Non-dimensional Factor Research Articles

Advances in low cycle fatigue probabilistic modeling

New advances in the probabilistic S-N model proposed by Castillo and Canteli are presented. The requirements for a S-N model derivation to be valid are emphasized, in particular, that of the compatibility between the statistical distributions of lifetime and stress reference variable. The definition of the generalized reference variable (GRV) in the S-N field, as GRV=ψ·σM, where ψ is a non-dimensional factor derived from the σ-ε law of the material, allows the former model to be applied to LCF data. The new model ensures the incontrovertible and unitary definition of the scatter band in the S-N field and the justification of an asymptotic lower limit of the lifetime, N0. As a result, the stress- and strain-based approaches can be envisaged as a unique probabilistic ψσM-N approach applicable in the three conventional, i.e., LCF, HCF and VHCF domains. An extension as the ψσM-R-N model that includes the stress ratio effect is presented. The utility of the model is confirmed with the assessment of LCF data from different external experimental campaigns.

Impact of Autocatalytic Chemical Reactions and Convective Boundary Conditions on NaC6H7O6–SiO2-Based Nanofluid Oblique Stagnation Point Flow Across a Stretching Sheet

The main motivation of this study is to examine the effects and behavior of Casson nanofluid mainly in reference to oblique stagnation points across a stretching surface. Oblique stagnation point (OSP) motions have so many applications, like artificial fibers, sticky materials, drying paper, and freezing electrical equipment, and numerous applications for endothermic and exothermic processes exist, including in heat exchangers, cooking, and drying damp clothes. Because of these applications on various domains, the Casson nanofluid OSP motion via a stretching sheet is studied with endothermic/exothermic chemical processes and convective boundary conditions (CBC). Similarity transformations are employed to convert partial differential equations (PDEs) into a collection of ordinary differential equations (ODEs). Furthermore, some significant engineering coefficients are discussed and also evaluated the behaviors of several nondimensional factors using the Runge–Kutta–Fehlberg-45 numeric method with a shooting scheme and graphical representations. The outcomes signify that temperature and concentration both rise with a rise in the Casson parameter and activation energy (AE) respectively. A higher Biot value leads to a higher temperature profile. A temperature profile increases with an enhance in the Casson parameter. The addition of a solid fraction will enrich the mass transmission rate in combination with AE.

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.

Suction and double stratification effect on unsteady MHD heat transfer nanofluid flow over a flat surface

The objective of the current work is to examine the influence of suction on the unsteady Magnetohydrodynamic (MHD) thermal and mass transfer of a nanofluid flow past a flat sheet in the occurrence of double stratification. The governed highly non-linear PDEs along with corresponding appropriate boundary circumstances are first converted into dimensionless system by the use of similarity translations. The numerical methodology used for solving the transformed ordinary differential equations (ODEs) is often known as the Keller box procedure. This study investigates and visually represents the impact of non-dimensional factors such as Hartman number, Prandtl number, Suction, Eckert number, unsteadiness factor, thermal and solutal stratification on the distributions of velocity, concentration, temperature, drag force, Nusselt, and Sherwood number. The numerical calculation and graphical presentation are conducted to evaluate the impacts of several significant quantities on the flow model. It has been discovered that a rise in the suction parameter leads to an enhancement in the velocity gradient, while simultaneously causing a reduction in the concentration and temperature profiles. The outcomes of the study could have implications for various engineering and industrial applications that control and manipulate fluid flows and heat transfer. The results of the research may have ramifications for a wide range of industrial and engineering applications that control and regulate heat transfer and fluid dynamics.

Modeling of magneto bioconvection Williamson nanoliquid through modified heat flux: The significance of entropy

The combination of microbes and nanofluids has noteworthy consequences for technological and engineering progress, particularly in the realm of heat transfer applications. This study explains radiative flow with chemical reactions affect the emergence of microorganisms in magnetic mixed convective Williamson nanofluid flow. The Cattaneo-Christov heat flux theory and the effects of heat source/sink have been examined about the energy equation. The prime idea of this analysis is to enhance heat and mass transport. The modelled equations have been converted to dimensionless by considering suitable alteration. The dimensionless expression is then numerically tackled using MATLAB's bvp4c approach. The graphs for different profiles—that is, momentum, temperature, concentration and concentration of microorganisms that move—are made visible for particular nondimensional factors. Furthermore, entropy generation minimization has been obtained through law of thermodynamics. The drag friction, heat and mass transfer rate, and microbe density are also computed in a tabular manner. The most important findings that are pertinent to this study are that an increase in the values of the Brownian motion, thermal radiation and thermophoresis significantly enhance heat transfer characteristics. A consistent pattern can be observed when comparing the current results with earlier research.

Enhancing heat transfer in rectangular solar air heater channels: a numerical exploration of multiple Boomerang-shaped roughness elements with variable gaps

ABSTRACT In the current study, numerical investigations are carried out to enhance the convective heat transfer rate in a solar air heater embedded with multiple boomerang-shaped roughness. The boomerang roughness is attached to the absorber plate which is supplied with uniform heat flux. The boomerang roughness geometry is defined by the ratios of height to hydraulic diameter (e/Dh) at 0.09, pitch space to height (P/e) of 10.5 to 18, and the gap between the multiple boomerang arm (g) at 8.5 to 13.1 mm. These parameters are examined for turbulent flow conditions having Reynolds number (Re) ranging from 4000 to 22,000. Heat transfer and friction characteristics in the present work are defined and examined by nondimensional parameters Nusselt number (Nu) and friction factor (fr), respectively. The study compared Nusselt number and friction factor readings to measurements of a smooth channel under similar flow conditions. It compared friction and the Nusselt number coefficient to a smooth rectangular channel and a rough, purposely rough channel. The aim was to determine better heat transfer and reduced friction. The study found that the average Nusselt number (Nu/Nus) and convective heat movement were 3.39 times higher at g = 8.5 mm (θ = 90º) compared to g = 10.9 mm (θ = 80º) and 13.1 mm (θ = 70º) at p = 71. mm and Re = 22,000. The lowest Nu/Nus was 1.75 times for g = 13.1 mm and p = 71.3 mm at Re = 4000. Thinner boundary layers increased the average Nusselt number and convective heat transfer coefficients in systems with smaller gaps. The design model has a maximum THPP = 1.93 at a pitch space between roughness (p = 71.3 and P/e = 15.5, where e = 4.6 mm), gap (g = 8.5), and Re = 22,000.

Interaction between microcapsules and crack using XFEM and data-driven fracture toughness predictive model

The interaction mechanism between microstructures of materials, including microcrack, inclusion and interface defect, is crucial for studying the microscopic damage of materials. The interaction between microcapsules and cracks in self-healing material is examined using a combination of the extended finite element method (XFEM) and the interaction integral method, which is implemented by a program written in Fortran language. The non-dimensional stress intensity factors (SIFs) of a crack with a single microcapsule, a pair of microcapsules and a cluster of microcapsules are investigated. Moreover, the data-driven fracture toughness predictive model using a genetic programming-based symbolic regression (SR) technique is proposed by training the data from the XFEM program. Results reveal that the non-dimensional SIFs are related to the mechanical property, geometry and interface defect of microcapsule. The influence of microcapsule on the SIF is limited within a distance of five times the microcapsule radius. The predictive model quantifies the contribution of microscopic structures on the macroscopic fracture parameter, highlighting the potential of machine learning in guiding the quantitative design and discovery of high-performance smart materials.

Aeroelastic Scaling of a High-Aspect-Ratio Wing Incorporating a Semi-Aeroelastic Hinge

There has been a growing interest in utilizing flared folding wingtips as an in-flight load alleviation device to enable increased wing spans that meet airport gate limits but with little increase in wing weight. The semi-aeroelastic hinge (SAH) concept is implemented in high-aspect-ratio wings to enable wingtips to be released during severe load cases such as maneuvers and gusts to alleviate the bending moments while maintaining optimum aerodynamic shape for the rest of the flight. In this paper, scaling methods for wings incorporating the SAH are explored, allowing for the development of equivalent scaled unmanned aerial vehicles or wind tunnel models with similar aeroelastic behavior as full-size aircraft. Three scaling approaches are considered in this study, namely, Iso-Froude, Iso-Frequency, and Iso-Strain, where a set of governing nondimensional quantities and scaling factors are determined. Despite the significant nonlinearities resulting from large wingtip fold angles, it is shown that a linear scaling approach can be appropriate for such a wing configuration. Furthermore, the aeroelastic properties of each scaled model are compared to those of the full-scale model, where the best match was obtained from the Iso-Strain model, although it is challenging to meet the required operational conditions.

Flow over a stretchable cylinder with nonlinear heat sources/sinks: Magnetic dipoles application

This work contributes mainly an analysis of the impact of a generated magnetic dipole on the magneto heat transport inside a deformable cylinder. Magnetic dipole signifies, magnotherapy and spectroscopy which are medical applications, generate static magnetic fields. The investigation considers the influence of non-linear heat sources and sinks, which result in a noteworthy phenomenon. The flow field is governed by accurate and nondimensional factors, which are used to convert the initial set of highly nonlinear and coupled partial differential equations into a set of nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved mathematically using the bvp4c function in MATLAB, taking into account the boundary conditions. Ultimately, this section provides an overview of the ramifications stemming from various physical constraints on the movement of fluids, including nonlinear source/sink effects and other more factors. Ultimately, the discovered results that impose limitations are juxtaposed with those documented in the scientific literature, revealing a significant connection.

A WILLIAMSON NANOFLUID WITH MOTILE MICROORGANISMS ACROSS A VERTICAL EXPONENTIALLY STRETCHING POROUS SHEET WITH VARYING THERMAL CHARACTERISTICS

The present work demonstrates a boundary layer movement of an incompressible non-Newtonian Williamson nanoliquid. The boundary layer is around an exponentially stretching permeable vertical surface. Moving motile microorganisms are implicated in the movement throughout a permeable medium considering modified Darcy law. The buoyancy-driven flow is presumed, where the density is expressed as being multiplied by gravity and chosen as a linear function of heat, nanoparticle, and microorganism concentrations. Analogous to the exponentially stretching sheet, an exponential variable magnetic strength is taken normal to the surface. Variable thermal conductivity and mass diffusivity are considered together with chemical reactions. The motivation for this study arises from the involvement of microorganisms in the flow and the contribution of its density equation with the velocity, temperature, and nanoparticles system of equations with suitable boundary restrictions. The fundamental governing scheme of nonlinear partial differential equations (PDEs) is transferred to ordinary ones (ODEs) by employing convenient similarity transforms. These equations are analyzed by the homotopy perturbation method (HPM). Therefore, a major objective graphical formation of the distributions is concluded to recognize the impacts of the produced nondimensional physical factors. Some important physiognomies are concluded from the results. The nanoparticle distribution enhances most of the effective parameters and in turn improves heat transmission, which is a good finding that can be useful in several applications. Microorganisms tend to collect with the growth of the Lewis number and infinity value, whereas its condensation damps with the rise of the bioconductivity and the Peclet number. Those results can be useful in identifying factors that help to get rid of microbes, viruses, and harmful bacteria from surfaces.

Bearing capacity factor for strip foundations on unsaturated clay

ABSTRACT The matric suction in unsaturated soil depends on the type of soil and various flux conditions i.e., infiltration, evaporation and no flow. The shear strength of unsaturated soil changes with change in matric suction leading to varying resistance of soil under various flow conditions. In this study, the bearing capacity of strip foundations resting over unsaturated clay considering variation of matric suction with depth for different surface flux conditions and position of water table, has been obtained using finite element lower bound limit analysis. Modified Mohr-Coulomb yield criteria based on unified effective stress approach has been employed to incorporate the contribution of matric suction stress to the failure condition. A non-dimensional bearing capacity factor was introduced to estimate the bearing capacity of strip foundations and presented as a function of different influencing parameters such as foundation width, water table depth, soil properties, various flow conditions and their flow rate, and surcharge pressure. The influence of variation of unit weight of soil in the unsaturated zone, air entry and pore size distribution parameters, residual degree of saturation of soil, specific gravity of soil solids, and foundation-soil interface roughness on the bearing capacity has also been examined and found to be insignificant.

Effect of Diffusion-Thermal on Mixed Convective Casson Fluid Flow in a Porous Channel

The main purpose is to study analytically about the Diffusion-thermo impact on mixed convective flow of Casson fluid in a vertical channel in occurrence of porous media, uniform magnetic field and amplification. Similarity transformation is implemented to transform nonlinear coupled PDEs into ODEs. Further, obtained equations were solved using perturbation technique and studied the characters of heat, velocity and concentration of the corporeal system. The influence of nondimensional factors such as Darcy number Da, buoyancy parameter of concentration N, M2 Hartmann number, dufour number df, rate of chemical reaction γ, Schmidt number Sc, thermal buoyancy parameter λ, Prandtl number Pr, Casson parameter β, and Reynolds number R on concentration, temperature and velocity deliberated explicitly. Few important computational work reveals that the Dufour effect Df enhances the concentration, temperature and fluid flow whereas Casson fluid parameter β diminishes the profiles. The earlier work and present work have been compared for a particular case in the nonexistence of Dufour effect and porous media and were found to be coinciding.

A computational ascertainment of Hall and ion slip implications over a stretched regime with chemical reaction and internal heat source

This study is inspired by the emerging importance of micropolar fluids in a variety of scientific and technical fields due to varied uses and effective thermal activities. Potential applications of these fluids include cancer treatment, magnetic refrigeration, drug delivery and magnetic resonance imaging. Hall and ion repercussions on unstable magneto micropolar liquid beyond a stretched sheet are described in this article. By using the bvp4c, the resulting non-sequential coupled PDEs are transfigured into a system of coupled non-consecutive ODEs, which are remedied by a numerical procedure. An impact of various governing non-dimensional factors on velocity, angular momentum, temperature, concentration, wall friction, couple stress, local Nusselt and Sherwood numbers, is indicated graphically. The main finding specifies that Hall and Ion impacts influence velocity and with increased Hall and Ion effects, velocity raised as well as thermal boundary layer reduced. When compared to previous findings in the literature, the current findings indicate a splendid agreement. The predominant uses of this issue are in solar cell systems, such as solar water pumps, manufacturing and production processes, motion in plasmas, furnace design, nuclear power plants, and solar aircraft wings.

Numerical Study of Inverted Shell Footing Behavior on Sandy Soil

Inverted and upright shell foundations, are increasingly utilized in engineering projects as structural elements beneath buildings, towers, curved dams, and other structures. They serve as economical alternatives to shallow foundations when encountering high loads transmitted through weak soil. The purpose of this research is to use the numerical modeling program Midas GTS NX to better understand the load-settlement behavior of inverted shell footings subjected to vertically applied loads. The study involved variables related to the properties of shell cross-sections, embedment depth of footing, and angle of side slope of footing. Also, the shell efficiency factor and the non-dimensional settlement factor for the shell footing are studied. The results show that inverted shell footings exhibit higher load-carrying capacity compared to traditional flat footings. Furthermore, it was found that inverted shell footings within the range of side slope angles of 15°–30° have a higher load-carrying capacity than traditional flat footings. Additionally, an increase in embedment depth was shown to be effective in enhancing the load-carrying capacity of inverted shell footings. From the obtained results, it was also concluded that the shell efficiency factor (η) of inverted shell footings is high. In particular, the inverted pyramid shell footing with an angle of 15°–30° exhibited higher efficiency compared to other footings, by 48.3% and 39.8%, respectively. The settlement improvement factor (Fa) of inverted shell footings was found to be low with the inverted pyramid shell footing at an angle of 15°–30° having a lower value compared to others by 5x10-4 and 507x10-4, respectively.

Experimental investigation on wind-induced vibration of photovoltaic modules supported by suspension cables

Under the background of the global energy crisis and excessive carbon emissions, solar power stations have increased rapidly in number and size in recent years. To satisfy the construction needs on complex or special sites (e.g. intertidal zone, mountainous area, fishponds, etc.), a suspension cable supported photovoltaic (PV) module was developed recently and quickly aroused market interest; however, such cable-supported flexible PV systems are susceptible to wind loading and associated aerodynamic effects thereon remain unclear. Therefore, both aeroelastic and rigid model wind tunnel tests were conducted to investigate the wind-induced vibration (WIV) characteristics of a typical cable-supported PV module. The effects of module tilt angle, cable pre-tension, and wind speed on the vertical displacement response and the aerodynamic damping were evaluated. Based on wind pressure tests and finite element simulation, the three-dimensional WIV behavior of PV modules could be investigated. The non-dimensional gust loading factor representing the load dynamic amplification was presented based on multi-target equivalent static wind loads. Results show that wind-induced vertical vibration of the PV modules increased with tilt angle but reduced with increasing cable pretension. The fluctuating displacement shows a quasi-linear increase with the square of the wind speed. Negative aerodynamic damping was found for a tilt angle of 10° under high wind speeds. Compared to vertical vibration, horizontal and torsional responses were insignificant for the tested PV modules. The estimated gust loading factor for the PV module with tilt angle of 10° was between 1.1 and 2.5.

Machine learning approach to predict heat transfer and fluid flow characteristics of integrated pin fin-metal foam heat sink

Integrated pin fin-metal foam (PF-MF) heat sink offers enhanced thermal performance owing to the higher surface area and flow mixing. By realizing the strong influence of geometrical parameters of PFs, morphological properties of MF, and coolant hydrodynamics on the thermal-hydraulic performance of the PF-MF heat sink, this article presents a machine learning (ML) surrogated multiparameter and multi-objective optimization framework to determine optimal PF-MF heat sink layouts within the laminar flow regime to enhance the thermal performance of the heat sink with a minimal pumping power penalty. Four supervised regression ML models, namely random forest, extreme gradient boosting, support vector regressor, and artificial neural networks (ANN), were considered while searching for the best surrogate. Four geometrical parameters of PFs, such as PFs diameter (D), height (h), longitudinal pitch, transverse pitch, two morphological properties of MF, i.e., pore density porosity and coolant flow condition, i.e., Reynolds number have been considered as design parameters. The heat transfer and fluid flow performance of the heat sink are evaluated using nondimensional Nusselt number and friction factor A high-fidelity 3-D computational fluid dynamics/heat transfer (CFD/HT) model has been developed to evaluate the thermal-hydraulic performance of all PF-MF heat sink layouts. Furthermore, utilizing the numerical data, ML models have been trained and fine-tuned to accurately predict the overall performance of the PF-MF heat sink. Upon testing the prediction and interpolation capability of all considered ML models, ANN outperforms other models, hence, ANN model has been coupled with genetic algorithm (GA) optimizer to identify three different optimized PF-MF heat sink layouts at three different Finally, the result shows that the ANN surrogated GA-optimized PF-MF heat sink layout can improve the overall thermal-hydraulic performance by approximately 19–35% compared to the best PF-MF heat sink layout among the used input feature space for ML model.

Enhanced thermal and mass transfer of harnessing microbial mediation in electrically conducting Oldroyd-B nanofluid flow: Eukaryotes microorganisms in biological applications

In bioremediation, pollutants are broken down or detached from an atmosphere using microorganisms like bacteria or fungus. These bacteria can either ingest contaminants or be enzymatically converted into innocuous molecules. Bioremediation can be enhanced by several techniques, such as bioaugmentation (the introduction of specific microorganisms), biostimulator (the provision of nutrients to stimulate microbial activity), and bioventing (the provision of air or oxygen to encourage microbial growth). The creation and dissipation of heat in a convective non-Newtonian Oldroyd-B fluid flow across a nonlinear stretching sheet in a three-dimensional boundary layer is examined in this study. The boundary layer flow's highly nonlinear partial differential equations are transformed into ordinary differential equations in the study via similarity transformations. The bvp4c technique of MATLAB is then used to resolve these equations. The study looks at some variables, including as temperature, concentration, the presence of microorganisms, velocity, heat transfer rate, and shear stress. These parameters are evaluated graphically and presented in tabular form, with a focus on the local Deborah numbers (β₁ and β₂), the local buoyancy parameters (λ₁ and λ₂), the Prandtl number (Pr), the Schmidt number (Sc), the Bio-convection Schmidt number (Sb), and the Peclet number (Pe). The results show that raising the local buoyancy parameter improves the boundary layer flow's velocity field and rate of heat transfer. Visual representations of the effects of non-dimensional factors on non-dimensional velocity, concentration, motile microorganism, and temperature profiles help to comprehend the underlying physical properties clearly.

J-integral testing on micro-scale cantilever beam specimens

The current paper presents a modified procedure for the J-integral testing on micro-scale cantilever beam specimens. For such tests, a non-dimensional factor is required that relates the plastic part of the area below the load vs. load-point displacement curve to J. This parameter is called the “plastic eta-factor”, ηpl. Up to now, a constant value of ηpl≈2 has been used, which is also valid for deeply notched single-edge bend specimens. A comprehensive numerical case study is performed to determine ηpl for cantilever beam specimens as a function of the relative crack length a/W, the relative cantilever length L/W, the relative base distance d/W, and the load, i.e. the degree of plasticity in the specimen. It is shown that ηpl≈2 is applicable only, if the crack length is large, a/W⩾0.5. For smaller a/W-ratios, which are commonly used in the fracture mechanics testing of nano- and micrometer sized materials, ηpl can become much smaller and also dependent on the d/W-ratio. A fitting procedure is presented that enables the determination of the correct value of ηpl, and modifications of the J-integral testing procedure for cantilever beam specimens are proposed. Finally, a numerical validation of the procedure is presented.

New insights into the dynamics of heat and mass transfer in a hybrid (Ag-TiO[formula omitted]) nanofluid using Modified Buongiorno model: A case of a rotating disk

The activation energy model is used in this work to examine how hybrid nanoparticles affect the flow across a rotating disk. Here, we considered nanoparticles of silver (Ag) and titanium dioxide (TiO2) dissolved in water, a base liquid. These nanoparticles have real applications such as photography, photocatalysis, water purification, and solar energy conversion. The current study investigates the combined effects of a changing magnetic field, Darcy Forchheimer, porosity, thermal radiation, Brownian motion, and thermophoresis on hybrid nanofluid flow across a rotating disk. By applying similarity transformations, the partial differential equations system of the current scheme is converted into an ordinary differential equations system, after which it is calculated with MATLAB using the bvp4c scheme. Graphs are used to assess the investigation of mass and heat transport. Also, the change in concentration, temperature, and velocity profiles for various non-dimensional factors are discussed briefly using corresponding graphs. It has been noted that the velocity gradient of mono and hybrid nanofluids is reduced as the magnetic parameter inputs increase. The velocity profiles decline as the input of the Darcy-Forchheimer parameter increases. The outcome demonstrates that temperature and concentration increase as the thermophoresis parameter rises. The concentration profile is enhanced as an activation energy parameter increases. Moreover, the average Nusselt number is 37.73 % at M=0.8, and when M=2.2, the value of the average number decreased by 29.43 %. The concentration of silver (Ag) and titanium dioxide (TiO2) is (0−6)%.

Novel algorithm for compressible Newtonian axisymmetric thermal flow

In this paper, we mainly focus on the development of the Taylor-Galerkin/Pressure-Correction method (TG/PC) method to solve the flow of a compressible Newtonian fluid under nonisothermal conditions. The process of development needs applying the two-step Lax–Wendroff method on the energy equation, after which two new steps for energy equations will be obtained within the TG/PC algorithm. In addition, for the density component, the Tait equation of state is adopted to relate density to pressure, which also yields a new step within the novel method to give the correction formula of compressible pressure. To perform the analysis of the new algorithm, Poiseuille flow through axisymmetric rectangular channel for the Newtonian thermal flow is utilized as a simple problem test. The effect of nondimensional factors such as Reynolds number (Re) and Prandtl number (Pr) is discussed in this study. The influence of thermal conductivity [Formula: see text] and viscosity [Formula: see text] on the solution components is presented as well. Also, comparison for both compressible and incompressible flows is provided in addition to a comparison between both cases’ convergence, as it turns out that the convergence of the incompressible case is better than the compressible case. All the results of the effects presented in this study agree well with the approved physical trend.