Nonlinear Momentum Equations Research Articles

Numerical Investigation of Turbulent Convection Flow in a Rectangular Closed Cavity

Natural turbulent convection in closed cavities has many practical applications in the field of engineeringsuch as the design of electronic computer chips, atomic installation and industrial cooling among others. Inparticular, it enables in achieving a desired micro-climate and efficient ventilation in a building. Recent studiesshow that turbulent flow is affected by variations in Rayleigh numbers, aspect ratio, and heater positionamong others. Temperature is kept constant in all these studies hence inadequate literature on the effectsof temperature on a turbulent flow. In this study, aspect ratio and Rayleigh numbers are kept constant at2 and 1012 respectively and natural turbulent convection flow in a closed rectangular cavity is investigatednumerically as the operating temperature is varied from 285.5K to 293K. The rectangular cavity’s lower wallwas heated and cooling done at the top face wall while the rest of the vertical walls were kept in adiabaticcondition. Material properties such as density of the fluid kept on changing at any given temperature. Thethermal profile data generated influenced the nature of the turbulent flow. The non-linear averaged continuity,momentum, and energy equation terms were modeled by the SST k − ω model to generate streamlines,isotherms, and velocity magnitude for a different operating temperature and presented graphically. The finitedifference method and FLUENT were used to solve two SST k − ω model equations, vortices, and energy withboundary conditions. It was discovered that, as the operating temperature increased turbulence decreaseddue to a decrease in the velocity of the elements and vortices became more parallel and smaller.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Implication of electromagnetohydrodynamic flow of a non‐Newtonian hybrid nanofluid in a converging and diverging channel with velocity slip effects: A comparative investigation using numerical and ADM approaches

AbstractThis study delves into the intricate interplay of magnetic and electric fields (EMHD) on the flow characteristics of a non‐Newtonian bio‐hybrid nanofluid, consisting of Ag+Graphene/blood, within converging and diverging geometries. The investigation takes into account the effects of velocity slip at the walls, offering a comprehensive examination of this complex fluid system. A novel bio‐hybrid nanofluid model was introduced, featuring a unique combination of Ag+Graphene/blood nanoparticles. To address this multifaceted problem, the research employed mathematical modeling based on nonlinear partial differential equations (PDEs), encompassing continuity and momentum equations. These PDEs were then transformed into a system of nonlinear ordinary differential equations (ODEs) through similarity transformations. The study explored both numerical and analytical solutions, with a particular focus on the application of the Adomian decomposition method (ADM). To validate the findings, the study compared the analytical results with those obtained using the HAM‐based Mathematica package and the Runge–Kutta Fehlberg 4th–5th order (RKF‐45) method in specific scenarios. Active parameters, including nanofluid volume fraction, slip factors, and the influence of magnetic and electric fields, were systematically examined to unveil their impacts on velocity and skin friction within this multifaceted nanofluid system. It is found that the skin friction coefficient decreases with the Increasing both the nanoparticle volume fraction, Hartmann number and the angle in both channels. Results obtained also reveal an in the converging section, higher Casson parameters lead to increased yield stress but are offset by the higher shear rates, resulting in a higher velocity profile. In the diverging section, the fluid resists flow due to the reduced shear stress, leading to a decreased velocity profile.

Insight into the peristaltic motion through a tapered channel with Newton’s cooling subject to viscous dissipation, Lorentz force, and velocity slip

Peristalsis has gained significant attention due to its numerous applications in the medical field, engineering, and manufacturing industries. Therefore, the current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by viscous fluid through a tapered channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The constitutive relation for energy is formulated with the addition of viscous dissipation and heat generation/absorption. The assumption of velocity slip along with the convective boundary condition energizes the thermal system as well as the flow phenomena. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution were obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity. The effects of various relevant parameters on flow properties were investigated through graphical analysis. The results show that the maximum velocity does not occur in the middle of the tapered channel, but moves toward the upper wall with the increase in the variable viscosity difference between the walls. The application of viscosity is essential in many engineering and industrial processes.

Effect of the Non-Linear Radiative Unsteady Mixed Convective Flow over a Curved Stretching Surface with Soret and Dufour Effects: A Numerical Study

The subject of unsteady convective flow with non-linear thermal radiation has become an important issue of research, due to its implications in advanced energy conversion systems operating at high temperature, solar energy technology and chemical process at high operation temperature. Due to the importance of this issue, a time dependent incompressible viscous fluid flow, heat and mass transfer over a curved stretching surface has been numerically analysed by taking into account the heat flux due to concentration gradient and mass flux due to temperature gradient. Together with this the Rosseland approximation is being employed for the nonlinear thermal radiation impact in presence of thermal slip. With the aid of non-dimensional variables and the corresponding physical boundary conditions, the leading nonlinear momentum, energy, and species equations are converted into a set of coupled ordinary differential equations. These equations are then resolved using the MATLAB bvp4c solver. The stability of the numerical technique has been verified and compared with available literatures. The resultant parameters of engineering interest and the boundary layer flow field parameters and have been presented using tables and graphically plots. The study concludes that for lesser curvature parameter (0.5≤K≤0.7) the surface drag force, heat and mass transfer rates can improve by about 9.59%, 2.87% and 1.67% each respectively. The presence of the temperature ratio parameter and the non-linear thermal radiation are found to greatly influence the temperature profile and the heat transfer rate of the system. Results show that the heat transfer rate improves by about 24.39% and 16.66% for varying non-linear thermal radiation (1≤Rd≤1.5) and temperature ratio parameter (1.2≤θw≤1.4) respectively. Results obtained also show that improving the thermal slip parameter (0.4≤L≤0.6) can reduce heat transfer rate by about 13.62% and reduce the surface temperature profile.

Non-Newtonian Fluid Flow in an Incompressible Isothermal Cylindrical Pipe and Temperature-Dependent Viscosity

This study centres on non-Newtonian fluid flow in an incompressible isothermal cylindrical pipe and temperature-dependent viscosity. The coupled nonlinear momentum and energy equations were solved using the regular perturbation technique Reynold’s model viscosity is introduced to account for the temperature-dependent viscosity, while the third grade fluid is accommodated to model the non-Newtonian fluid feature. Results show that the third grade and the magnetic field parameters have the tendency of reducing both the velocity of the fluid flow and can enhance the temperature of the cylindrical walls. The Eckert parameter is seen to increase the temperature within the constant viscosity model, but reduces the temperature at the Reynold’s model. Results further show the exponential constant parameter n for Reynold’s model viscosity reduces both the velocity and the temperature profiles. The results of other sundry parameters associated with this analysis are presented

IMPACT OF POROUS AND MAGNETIC DISSIPATION ON DISSIPATIVE FLUID FLOW AND HEAT TRANSFER IN THE PRESENCE OF DARCY-BRINKMAN POROUS MEDIUM

In this article, the boundary layer flow of an electrically-conducting fluid through a porous medium attached with a radiative permeable stretching sheet is analyzed. Following the Brinkman theory, an extended Darcy model (Darcy-Brinkman model) is utilized for the model momentum equation. Heat transfer analysis is also performed in the presence of viscous and Joule dissipation. Moreover, in the modeling of the energy equation, the effects of internal heating resulting from the mechanical effort required to squeeze out the fluid through the porous medium are also included in porous dissipation. Suitable dimensionless variables are introduced to convert the governing boundary layer equations into a dimensionless form, which are then converted into self-similar, nonlinear ordinary differential equations by utilizing similarity transformations. The exact solution of the nonlinear self-similar momentum equation is obtained in the form of the exponential function. In contrast, the solution of the energy equation is computed through the Laplace transform technique in the form of Kummer confluent hypergeometric functions. Effects of involved physical parameters on the momentum boundary layer (MBL), thermal boundary layer (TBL), wall shear stress, and local Nusselt number are explored through graphs and tables. Moreover, the slope linear regression (SLR) technique is used to calculate the rate of decrease/increase in shear stress and the rate of heat transfer at the boundary. The velocity and momentum boundary layer decreases for large values of porosity parameter and increases by increasing the viscosity ratio. The shear stress increases by increasing the porosity parameter, Hartman number, and suction parameter, while the opposite effect is examined with increasing values of viscosity ratio parameter. Heat transfer rate also enhances by increasing the Brinkman viscosity ratio parameter and wall suction velocity.

Melting heat effect in MHD flow of maxwell fluid with zero mass flux

This study delves into the investigation of Maxwell fluid flow across a sheet with a particular effort on the melting heat and zero mass flux at the boundary. A Maxwell fluid, characterized by both viscous and elastic responses, plays a pivotal role in various industrial and biological applications. The mathematical model describing Maxwell fluid flow is represented using non-linear momentum and energy equations, incorporating MHD. Similarity transformation is used to change from partial differential equation to ordinary differential equation. The introduction of a phase change term in the energy equation accounts for the melting heat effect at the boundary. The BVP4C solver using MATLAB is hired to numerically answer the system of equations, enabling the determination of the steady-state solution. The solution of this investigation offers valuable insights into the interplay between viscoelasticity and melting heat effects on various flow characteristics, including velocity and temperature profiles. The practical significance of this research is evident in polymer processing, food processing, and materials engineering, where the understanding of Maxwell fluids and their interaction with melting boundaries is essential for process optimization and product quality. So far in the literature survey no one have considered Melting heat effect along with Maxwell fluid. The conclusion for this study is that Melting heat effect increases velocity profile and decreases the temperature profile. This is the main conclusion of this research.

Computational biomedical simulations of Cattaneo Christov heat flux model in diseased arteries with a combination of aneurysm and stenosis

In present article, computational biomedical simulations of Cattaneo Christov heat flux model in diseased arteries with a combination of aneurysm and stenosis is implemented in order to investigate its effects on the blood flow across the cylinder, the magnetic field is also applied. Stenosis causes a decrease in cross sectional area of the vascular lumen and is produced by the addition of fats and other hydrocarbons below the vascular endothelium of the arterial wall. For the heat transfer, Fourier law has parabolic nature which represents the temperature field moves fast with initial disturbance and spreads in whole substance. Cattaneo introduced additional parameter of relaxation time in the classical Fourier's law to get around this problem, creating the option of carrying heat by the motion of thermal waves with a slow pace. Using a mild stenotic assumption, we normalized the bi-directional, non-linear momentum and energy equations and reduce them to a unidirectional flow. Using the finite difference method, we discretized the associated partial differential equations. The resulting algebraic problem is solved numerically by using Matlab software. As a result, numerical solutions are obtained and these results are used to test the effects of different emerging parameters on flow pattern that are demonstrated in velocity, temperature, wall shear stress and flow rate profiles. The cross-sectional behavior of the blood flow patterns is also developed using streamlines for general readers.

Numerical Analysis of Magnetohydrodynamic and Dissipated Hybrid Casson Nanofluid Flow Over an Unsteady Stretchable Rotating Disk with Cattaneo-Christov Heat Flux Model

The study scrutinized MHD and dissipated (SWCNTs-Fe3O4)/C2H6O2 hybrid Casson nanofluids flow over an unsteady stretchable rotating disk with a Cattaneo-Christov heat flux model. By means of proper similarity conversion, the boundary layer flow governing PDEs was changed into systems of dimensionless coupled nonlinear ordinary differential equations. Subsequently, the consequent nonlinear momentum and energy equations with their boundary conditions were worked out numerically employing the spectral quasilinearization method (SQLM). The convergence, stability, and accuracy of the SQLM were established as a computationally efficient method to solve a coupled system of boundary layer problems. It is specified that 5% of SWCNTs, 20% of Fe3O4, and 75% of C2H6O2 being taken for the preparation of (SWCNTs−Fe3O4)/C2H6O2 hybrid nanofluid with shape factor n1 = n2 = 3, and the values of the parameters used are fixed to M = 5, S = 0.5, β = 5, κ = 0.5, Ec = 2, Λ = 2, Pr = 7.3, α = 0.5, δ = 0. The effects of more perceptible parameters on velocity and thermal flow fields were considered and scrutinized carefully via graphs and tables. The results disclose that the momentum and thermal boundary layer thickness markedly declined with more value of the unsteady parameter. The local heat transfer rate improves nearly by 14% as 0.2 volume of Fe3O4 nanoparticles dispersed in 0.05 volume of SWCNTs and 0.75 volume of C2H6O2 nanofluid, hence, in realistic uses adding more values of nanoparticles in the hybrid nanofluids is useful to progress the heating process. The study is novel since to the best of the author’s knowledge, no paper has been published so far on the unsteady flow of (SWNT-Fe3O4)-Ethylene glycol hybrid Casson nanofluid with the effects of the Cattaneo-Christov heat flux model. As well, the model used for the thermophysical properties of the hybrid nanofluid is a new approach. Generally, hybrid nanofluids of (SWCNTs-Fe3O4)/C2H6O2 show better flow distributions with good stability of thermal properties than their mono counterparts.

Flow and heat transfer analysis of Couette and Poiseuille flow of a hybrid nanofluid with temperature-dependent viscosity and thermal conductivity

The purpose of this research is to quantify the influence of a number of independent parameters (−0.5≤α1,β1,β2≤0.5) on the heat transmission rate and the temperature of a nanofluid hybrid flowing between parallel plates. The linked nonlinear momentum and energy equations are solved using the regular perturbation method for two different cases resembling the plane Couette flow and Poiseuille flow. By combining engine oil with multiwalled carbon nanotubes (MWCNT) and aluminum oxide nanoparticles, a hybrid nanofluid is produced with wide-ranging lubricating and industrial applications. It has been found that the hybrid nanofluid can function as a coolant provided the relevant parameters are adjusted appropriately. It is demonstrated that these additives have a tendency to stabilise the thermal and the volume flow rate, hence decreasing randomization that is necessary for a good lubricant to function. The findings of the study indicate that β1 has a greater influence on temperature, while β2 has a stronger effect on velocity. In addition to the variable model, the results for the constant model have also been deduced, and the novel study demonstrates that the considered variable viscosity model tends to produce a more uniform temperature distribution.

Numerical examination of concentration-dependent wastewater sludge ejected into a drinking water source

One of the significant water-related health challenges globally is due to pollutant fate. Contaminants endanger the lives of humans, animals, and even plants. The present mathematical analysis explains reactive wastewater sludge ejected into a drinking water source from wastewater treatment plants. The assumption that wastewater sludge follows a power-law constitutive relation leads to nonlinear momentum and concentration equations. The contaminants are assumed to follow a nonlinear irreversible first-order sorption model. The numerical solution of the coupled problem is solved using the Bivariate Spectral Local Linearization Method and validated with the spectral Chebyshev weighted residual method. Profiles are presented for dimensionless flow velocity and concentration. Comprehensive explanations for the obtained results are provided with relevant applications.

First and second laws analysis of viscoelastic fluid with temperature dependent properties for Couette-Poiseuille flow

The entropy analysis of viscoelastic fluid obeying the simplified Phan-Thien-Tanner (SPTT) model with variable thermophysical properties are obtained for laminar, steady state and fully developed Couette-Poiseuille flow. The homotopy perturbation method (HPM) allows us to solve nonlinear momentum and energy differential equations. The Reynold's model is used to describe the temperature dependency of thermophysical properties. Results indicate that the increase of the group parameter (Br/Ω) and the Brinkman number (Br) which show the power of viscous dissipation effect; increases the entropy generation while increasing fluid elasticity (εDe2) decreases the generated entropy. Increasing the Reynolds variational parameter (α) which control the level of temperature dependence of physical properties attenuate entropy generation when moving plate and applied pressure gradient have the opposite direction and decreases entropy generation when moving plate and applied pressure gradient have the same direction or both plates are at rest. Also, increasing elasticity reduces the difference between variable and constant thermophysical properties cases. These results may give guidelines for cost optimization in industrial processes.

Numerical Investigation of a Combustible Polymer in a Rectangular Stockpile: A Spectral Approach

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values.

A Mathematical Investigation of Flow of Third Grade Fluid in Channel Filled with Porous Media with Heat Source

In this study on flow of third grade fluid in channel filled with porous media in the presence of heat generation, the researcher considered and analyzed the effects thermo-physical parameters involved the momentum and energy equations. The nonlinear momentum and energy equations arising from the flow regime is solved analytically using perturbation technique. Explicit expression for the velocity field and energy balance have been obtained Results show that a little increase in the third grade parameterß , Grashof number,G, and the magnetic field parameter,M, reduces the velocity of fluid flow but enhances the temperature of the system greatly.

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

AbstractInvestigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third‐grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third‐grade fluids for EMHD flow and heat transfer behavior. The least‐square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third‐grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third‐grade fluid increases.

Fractional modeling and analysis of unsteady squeezing flow of Casson nanofluid via extended He-Laplace algorithm in Liouville-Caputo sense

The objective of this manuscript is to model the fully fractional unsteady Casson nanofluid flow between two parallel plates influenced by magneto hydrodynamic forces and Darcian effects in both slip and no-slip case. Casson nanofluid model is fractionally transformed through mixed similarity transformations into a non-dimensional fully fractional model. In modeled fluid problem the continuity equation is identically satisfied and fractional order highly non-linear momentum equation is obtained. The obtained fractional model is further validated by putting α=1 and obtaining the integer order Casson fluid model already existing in literature. In order to solve the flow problem, a hybrid of homotopy perturbation method and Laplace transform, namely He-Laplace method (HLM) is utilized. The obtained results are validated with existing results in literature and through residual errors and average error plots with increasing order of approximation. It is observed that results obtained through HLM are better in terms of accuracy than existing results. Moreover, the errors reduce substantially as order of approximation in HLM increases, depicting the convergence of proposed scheme. Graphical analysis is also performed to analyze the behavior of normal and radial velocity. Furthermore, contour plots are presented for flow rate and skin friction of Casson nanofluid. It is observed that fluid parameters present different behavior incase of fractional environment when compared with existing integer order results. Also, the behavior of velocity profile in no-slip case is in contrast to the behavior noted in slip case of Casson nanofluid. These finding confirm the importance of fractional modeling in terms of capturing more generalized physical phenomena.

Approximate Analytical Study of Natural Convection Flow of Non-newtonian Fluid Through Parallel-Pates With Heat Generation

In this present paper, approximate analytical study of natural convection flow of non-Newtonian fluid through Parallel-plates with heat generation is considered. The coupled non-linear momentum and energy equations was solved using perturbation technique. The cases of constant viscosity and temperaturedependent viscosity are treated with the case of temperature-dependent viscosity considered in two models: Reynold's model and Vogel's model. Within the constant viscosity case, results show that increase in the non-Newtonian parametersß, M, decreases the velocity of the fluid flow and increase in these parameters enhances the temperature of the plates. The effects of non-Newtonian and viscosity indices of both Reynold's and Vogel's models on velocity and temperature profiles are presented.

The Effect of Nanoparticles on MHD Blood Flow in Stretching Arterial Porous Vessel with the Influence of Thermal Radiation, Chemical Reaction and Heat Generation/Absorption

Numerical and theoretical analysis of the effect of nanoparticles on MHD blood flow in stretching arterial porous vessel with the influence of thermal radiation, chemical reaction and heat generation/absorption has been examined. The governing non-linear partial differential equations of momentum, energy and nanoparticles concentration are converted into ordinary differential equations using similarity transformations which are solved numerically. The dimensionless governing equations are solved using Runge-Kutta-Fehlberg fourth-fifth order along with shooting method.

EFFECT OF A VARIABLE MAGNETIC FIELD ON PERISTALTIC SLIP FLOW OF BLOOD-BASED HYBRID NANOFLUID THROUGH A NONUNIFORM ANNULAR CHANNEL

This paper analyzes the impact of hybrid nanoparticles (Cu–TiO2) on a two-dimensional peristaltic blood flow pattern in a nonuniform cylindrical annulus in the presence of an external induced magnetic field with wall slip. Further, this study focuses on the flow dynamics of single and hybrid nanofluids through endoscopic or catheterized effects. The mathematical model consisting of continuity, linear momentum, thermal energy, and Maxwell’s equations is simplified under the assumptions of long wavelength and negligible Reynolds number. The Homotopy perturbation method (HPM) is employed to get an approximate analytical solution of nonlinear dimensionless momentum equations. Based on the mathematical relationships and graphic visualization, the influence of the pertinent parameters described the velocity profile, temperature distribution, induced magnetic field, current density distribution, wall shear stress, and heat transfer coefficient. With the help of contours, the trapping phenomenon is also presented. The results reveal that the Lorentz force significantly reduces the Cu–TiO2/blood nanofluid velocity, whereas the elevating Grashof number does the opposite. Compared with copper nanoparticles, hybrid nanoparticles have a higher wall shear stress. The increasing values of Reynolds numbers amplify the induced magnetic field on annular surfaces. In the axial direction, Lorentz force significantly decreases the current density distribution for hybrid nanofluid. Moreover, hybrid nanoparticles (Cu–TiO2) exhibit superior heat transfer than Copper (Cu) nanoparticles in the blood-based fluid. According to the graphical outcomes, hybrid nanoparticles are comparatively more effective than unitary nanoparticles in the blood.