Non-dimensional Form Research Articles

Effect of Newtonian heating on double convection flow fractional differential type fluid

The influence of Newtonian heating (NH) is studied on heat-mass transfer problem of fractional differential type fluid. The proposed problem is modeled by using Caputo-Fabrizio fractional order derivative. A steady magnetic field of uniform strength is enforced in a perpendicular direction of flow. The set of governing equations in dimensional form accompanied by suitable initial and boundary conditions are changed into non-dimensional form by making use of some non-dimensional variables. The resulting problem is then converted into a model employing fractional differential operator by using the new Caputo-Fabrizio fractional differential operator. The analytical exact solution has been obtained by making use of Laplace transform technique. The numerical results are computed via MATHCAD software and displayed in various plots for different physical parameters and discussed.

Solar radiation and lower gravitational effects on wave oscillations in heat transfer along magnetic-driven porous cone in the presence of Joule heating

Solar radiation is a very useful form of energy such as heat and current density in gas turbines, nuclear power plants and thermal energy storage. The fundamental source of heat for multiple reactions in the climate, oceans, and ecological system is solar radiation. The current radiative flow model has significant applications in nuclear power generation, radioactive reactor cooling mechanisms, heating boilers, recycling of underground radioactive materials, fabrication of glass-fiber material and thermal textiles. The significance of study to reduce excessive heating by using magnetized surface. The main goal of current research is to report the Joule heating effect on heat and magnetic flux along the magnetic-driven porous cone under solar radiations and lower gravitational region. The novelty of this work is to explore wave oscillations in heat and magnetic flux with solar radiations under lower gravitational region. The Joule heating is applied to control the thermal boundary layer along gravity-driven cone. The coupled mathematical model is changed into non-dimensional form for physical parameters. The steady and oscillatory parts are obtained by using Stokes conditions. For smooth programming in FORTRAN computing tool, the primitive variables are used. The efficient finite difference scheme is used to plot the numerical findings with Gaussian elimination technique. The impact of governing parameters involved in the problem on wave oscillations of magnetic flux and heat transmission are drafted physically and numerically. It is noted that the fluid velocity enhances with significant amplitude as lower gravity and solar radiation increases along porous cone. It is found that wave oscillations of heat and magnetic flux increases as magnetic Prandtl number enhances under lower gravitational region.

Triple-Diffusive Bioconvection Flow of Sutterby Nanofluid Over an Oscillatory Stretchable Surface Immersed in a Darcy-Forchheimer Porous Medium

To respond to the demands of modern technological processes, the employment of nanofluids to maximize energy efficiency has been a topic of interest to many scientists. The stability of such nanofluids can be appropriately enhanced with the use of gyrotactic microorganisms. In the current framework, we inspect the triple-diffusive bioconvection flow of electro-magnetized Sutterby nanofluid via an oscillatory stretchable surface with Brownian diffusion of both nanoparticles and microorganisms, thermophoresis, buoyancy, and inertial forces. With the utilization of acceptable dimensionless variables, the governed flow equations are first metamorphosed into non-dimensional form, and solutions of the resulting equations are computed using the overlapping grid spectral collocation scheme. The rationale for choosing this numerical approach is provided by computing residual errors and condition numbers. The significance of physical parameters on the quantities of engineering interest and flow profiles is discussed. The main results include that reduced surface shear stress and minimal oscillatory nature of velocity are achieved with the inclusion of porous media, inertial forces, bioconvection, and nanofluid buoyancy forces. Temperature and rate of heat transfer are upsurged with the existence of variable thermal conductivity, nonlinear radiation, and convective heat conditions, which advocate that such features promote superior heat transport within the Sutterby working fluid. Growth in solutal Dufour Lewis number increases solutal concentration while reducing solutal-mass transfer rate. Improvement in microbial Brownian diffusion parameter causes enhancement in the rate of motile microorganisms transfer and reduction in the concentration of gyrotactic microorganisms. This implies that the random motion of motile microorganisms plays a prominent role in the dynamics of microorganisms.

Performance of carbon nanotubes (CNTs) on the development of radiating hybrid nanofluid flow through an stretching cylinder

In various industries, one of the important aspects is the cooling processes for which the material exhibits its perfect shape and size. Intending to the aforementioned property the current investigation leads to carry out the features of the materialistic property of thermal radiation and the dissipative heat by incorporating these in the water-based hybrid nanofluid. The fluid past a stretching cylinder embedded with a permeable medium and the impact of the magnetic field, and thermal radiation are depicted in momentum and energy profiles. In addition to that, the role of the Hamilton-Crosser conductivity model for the behavior of various shapes of the carbon nanotube (CNT) nanoparticles with their volume concentration is also vital. The transformation of the dimensional form of the governing equations into the non-dimensional form is obtained with the use of proper transformation rules. Further, the proposed designed model is handled by employing the traditional shooting-based Runge-Kutta fourth-order technique. The significant properties of different components are deployed graphically and the validation with earlier study shows a good correlation. Moreover, the important characteristics of the outcomes are; the surface cooling, driven by increased thermal buoyancy, promotes fluid velocity while simultaneously influencing the curvature parameter and profile to slow down the accumulation of nanoparticles.

Energy transfer through third‐grade fluid flow across an inclined stretching sheet subject to thermal radiation and Lorentz force

The heat and mass transfer through the third grade fluid (TGF) flow over an inclined elongating sheet with the consequences of magnetic field and chemical reaction is reported. The impact of activation energy, heat source/sink, and thermal radiation is considered on the TGF flow. Fluid that demonstrate non-Newtonian (NN) properties such as shear thickening, shear thinning, and normal stresses despite the fact that the boundary is inflexible is known as TGF. It also has viscous elastic fluid properties. In the proposed model, the TGF model is designed in form of nonlinear coupled partial differential equations (PDEs). Before employing the numerical package bvp4c, the system of coupled equations are reduced into non-dimensional form. The finite-difference code bvp4c, in particular, executes the Lobatto three-stage IIIa formula. The impacts of flow constraints on velocity field, energy profile, Nusselt number and skin friction are displayed through Tables and Figures. For validity of the results, the numerical comparison with the published study is performed through Table. From graphical results, it can be perceived that the fluid velocity enriches with the variation of TGF factor and Richardson number. The heat source parameter operational as a heating mediator for the flow system, its influence enhances the fluid temperature.

Stagnation point flow of hybrid nanofluid flow passing over a rotating sphere subjected to thermophoretic diffusion and thermal radiation

The effects of thermal radiation and thermophoretic particles deposition (TPD) on the hybrid nanofluid (HNF) flow across a circling sphere have momentous roles in research and engineering. Such as electrical devices, projectiles, thermal conveyance, sheet production, renewable energy, and nuclear-powered plants. Therefore, the current study presents the stagnation point flow of HNF flows about an orbiting sphere. The HNF is organized with the accumulation of aluminum alloys (AA70772 and AA7075) nanoparticles in the water. The HNF flow model equations are changed into the non-dimensional form of ODEs through the similarity variables and then numerically solved through the parametric simulation. It has been perceived that the significance of the rotation factor boosts the velocity curve, while the flow motion drops with the increasing numbers of AA7072 and AA7075 nanoparticles. Furthermore, the addition of AA7072 and AA70775 nano particulates in water lessens with the temperature profile. The energy distribution rate in case of hybrid nanoliquid enhances from 3.87 to 13.79%, whereas the mass dissemination rate enhances from 4.35 to 11.24% as the nanoparticles concentration varies from 0.01 to 0.03.

Viscoelastic effect on the triple diffusive oscillatory flow in a fluid-saturated porous layer

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields.

Control of radiating heat on the heat transfer of polar hybrid nanofluid flow through a vertical permeable plate

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature.

Numerical study on thermal resistance of PCMs incorporated in novel roof structures against energy loss

Incorporating Phase Change Materials (PCM) into building enclosures is one of the passive techniques to improve thermal comfort and reduce energy costs. The present study is dedicated to the assessment of various configurations of PCM incorporation in a roof structure in order to evaluate their impact on thermal resistance and consequent reduction in energy losses. Several arrangements of the PCM and brick are tested: small PCM blocks distributed through the structure, multiple long PCM blocks distributed horizontally or vertically, single PCM block occupying either the right half or the left half, and single PCM block occupying the top half or bottom half. The equations governing the flow and thermal transfer in the PCM, as well as heat transfer in the plaster and brick, are defined and derived in the non-dimensional form. The hydro-thermal behavior of the melting PCM is assessed in the different configurations and for two values of Rayleigh number. The results indicate that for low Ra, the highest thermal resistance is obtained when a single PCM block is located at the top of the cavity and separated from the hot source by brick. For high Ra, the maximum resistance is found when the PCM is placed in multiple vertical blocks. Putting the PCM in multiple horizontal blocks or in small blocks does not change the PCM melting when Ra is varied. In all cases, the fastest PCM melting is obtained when the PCM block is close to the hot source and is either in one single block or in multiple vertical blocks.

Magnetohydrodynamic (MHD) Convective Flow in a Porous Medium in the Presence Variable Pressure and Injection/Suction

This article investigates MHD convective flow with variable pressure and injection/suction in a porous medium. The governing equations are modeled using partial differential equations (PDEs) in dimensional form. The PDEs describes the unsteady flow of an incompressible electrically conducting fluid are expressed for the momentum, energy and concentration of the fluid flow. Also, the PDEs were transformed to non-dimensional form using some dimensional variables. Perturbation method was used to obtain the solutions for the velocity, temperature and concentration. The non-dimensional Skin friction, Nusselt number and Sherwood number were obtained. Effects of physical parameters associated with the present study was examined and discussed. It was observed that the concentration, temperature and velocity of the fluid rises with increase in injection parameter and an opposite trend was observed when suction parameter became significant. It is found that the temperature of the fluid reduces as the Prandtl number increase. However, an opposite trend is seen for heat source/sink.

Flow analysis of radiated micropolar nanofluid on a stretching/shrinking wedge surface under chemical reaction and multiple convective conditions

This paper reports the flow features and distributions of concentration and temperature of a micropolar type nanofluid (water-based) past a stretchable and shrinkable wedge, influenced by variable magnetic force, nonlinear sort thermal radiation and chemical reaction. Along with the consideration of multiple convection, the model of Buongiorno is stated. The Brownian motion and thermophoresis have been kept in the analysis. Suitable similarity alteration is approached to renovate the foremost equations to dimensionless ordinary differential equations (ODEs). Associated conditions became nondimensional forms according to this conversion. Then the numerical solutions of the reduced governing equations with boundary conditions are obtained by adopting the RK-4 technique with shooting criteria. The language MAPLE 17 assisted in developing this solution. Significant upshots of prime parameters on the fluid transmission, mass and heat transport properties are represented with suitable tables and graphs. In tabular form, we have reckoned the physical quantities of heat, mass transfer rates and drag friction coefficients to fulfill the engineering interest. This study acquaints that the material parameter negatively influenced nanofluid’s angular velocity. The fluid’s temperature improves with thermal and mass Biot numbers, but this response goes opposite for the parameter of wedge angle. Chemical reaction and wedge angle parameters amplify mass transport. This study can be beneficial in the blowing of chilled air by AC panels, the abstraction of crude oils, the nuclear power hub, the working of warships, making flaps on the wings of aeroplanes for advanced lift, submarines, the extraction of polymers and several other sectors in advanced science and industrial developments.

Illustration of thermal radiation on the flow analysis of hybrid nanofluid within an expanding/contracting channel

The current analysis deals with the physiological flow of hybrid nanofluid within an expanding and contracting vertical annulus embedding with a permeable medium. Additionally, in the free convective viscous flow, the impact of thermal radiation on the heat transport phenomenon is vital. The significance of this research lies in the utilization of Hamilton–Crosser thermal conductivity to investigate the behavior of nanoparticles with different shapes. In this study, both oxide nanoparticles like Al2O3 and metal nanoparticles like Ag are incorporated into the blood, which serves as the base fluid. This incorporation aims to enhance the performance of hybrid nanofluids in influencing flow phenomena. The proposed mathematical model designed for the above-mentioned constraints is solved analytically following the transformation into their corresponding non-dimensional form. The statistical behavior of the diversified parameters is presented graphically and the numerical results for the rate coefficients are deployed via table. Further, the important characteristics of the results are depicted as follows: the combined effect of the particle concentration used in hybrid nanofluid favors in reducing the fluid velocity greatly than that of nanofluid and pure fluid.

Controlling energy loss from roof structures equipped by round-corner double semi-hexagonal ferro- phase change material layer using magnetic field

Improving the thermal characteristics of building enclosures is a must in the context of rising global energy consumption. Heat losses through roof enclosures are one of the main causes of excessive energy consumption in the Heating, ventilation, and air conditioning systems in buildings. Designing novel roof structures to reduce heat losses is essential. The Phase Change Materials through their thermal properties can provide an effective passive solution in this regard. The present paper is dedicated to the analysis of a roof structure incorporating a Ferro-Phase Change Material enhanced with nanoparticles and subjected to an external magnetic field. The Ferro- Phase Change Material is placed in a round-corner semi-hexagonal block that can be oriented horizontally or vertically in the roof structure. The equations governing the heat and flow are developed and presented in the non-dimensional form. The set of equations were discretized and solve using control volume based finite element method. The effect of Hartmann number, the inclination of the magnetic field and the orientation of the Phase Change Material block on the flow and thermal behaviors of the Phase Change Material and on the thermal resistance of the roof structure are assessed. It is found that when the Ferro- Phase Change Material block is oriented vertically, it offers 30% less thermal resistance than the horizontal configuration in the absence of magnetic field. Increasing Hartmann number from 0 to 200 raises the thermal resistance by 80% for the vertical case and 45% for the horizontal case. Changing the inclination angle of the magnetic field has more effect on the Phase Change Material when its block is oriented vertically, with 30% faster melting and 45% decrease in the thermal resistance are found when the magnetic field is applied vertically instead of horizontally.

An EEDI based method to better the selection of form and propulsion parameters and improve energy efficiency during preliminary designs of single screw seagoing general/bulk cargo ship

The third phase of the Energy Efficiency Design Index (EEDI) regulations, which came into force in 2022, states that new ships should reduce their emissions by at least 30% compared to the minimum energy efficiency level (EEDI baseline) set by the IMO's MEPC in 2013. Apart from its vital role in decarbonizing the global fleet and improving the transportation efficiency, the EEDI that is considered herein is a measure of vessel's mechanical performance. A simplified EEDI (SEEDI) is used to judge a series of designs in order to identify all possible efficient designs and to select the best option. A code was employed to iterate over all practical ranges of hull and propeller parameters to extract complete designs from methodical design and propeller series. All possible methods of manipulating form and propulsion parameters that might lead to reducing the SEEDI were investigated. The modifications were made while taking into consideration the practical and economical ranges of the non-dimensional ratios and form coefficients. Compared to the use of energy saving devices and slow steaming, significant reductions (up to 25%) in the SEEDI have been achieved after applying the proposed method.

Implication of radiation on the thermal behavior of a partially wetted dovetail fin using an artificial neural network

The simultaneous convection-radiation heat transfer of a partially wetted dovetail extended surface is investigated in this study. Also, the temperature variance behavior of the dovetail extended surface (DES) is estimated through thermal models for partially wet and dry conditions using the neural network with the Levenberg-Marquardt scheme (NNLMS). The corresponding governing energy equations of a dovetail fin are presented as a set of ordinary differential equations (ODE), which are reduced to a non-dimensional form using dimensionless terms. Further, the resulting coupled conductive, convective, and radiative dimensionless ODEs are numerically solved utilizing the Runge-Kutta-Fehlberg fourth-fifth order (RKF-45) scheme. Using graphical illustrations, the resultant solutions are physically determined by considering the effects of various nondimensional variables on thermal behavior. From the outcomes, it is established that the thermal conductivity parameter enhances the thermal distribution in a partially wetted dovetail fin, and an upsurge in convection-conduction variable, temperature ratio parameter, radiation-conduction, and wet parameter diminishes the temperature profile of the considered extended surface. The modelled problem's NNLMS efficacy is demonstrated by achieving the best convergence and unique numerically assessed quantified results. The outcomes indicate that the strategy successfully resolves the partially wetted fin problem.

Analyzing heat transfer variations at specific locations in a cave filled with porous media, emphasizing non-equilibrium conditions

ABSTRACT This study focuses on the analysis of conjugate natural convection heat transfer in a cavity filled with a permeable medium. It specifically considers the influence of confined thermal non-equilibrium and the presence of circular solid walls with partially active arcs. The study also explores the bifurcation of heat transfer at the interface of the permeable medium and solid walls. A finite element approach is employed to solve the governing equations for heat transfer in porous spaces, including porous matrices and solid walls, represented as partial differential equations. These equations are transformed into nondimensional forms based on boundary conditions and solved using the finite element method (FEM). The study examines local and overall heat transfer, varying nondimensional parameters, and the influence of active wall positions on flow patterns. Interestingly, the results demonstrate that the position of the active walls has a significant impact on the isotherms and streamlines contours in the permeable region, as well as the isotherms in the concrete walls. Specifically, an angle of 120 ∘ between the warm component and the radiator, both positioned vertically and facing each other, results in the maximum overall temperature transmission. Conversely, the lowest total heat transfer rate occurs when the angle between the hot element and cold radiator is 180°, indicating complete alignment. Moreover, the case (e) exhibits the lowest temperature transmission ratio for both the liquid and the concrete stages of the permeable medium. In the case of modifying of R k from 10 to 0.1, decrease in the temperature transmission by creating isolation regions that perform as thermal walls beside the dynamic fences. This research sheds light on the complex heat transfer behavior in a cavity with permeable media and highlights the crucial role of active wall positioning in shaping flow patterns and temperature distribution.

A numerical study on MHD Cu-Al2O3/H2O hybrid nanofluid with Hall current and cross-diffusion effect

A numerical investigation has been performed to analyze an unsteady magnetohydrodynamic gravity-driven flow of a Newtonian hybrid nanofluid (Cu-Al2O3/H2O) along an impermeable vertical plate with linearly accelerated temperature and concentration. The Hall current, nanoparticle volume fraction, inclined magnetic field, and Soret effect on water-based Cu-Al2O3 hybrid nanofluid are incorporated into the flow model. The model's governing nonlinear partial differential equations are formulated and transformed into a non-dimensional form by introducing suitable variables and parameters. The finite difference method is implemented via the MATLAB solver fsolve to resolve the model equations numerically. The evolution of the primary and secondary velocities, temperature, and species concentration profiles is discussed via graphical illustration. Furthermore, a comparative analysis is performed on the coefficient of skin friction, rate of heat, and mass transport for hybrid nanofluid and nanofluid through tabular values. The novelty of the investigation reveals that a deceleration in the primary velocity and acceleration in the secondary velocity with the increasing magnetic field inclination parameter exists. The rising value of Cu nanoparticle volume fraction augments the primary, secondary skin friction coefficients, and the heat and mass transport rates at the plate. The Dufour number stimulates a reduction in the heat transport rate, while an enhancement occurs with the Soret number. The present investigation demonstrates that the heat transfer rate for water-based Cu-Al2O3 hybrid nanofluid is higher than that for water-based Cu nanofluid. The current research can be implemented to augment the efficiency of the cooling mechanism of heat exchangers, solar collectors, nuclear reactors, and many more.

Bioconvective periodic MHD Eyring-Powell fluid flow around a rotating cone: Influence of multiple diffusions and oxytactic microorganisms

Investigating the effects of periodic magnetic field and triple diffusion on bioconvection flow through a rotating cone populated by oxytactic bacteria and an Eyring-Powell fluid is innovative and significant. The magneto-bioconvection flow of an Eyring-Powell multi-diffusive fluid across a spinning cone is investigated in this paper, considering the effect of oxytactic microorganisms. The non-similar technique is used in the mathematical analysis of the flow over a spinning cone. The flow under consideration contains two diffusive species: liquid hydrogen and liquid oxygen. In light of the periodic magnetic field, the surface gradients, notably skin friction, exhibit wavy effects in the boundary layer domain. The governing equations for the fluid flow in the current flow problem, accompanied by heat diffusion, species diffusion, rotation, bioconvection, and periodic magnetic, are highly coupled nonlinear PDEs dependent on the proper initial and boundary conditions. Mangler's transformations convert them into non-dimensional forms, and numerical non-similar solutions are produced using implicit finite difference approximation and quasi-linearisation. The enriching values of bioconvective Rayleigh number Rb decline the velocity F, as a result, lessen the friction between the surrounding fluid and the cone's surface. The improving Peclet number Pe and microbial density difference σ reduced the microorganism density profile and heightened the microorganism density number Re-1/2Nn.

Numerical study on permanent magnetic heat transfer inside a dual semicircle enclosure: Controlling by magnet position

Cooling is vital in electronic devices from which excess heat should be removed. Heat transfer can be controlled in this context through the dispersion of magnetic nanoparticles in the working fluid and subjecting it to an external magnetic field. Such a field can be obtained effectively and passively with permanent magnets. The resulting phenomenon is called thermomagnetic convection. The present study is dedicated to the numerical analysis of the heat transfer of a ferrofluid in a compact circular cavity subjected to two permanent magnets to assess the impact of the magnets' location and magnetic convection properties on the heat transfer behavior of the ferrofluid. The various equations governing the thermomagnetic in the enclosure are developed and presented in the non-dimensional form. The finite element method using Comsol Multiphysics is employed to model the problem. The effects of magnetic Rayleigh number, temperature factor, thermomagnetic number, and the position of the permanent magnets on the thermal and hydrodynamic response of the ferrofluid are investigated. It is found that the magnetic Rayleigh number and the temperature factor are the main parameters affecting the intensity of the heat transfer in the enclosure. The magnets' orientation affects the ferrofluid's thermal behavior mainly when the magnetic Rayleigh number is high. In that case, up to 64% rise in the average Nusselt number is reached when the inclination angle of the magnetic field is reduced from 75° to 15°. The impact of raising the magnetic Rayleigh number is also more important for lower inclination angle. Increasing this number from 5e3 to 5e7 leads to an augmentation of 91% and 11%, for the angles 15° and 75°, respectively Finally, multiplying the temperature ratio by 5 can increase the average Nusselt number by 2.

Analysis of pulsatile blood flow through elliptical multi-stenosed inclined artery influenced by body acceleration

The effect of body acceleration on the pulsatile flow of blood through the elliptical artery having stenosis at the multiple positions of its wall is investigated in the current study. The artery is inclined at angle θ with horizontal, and blood is considered as Casson fluid. The mathematical model is processed into non-dimensional form and simplified using assumptions of mild stenosis. The analytical solution of mathematical equations is obtained in the elliptic bounded domain by employing the perturbation technique with Womersley frequency as a perturbation parameter and validated through case comparison with the previous study. The impacts of external acceleration, stenosis height, shape, gravitational acceleration, yield stress, and inclination angle on the flow velocity, flow rate, wall shear stress, and flow resistance are analyzed. It is found that body acceleration, gravitational acceleration, and inclination angle increase the flow rate and diminish the frictional resistance. The more significant yield stress and stenosis height enhance the flow resistance and reduce the flow rate. Moreover, fluid has higher velocity in the case of the non-symmetric shape of stenosis compared with the symmetric form.