of buoyancy force and an irregular heat source on slip flow of NNFs moving through Darcy porous medium. Varying velocities, surface frictional forces, and Nusselt numbers are examined. Resulting entropy is also examined using computational flow problem investigation. Model-simulated results suggested that various factors play critical role in constructing thermal systems. It is asserted that Hall parameter, mixed convection parameter, Biot numbers, and thermal relaxation time improve heat transference rates by directly affecting fluid molecules temperature.

Mastite xantogranulomatosa em fêmea canina

Xanthogranulomatous mastitis (MXG) is a rare chronic inflammatory condition of the breast. In women, it raises concern and requires a biopsy due to the clinical-radiological similarity with breast neoplasia. The definitive diagnosis is given through histopathological examination. In canine females, chronic benign non-neoplastic lesions in the mammary glands are not frequently described, such as MXG. The objective of this work is to describe the clinicopathological findings of a case of xanthogranulomatous mastitis in a female canine. The case occurred in a female Pinscher breed, 8 years old, not castrated, who presented irregular heat, in addition to a history of galactorrhea and treatment with antigalactogenic drugs. The physical examination revealed the presence of a nodule in the left mammary chain, affecting the caudal thoracic mammary gland (M2E). Due to the fear that it was a malignant neoplasm, the treatment was a radical mastectomy of the left mammary chain, followed by an anatomopathological examination of all glands. Histologically, the M2E nodule was made up of cracks and cholesterol crystals associated with the presence of numerous lipid-laden macrophages and multinucleated giant cells, characterizing it as xanthogranulomatous mastitis.

Impact of Shape Factor on a Couple Stress Flow of a Ternary Hybrid Nanofluid over an Inclined Flat Plate when Non-Uniform Heat Source and Thermal Radiation are Significant: A Darcy-Forchheimer Model

Abstract The study of fluid flow over an inclined flat plate finds applications in a diverse range of engineering fields including aerodynamics, energy production and automotive design. This study theoretically investigates the steady and radiative flow of a ternary hybrid nanofluid (Water + TiO2 + CoFe2O4 + MgO) with couple stress, using the Darcy-Forchheimer model. The flow occurs through a tilted flat plate and is subjected to irregular heat source parameter and entropy generation. The problem’s equations have been transformed into a collection of ordinary differential equations (ODEs), which has been skillfully resolved using the bvp4c solver. Graphs are utilized to elucidate outcomes for two instances of shape components, namely platelet and spherical. An escalation in the couple stress parameter (S) is demonstrated to be inversely related to the fluid velocity, resulting in a drop. Specifically, when 0.5 ≤ S ≤ 3, the friction factor exhibits a decline, with rates of 0.306201851 (for Platelet shape) and 0.304466755 (for Spherical shape). An intriguing observation reveals an augmentation in the generation of entropy as the volumetric fraction of TiO 2 rises. Upon investigation, it has been determined that when the Eckert number (Ecn) increases within the range of 0 ≤ Ecn ≤ 0.3, there is a significant reduction in the Nusselt number. Specifically, the decline is measured to be 0.328685192 for the platelet shape and 0.308939422 for the spherical shape. The utility of the Forchheimer number in regulating the fluid’s motion has been unveiled.

A finite element model with multi-flow fields for the quenching process of mill liner component made of bainite and martensite: simulation and experimental validation

Controlling the type and location of microstructure transformation through heat treatment processes is the key to improving the property of workpieces, especially they are large-sized and highly thick irregular. Such as mill liner, the worst wear in mining machinery, of which microstructure inhomogeneity is key to developing cost-efficient mining process. In order for advanced high strength steel (AHSS) to be used in mining machinery, its microstructure uniformity must be optimized, usually by adjusting the process parameters of the heat treatment process to optimize the microstructure distribution uniformity. However, the research on the simulation of large-sized and highly thick irregular heat treatment process is limited. Previous studies usually controlled the heat transfer process by using the heat transfer coefficient as the boundary condition, but only applied to small size and simple structure of the workpiece. As the heat transfer coefficient is a process quantity, its size depends on the thermal property parameters of the fluid on both sides of the wall, the flow rate, the shape of the solid surface, the thermal property number of the material and other factors, which is not suitable for large-sized and highly thick irregular. Therefore, for the large-sized and highly thick irregular heat treatment simulation process, the equivalent heat transfer coefficient of flow field was introduced as the boundary condition, and the temperature field, microstructure field and stress field were coupled to improve the accuracy of the numerical model. The accuracy of the finite element model is verified by comparing the temperature simulation error of less than 10% through temperature measurement experiments of the quenched workpiece. The evolution process of heat transfer in large-sized and highly thick irregular water bath quenching is obtained through the finite element model data. The difference in the flow rate of the wall fluid is the fundamental reason for the difference in cooling effect, and the wetting process of the wall is the secondary reason. At the same time, the corresponding microstructure and surface hardness distribution of different cooling regions are obtained, which can provide more accurate guidance for the optimization of heat treatment process of large size and thick special-shaped parts.

Thermal analysis of AA7075-AA7072/methanol via Williamson hybrid nanofluid model past thin needle: Effects of Lorentz force and irregular heat rise/fall

Hybrid nanofluids have received remarkable attention due their promising thermal performance compared to conventional nanofluids. The use of hybrid nanofluids is widely found in the pumping power, solar collector, electronic components, coolants in nano devices, and engine applications etc. Such types of applications grabbed the attentionof researchers and scientistswith the aim to understand in depththe problems involving the hybrid nanofluids. Therefore, the primary objective of the present investigationis to investigatethe thermal performance of hybrid nanofluid consisting of asuspension of aluminum alloys (AA7075-AA7072) in methanol-base fluid. The non-Newtonian Williamson fluid flow model under Lorentz force, and irregular heat rise/fall impact past incessantly moving thinneedleis considered. The governingflow equations are solved by bvp4c solver. Results are computed for governing flow parameters such as magnetic field parameter, needle thickness parameter, Weissenberg number, volume fractions, and irregular heat rise/fall constants. Graphs confirm that augmenting values of magnetic field parameter, needle thickness parameter, and Weissenberg number lead to downfall of velocity field but reverse behavior is noticed for increasing nanoparticles volume fraction. A rise in temperature field has been noticed by increasing the magnitude of magnetic field, irregular heat rise/fallparameter, and nanoparticles volume fraction but a decline in fluid temperature occurswithraising theneedle thickness parameter. Detailed discussion about the observed variation in physical properties under pertinent parameters effects is presented. The proposed model is validated by comparison with previouslypublished results.

Heat transfer mechanism of Falkner-Skan flow of Carreau nanoliquid induced by a wedge surface with radiation effect

Numerical investigation is performed to scrutinize the enhanced thermal transmission of Carreau nanoliquid above wedge geometry in the incidence of irregular heat rise/fall and radiation effects. In this research aluminum alloy AA7072 nanoparticles are suspended into the methanol liquid to achieve the better results. The arising system of nonlinear coupled equations is exercised numerically by employing suitable numerical scheme, i.e. bvp5c Matlab solver. The prime motive of this research is to determine the effectual thermal conductivity of the nanoliquid by using Maxwell/Xue models in order to achieve the enhanced energy transmission. The stimulus of pertinent constraints upon the flow factors viz. velocity and thermal gradients are illustrated through plots and also the wall friction and energy transmission rate are bestowed thru graphical trends and numerical values. Evidently, the deposition of Aluminum alloy nanoparticles in methanol liquid effectively amplified the thermal transfer mechanism in Xue nanomodel case than Maxwell nanomodel case.

Stability of magnetohydrodynamics free convective micropolar thermal liquid movement over an exponentially extended curved surface

Micro polar fluids have a wide variety of applications in biomedical, manufacturing, and technical activities, such as nuclear structures, biosensors, electronic heating and cooling, etc. The aim of this study is to investigate the properties of heat transfer on a magnetohydrodynamic free convection movement of micro polar fluid over an exponentially stretchable curved surface. The flow is non-turbulent and steady. The effects of Joule heating, varying thermal conductivity, irregular heat reservoir, and non-linear radiation are anticipated. The modelled PDEs are converted to ODEs via transformation, and the integration problems are then addressed using ND-Solve method along with bvp4c package. It is observed that velocity is reduced and the micro rotation field is increased as the micro rotation parameter is increased. It is witnessed that the temperature of the fluid enhances as the Eckert number is augmented. The velocity is increasing function of the curvature parameter while the decreases with increasing magnetic factor. The distribution of temperature is improved by a rise in temperature-dependent thermal conductivity characteristic. It is investigated that as the values of temperature ratio, Prandtl number, and the Biot number are increased the temperature distribution is enhanced. For the stability of the numerical results, the mean square residue error (MSRE) and total mean square residue error (TMSRE) are computed. For the confirmation of the present analysis, a comparison is done with the published study and excellent settlement is found.

Numerical analysis of irregular heat source/sink through a wall jet flow of spherical graphene oxide nanoparticle in the presence of thermophoretic particle deposition: The case of non-Newtonian Eyring–Powell fluid model

Random mobility and thermomigration of nanoparticles in the regular fluid are the requisite posited two key characteristics of nanofluids (NFs) that have the potential to influence not only the transport processes but also mass and heat transfer within the boundary layer and across the domain. Therefore, this paper inspects the wall jet Eyring–Powell fluid flow of heat and mass transfer conveying spherical graphene oxide (GO) nanoparticles with substantial influence of erratic heat generation/absorption and thermophoretic particle deposition. The governing system of equations is reformed into requisite posited ODEs via incorporating the similarity technique. The approach (bvp4c) based on finite difference scheme is applied to determine numerical solutions to these nonlinear ODE (similarity) equations. The impacts of several distinguished constraints on the dimensionless temperature distribution, concentration, and velocity fields are discussed. Also, the heat transfer rate (HTR), shear stress (SS), and Sherwood number were elaborated with the aid of tables. The results expose that the velocity grows as one raises the material parameter, but the temperature falls. Also, the temperature uplifts because of the factor of absorption and declines due to the internal generation factor. Moreover, the profile of velocity reduces with greater impacts of NF whilst the temperature distribution increases. Additionally, the existence of NF causes an upsurge in SS, HTR and mass transfer rate by about 0.82%, 0.72%, and 0.13%, respectively.

Computational analysis of heat and mass transfer flow of wall jet hybrid nanofluid with irregular heat source/sink effects and waste discharge concentration

Tailoring hybrid nanofluids to attain a specific and regulated heat transmission is done to fulfill the requirements of various applications, including cooling and cooling systems, as well as the automotive and aerospace sectors, among others. Because of its wide range of applications, the objective of this study is to present a numerically derived solution for a problem based on wall jet flow over a stretching surface. In this investigation, the authors have examined a non-Newtonian Eyring-Powell hybrid nanofluid consisting of water and nanoparticles of CoFe2O4 and TiO2. Additionally, the novelty of the paper is to investigate the influence of a magnetic field as well as the presence of an irregular heat sink/source and the waste discharge concentration. The numerical solution is obtained through the use of a similarity transformation technique and the “bvp4c solver implemented in MATLAB”. The higher values of external pollutant source variation parameter and local pollutant external source parameter causes MT rate to decrease. The temperature of the fluid increases significantly, as the heat source parameters become more dominant. The findings from this study hold relevance for a wide array of fields that make use of wall jet (WJ) applications. These fields include car defrosters, sluice gate flows, drying processes for vehicle or building spray paint applications, cooling systems for high-performance laptop CPUs, and cooling jets applied to turbo-machinery components, among others.

Rheological behaviour of Carreau liquid past a wedge surface with binary chemical reaction

The time-dependent stream of rheological Carreau nanoliquid carrying microbes through a rotating lodge through porous media in addition to irregular heat source or sink characteristics is the subject of this article. Due to the fact that the Carreau liquid can reveal the rheology of liquids with short-chain suspended particles, liquid crystals, surfactants, and human and animal blood, it is helpful to depict a range of physical problems. The influence of infinite shear rate thickness is combined to provide the mathematical formulation. Both the static and moving physical features are covered in great depth. Prior to using the finite element technique to solve revised equations numerically, pertinent similarity transformations are used to get equations in their dimensionless form. According to the findings of our study, the temperature and the thickness of the thermal boundary layer that corresponds to that temperature both improves the function that the thermal radiation factor plays in shear thickening and thinning liquids. Additionally, a moving wedge has a greater velocity than a static wedge. The thermophoresis factor's rising function is the concentration field. Furthermore, by increasing the Piclet number's magnitudes, the profile of microbes is diminished.

Impact of Arrhenius energy and irregular heat absorption on generalized second grade fluid MHD flow over nonlinear elongating surface with thermal radiation and Cattaneo–Christov heat flux theory

In this paper, the free convection flow phenomenon on magnetized second-grade nanofluid over a nonlinear elongating surface has been modeled under the assumptions of generalized Fick’s and Cattaneo–Christov heat flux relations. The non-uniform heat source and sink and thermal radiation effects are used in the energy equation with the Buongiorno nanofluid model. The effect on activation energy and chemical processes is also examined, making the current numerical scrutinization innovative. The current mathematical model begins with partial derivative equations (PDEs), which are then transformed into ordinary derivative equations (ODEs) using similarity transformations. The outcomes are obtained using a combination of the finite-difference scheme with the collocation method, approximated up to desirable accuracy, and the effects of various parameters on the modified second-grade nanofluid are discussed using tables and graphs. The temperature distribution for the thermal boundary layer is raised with nonlinear thermal radiation and Brownian motion parameters. The present thorough analysis identified several technical and industrial applications, including Biomedical applications in cancer treatment, electrical wire manufacturing, oil friction control in pipelines, manufacturing processes, and aerodynamic expulsion utilizations.

Insight into the dynamics of active and passive controls over the measurement of thermal conductivity of nanofluids subject to magnetic field and thermal radiation through the stretching surface

In comparison to conventional heat transfer fluids, nanofluids tend to significantly enhance thermal efficiency. This extensive study is to enhance heat transformation while accounting for the magnetohydrodynamic (MHD) nanofluid flow with the impact of non-linear thermal radiation and an irregular heat source over the stretching sheet. The impact of Arrhenius activation energy on active and passive controls of nanoparticles, thermophoresis, and Brownian diffusion has elaborated. The system of partial differential equations is first represented mathematically and then converted into the system of ordinary differential equations by using similarity transformations. The influence of various parameters is displayed numerically through tables, graphical impact, and surface plots on heat and mass transfer, micro-rotation distribution, and the Nusselt number. It is noticed that the temperature profile is intensified with increasing values of the temperature ratio parameter and thermal radiation (Rd) with active and passive controls. The impact of the magnetic field Biot number and thermophoresis parameter on the heat transfer rate has been scrutinized. .

Comparative analysis to study the Darcy–Forchheimer Tangent hyperbolic flow towards cylindrical surface using artificial neural network: An application to Parabolic Trough Solar Collector

Solar thermal collectors convert sunlight into useful thermal energy by absorbing its incoming radiation. Concentrated solar power technologies use the parabolic trough solar collector to collect solar energy with temperatures ranging from 325–700 K. The tangent hyperbolic fluid model is one of the most important non-Newtonian fluid models. Laboratory studies demonstrate that this model accurately predicts the shear thinning phenomenon. In addition, tangent hyperbolic fluid has a better heat transfer performance due to its rheological bearing at various shear rates. The current study investigates the heat transmission performance of Darcy–Forchheimer tangent hyperbolic radiative inclined cylindrical film movement in parabolic trough solar collector with an irregular heat sink/source utilizing the Levenberg–Marquardt technique and backpropagated neural networks. Through the implementation of required transformations, this system is turned into an equivalent nonlinear ordinary differential system. The findings are investigated for Newtonian and tangent hyperbolic fluid cases to understand the rheological characteristics. The outcomes are considered using graphical and mathematical evaluations. Fluids featuring tangent hyperbolic rheological conductivity are obligatory for active rate of heat diffusion. As a consequence, these fluids may be employed in Parabolic Trough Solar Collector for increased heat transmission rate and operational usage of solar energy. Furthermore, We create a dataset using the Runge–Kutta fourth-order shooting technique to create the proposed multilayer perceptron artificial neural network. The data points representing the MoD values are observed to be closely clustered around the zero deviation line. Additionally, it is important to highlight that these data points have relatively small numerical values. Moreover, when calculating the average MoD values for each output, it becomes evident that they are consistently very low.

Stability scrutinization and model development for mixed convective non-Newtonian hybrid nanomaterial flow in thermal system over a vertical shrinking surface

The development of a better extremely high-efficiency coolant classified as nanofluid for numerous engineering and industrial technologies has been made possible by recent advancements in nanotechnology. In this work, we investigate the impression of an irregular heat generation or heat absorption on the improvement of heat transfer of Williamson hybrid nanoparticles composed of water-based Ag and MgO over a porous surface that is shrinking and stretching. The assisting and opposing flows are also provoked. The non-linear model based on differential equations is derived and numerically handled via a bvp4c process based on some reasonable assumptions. In an appropriate region of mixed convection, mass transpiration velocity, and shrinking surface characteristics, two dissimilar branch outcomes are discovered with the change of the influential parameters. In addition, the analysis of the temporal stability to moderate disruptions is executed on these multiple solutions. It is also discovered that whereas the lower solution is unstable with negative lowest eigenvalues, the upper solution is stable and essentially realistic. In addition, the friction factor and the rate of heat transfer rose by nearly 0.129% and 0.039% for the upper branch solution for superior nanoparticle volume fraction, respectively, and decreases by nearly 0.101% and 0.044% for the lower branch solution. Moreover, the outlines of temperature escalates due to the heat source and decelerates due to the heat sink. Finally, the present fallouts are assessed with the prior findings in a specific case to demonstrate the correctness of the existing technique. This study has a wide range of intriguing applications like heating and cooling systems, geothermal energy plants, aerodynamics, and the manufacture of gate disc valves, etc.