Semi-implicit Method For Pressure-linked Equations Research Articles

Magnetohydrodynamic thermal characteristics of water-based hybrid nanofluid-filled non-Darcian porous wavy enclosure: effect of undulation

PurposeThe aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media saturated with Cu–Al2O3/water hybrid nanofluid and heated at the left wavy wall. The thermophysical phenomena are explored thoroughly by varying the amplitude (λ) and undulation (n) of the wavy wall and the inclination of the enclosure (γ) along with other pertinent physical parameters. Darcy–Rayleigh number (Ram), Darcy number (Da), Hartmann number (Ha) and nanoparticle volumetric fraction (ϕ). The effect of all parameters has been analyzed and represented by using heatlines, isotherms, streamlines, average Nusselt number and local Nusselt number.Design/methodology/approachThe finite volume method is used to work out the transport equations coupled with velocity, pressure and temperature subjected to non-uniform staggered grid structure after grid-sensitivity analysis by an indigenous computing code and the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The solution process is initiated following an iterative approach through the alternate direction implicit sweep technique and the tridiagonal matrix algorithm (TDMA) algorithm. The iterative process is continued until successive minimization of the residuals (<1e-8) for the governing equations.FindingsThis study reveals that the increase in the heating surface area does not always favor heat transfer. An increase in the undulation amplitude enhances the heat transfer; however, there is an optimum value of undulation of the wavy wall for this. The heat transfer enhancement because of the wall curvature is revealed at higher Ram, lower Da and Ha and lower volume fraction of nanoparticles. In general, this augmentation is optimum for four undulations of the wavy wall with an amplitude of λ = 0.3. The heat transfer enhancement can be more at the cavity inclination γ = 45°.Research limitations/implicationsThe technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc.Practical implicationsThis study is to address MHD thermo-fluid phenomena of Cu–Al2O3/water-based hybrid nanofluid flow through a non-Darcian porous wavy cavity at different inclinations. The amplitude and number of undulations of the wavy wall, permeability of the porous medium, magnetic field intensity, nanoparticle volumetric fraction and inclinations of the enclosure play a significant role in the heat transfer process. This analysis and the findings of this work can be useful for the design and control of similar thermal systems/devices.Originality/valueMany researchers have examined the problem of buoyancy-induced free convection in a wavy-porous cavity packed with regular fluids or nanofluids. However, the effect of magnetic fields along with the amplitude (λ) at different undulations (n) of the heated wavy wall of an inclined enclosure is not attended so far to understand the transport mechanisms. Most often, the evolutions of the thermo-fluid phenomena in such complex geometries invoking different multiphysics are very intricate. Numerical implementations for simulations and subsequent post-processing of the results are also challenging.

Numerical Study on Natural Convection of Alumina-water Nanofluid in a Square Cavity with Two Localized Heat Sources on Adjacent Surfaces

In the present work, results of a numerical study carried out using finite volume method, to investigate the fluid flow and heat transfer characteristics of Alumina ( Al2O3 ) nanoparticles in the base fluid (water) in a square cavity under natural convection mode are presented. The Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm was used to solve the discretized momentum and energy equations. Constant temperature heat sources of same strength are placed on bottom and left vertical surfaces whereas the right surface was kept cold, while the top surface was maintained as adiabatic. The impact of Rayleigh number (RaN) ( 1000 to 106 ) and nanoparticles volume fraction (Φ = 0 %, 5 %, 10 %, 15 % and 20 %) on fluid and heat flow characteristics were numerically investigated and presented in the form of streamlines, isothermal lines, mid line horizontal and vertical velocity components, local Nusselt number ( Nuloc ) and average Nusselt number ( Nuavg ). The obtained results indicate, for lower RaN ( i.e; 103 ), conduction dominates over convection near heated surfaces and results in lower fluid velocities and poor heat transfer. For higher values of RaN ( RaN = 105 and 106 ) and volume fraction of nanoparticles, there was a significant increase in mid horizontal and vertical velocity components, Nuloc and Nuavg due to increase in convective heat transfer and thermal conductivity of nanofluid.

Unsteady three dimensional radiative-convective flow and heat transfer of dusty nanofluid within porous cubic enclosures

Study of the convective transport of the dusty nanofluid is germane to dust ladder air, fluidization, gas cooling systems to enhance heat transfer process, environmental pollution, dust collection, sedimentation, and petroleum industry. Therefore, we aim in this article to deal with the transient three dimensional (3 D) radiative-convective flows and heat transfer of dusty nanofluid within porous cubic enclosures. Two systems of the differential equations are formulated for the nanofluid and dusty phases and two SIMPLE (Semi Implicit Method for Pressure Linked Equation) techniques are carried out for the distributions of the nanofluid and dusty pressures. The porous elements are the glass balls and the non-Darcy model is applied for the porous medium. All the porous properties are constants and taken into account during all the computations. The radiation flux is assumed in the normal direction and components of the system are in the thermal equilibrium state. The mixture is consisting of water as a host fluid and alumina as nanoparticles. The main findings revealed that the dusty parameters have significantly impacts on the heat transfer and hence they are important factors in such types of flows. Also, the increase in the nanoparticles volume fraction from 0% to 10% gives an enhancement in the average Nusselt number up to 12.88%.

Analysis of Turbulence on Cylinder with Additional Fairing with Free Surface

In this study, two dimensional unsteady flows of cylinder and cylinder with additional fairing close to a free surface were numerically investigated. The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE). The Volume of Fluid(VOF) method applied to simulate a free surface. Non- uniform grid structures were used in the simulation with denser grids near the cylinder. Under the conditions of Reynolds number 150624, 271123, 210874 and 331373, the cylinders were simulated with different depths of invasion. It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers. When the cylinder close to the free surface, the drag coefficient, lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding. With additional fairing, can effectively reduce the influence of the free surface on the drag coefficient. Fairing will reduce lift coefficient at high Reynolds numbers, but increase lift coefficient when Reynolds numbers are small. Fairing can effectively reduce Strouhal numbers, thus can well suppress the vortex induced vibration

Investigation of solution differences on natural convection in a tall cavity simulated by using the Boussinesq approximation and the real air density equation

Solution differences of natural convection in a tall cavity filled with air in which the density of the body force term are approximated by using the Boussinesq approximation (BA) and by using the real air density equation (RE) are numerically investigated. The main parameters for the investigation are Nusselt numbers and numbers of cells in the multi-cellular flow. The investigation is carried out for the Rayleigh number of 104, and the cavity aspect ratio equal to 60. The temperature differences of the vertical cavity walls are varied from 1 K to 200 K. These conditions are appropriate to form the multi-cellular flow in the tall cavity obviously, and close to the boundary of the laminar and turbulent flows. Consequently, the differences in both Nusselt numbers and numbers of the cells in the multi-cellular flow can be easily observed. The finite volume method with the Lagrange interpolating polynomial (LIP) scheme are selected to discretize the governing equations of the flow, and the Semi-implicit method for pressure linked equations (SIMPLE) algorithm is used to determine the pressure field of the flow. The maximum difference of the average Nusselt numbers of natural convection in the tall cavity simulated by using BA and RE is 0.436 % for the range of the investigation. This indicates that the difference of heat transfer solutions of natural convection in the tall cavity simulated by using BA and RE is insignificant for practical applications, but there is an obvious difference on the numbers of the cells in the multi-cellular flow, when the temperature difference of the vertical cavity walls is greater than or equal to 120 K.

Modeling and simulation of material distribution in the sequential co-injection molding process

Abstract In co-injection molding, the properties and distribution of polymers will affect the application of products. The focus of this work is to investigate the effect of molding parameters on the skin/core material distribution based on three-dimensional (3-D) flow and heat transfer model for the sequential co-injection molding process, and the flow behaviors and material distributions of skin and core melts inside a slightly complex cavity (dog-bone shaped cavity) are predicted numerically. The governing equations of fluids in mold are solved by finite volume method and Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm on collocated meshes, and the domain extension technique is employed in numerical method for this cavity to assure that the numerical algorithm is implemented successfully. The level set transport equation which is used to trace the free surfaces in co-injection molding is discretized and solved by the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme in space and 3rd-order Total Variation Diminishing Runger-Kutta (TVD-R-K) scheme in time respectively. Numerical simulations are conducted under various volume fraction of core melt, skin and core melt temperatures, skin and core melt flow rates. The predicted results of material distribution in length, width and thickness directions are in close agreement with the experimental results, which indicate that volume fraction of core melt, core melt temperature and core melt flow rate are principal factors that have a significant influence on material distribution. Numerical results demonstrate the effectiveness of the 3-D model and the corresponding numerical methods in this work, which can be used to predict the melt flow behaviors and material distribution in the process of sequential co-injection molding.

Assessment of VoF based numerical scheme for bubble rise in isothermal liquid layer, and some new insight in thermally stratified liquid layers

This paper aims at (a) comparative assessment of the different volume of fluid (VoF) based numerical schemes for a rising, single air bubble in isothermal liquid (water) layers and (b) investigation of bubble rise in thermally stratified liquid (therminol) layers. For numerical investigation of bubble rise in isothermal liquid layers, three available numerical schemes, Upwind, Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and Monotonic Upwind Scheme for Conservation Laws (MUSCL) schemes, combined with the pressure-velocity coupling(p-v) approaches, such as, Pressure Implicit with Splitting of Operators (PISO) and Semi Implicit Method for Pressure-Linked Equations (SIMPLE), are considered. The wake analysis revealed that the region of influence grows beyond 10 times the diameter of the bubble. Moreover, based on the comparative assessment, MUSCL scheme with PISO is selected, for investigating the bubble rise in thermally stratified therminol layers. Based on these investigations, a 3D diagram, describing bubble shape as f (Ra, Eo, Ga), is proposed, and a new insight to the micro-convection, inside the rising bubbles is provided. Furthermore, a time-scale analysis is performed to describe the heat transfer mechanisms, (a) inside air bubble, and (b) between air bubble and the external surrounding liquid. Thus, the findings will be useful for the design of heat exchangers or cooling devices, which rely on the heat transfer augmentation with rising air bubble.

Adapted SIMPLE Algorithm for Incompressible SPH Fluids With a Broad Range Viscosity.

In simulating viscous incompressible SPH fluids, incompressibility and viscosity are typically solved in two separate stages. However, the interference between pressure and shear forces could cause the missing of behaviors that include preservation of sharp surface details and remarkable viscous behaviors such as buckling and rope coiling. To alleviate this problem, we introduce for the first time the semi-implicit method for pressure linked equations (SIMPLE) into SPH to solve incompressible fluids with a broad range viscosity. We propose to link incompressibility and viscosity solvers, and impose incompressibility and viscosity constraints iteratively to gradually remove the interference between pressure and shear forces. We will also discuss how to solve the particle deficiency problem for both incompressibility and viscosity solvers. Our method is stable at simulating incompressible fluids whose viscosity can range from zero to an extremely high value. Compared to state-of-the-art methods, our method not only produces realistic viscous behaviors, but is also better at preserving sharp surface details.

Conjugate Heat Transfer Model Based on SIMPLE and Coupled Energy and Heat Equations

In this study, a numerical weak coupling strategy for the modeling of a conjugate heat transfer phenomenon is considered. Where the incompressible Navier-Stokes equations are solved using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) as a first step, and then the heat conduction equation for solid is solved in a second step considering the convective velocity field resulting from the first step. A finite-difference approach is used for both discretized time and spatial operators. In this paper, a two-dimensional simulation case study of a steady uniform streamwise flow around heated rectangular and triangle solids is presented. The simulation is forward in time until the steady-state regime is reached as the residuals converge and tend to zero. The spatial analysis of the temperature is obtained through the numerical resolution of the incompressible Navier-Stokes energy equation and the heat diffusion equation for the fluid and solid media, respectively. The results show the temperature, velocity, and pressure fields in the space domain. The code is written in MATLAB®, and the flow chart of the method is provided. It was noted that the convection was more dominant than the diffusion.

Local Thermal Nonequilibrium Natural Convection in a Cavity with Heat-Generating Porous Layer

Natural convection in a partially porous cavity with a heat generating source in the solid phase is studied numerically under a local thermal nonequilibrium condition. The right and left walls of the cavity are maintained at hot and cold temperatures, respectively. The horizontal walls are thermally insulated. The finite volume method and the semi-implicit method for pressure-linked equations (SIMPLER) algorithm are used to solve the conservation equations. The effects of relevant parameters, such as internal and external Rayleigh numbers , , interphase heat transfer coefficient , modified thermal conductivity ratio , and dimensionless porous layer thickness are discussed. The results revealed that at high values of the interphase heat transfer coefficient, the impact of an internal Rayleigh number on the dynamic and thermal fields decreases with an increase in the modified thermal conductivity ratio.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ТУРБУЛЕНТНОГО ТЕЧЕНИЯ В ЦЕНТРОБЕЖНОМ СЕПАРАТОРЕ

The numerical results of mathematical modeling of a two-phase axisymmetric swirling turbulent flow in a separation zone of a centrifugal separator are presented. The motion of the carrier gas flow is described by the Reynolds-averaged Navier-Stokes equations. A system of equations is enclosed by the Spalart-Allmaras turbulence model. The study is based on the obtained fields of averaged velocities of the carrier medium, with account for turbulent diffusion. Numerical solution to the problem is implemented using the semi-implicit method for pressure linked equations (SIMPLE). The results obtained when the solid phase effect on the air flow dynamics is taken into account are compared with those obtained when the effect is left out of account. The numerical calculations are validated using the experimental data.

The optimum interwell distance analysis of two-well-horizontal salt cavern construction

ABSTRACT Large-scale energy is often stored in underground salt caverns. Because China has abundant thinly bedded rocksalt, two-well-horizontal (TWH) caverns are considered as alternatives for large-scale energy storage, which possess higher construction rate and larger volume than the vertical caverns. To-date, the analysis of the development of shape and the control methodology with different interwell distances of TWH caverns are not fully understood. In order to eliminate these drawbacks, TWH-cavern construction has been simulated in the current work. A platform was established based on TWHSMC V2.0 simulation code to obtain the theoretical basis for TWH-cavern leaching construction for a more user-friendly visual analysis of the cavern development. Setting cavern construction efficiency as the objective functions for optimization, a series of theoretical simulations were conducted to analyze how the interwell distance affects the TWH-cavern construction. The results obtained illustrate that the interwell distance correlates with a rapid decrease in the leaching time until a tendency to stabilization is observed. The optimum interwell distance is 115 m at a flow rate of 300–500 cubic meters per hour. The interwell distance also influences the longitudinal span of the cavern. When the interwell distance is 115 m, the cavern has the smallest span in the longitudinal span. Therefore, the potential crossing of the interlayer can be minimized, which is good for the safety of cavern. Abbreviations: UGS: Underground gas storage; SPR: strategic petroleum reserves; CAES: Compressed air energy storage; SWV: Single-well-vertical; TWH: Two-well-horizontal; SIMPLE: Semi-Implicit Method for Pressure-Linked Equations; TWHSMC: Two-well-horizontal solution mining cavern; 2D: Two dimensional; VOF: Volume of Fluid; 3D: Three dimensional; API: American Petroleum Institute

Manninen’s mixture model for conjugate conduction and mixed convection heat transfer of a nanofluid in a rotational/stationary circular enclosure

PurposeThis study aims to investigate numerically the problem of conjugate conduction and mixed convection heat transfer of a nanofluid in a rotational/stationary circular enclosure using a two-phase mixture model.Design/methodology/approachHot and cold surfaces on the wall or inside the enclosure (heater and cooler) are maintained at constant temperature of Th and Tc, respectively, whereas other parts are thermally insulated. To examine the effects of various parameters such as Richardson number (0.01 = Ri =100), thermal conductivity ratio of solid to base fluid (1 = Kr = 100), volume fraction of nanoparticle (0 = φ = 0.05), insertion of conductive covers (C.Cs) around the heater in a different shape (triangular, circular or square), segmentation and arrangement of the conductive blocks (C.Bs) and rotation direction of the enclosure on the flow structure and heat transfer rate, two-dimensional equations of mass, momentum and energy conservation, as well as volume fraction, are solved using finite volume method and Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm.FindingsThe results show that inserting C.C around heater can increase or decrease heat transfer rate, and it depends on thermal conductivity ratio of solid to pure fluid. Also, it is found that by the division of C.B and location of its portions in a horizontal configuration, heat transfer rate reduces. Moreover, it is observed that external heating and cooling of the enclosure causes enhancement of heat transfer relative to that of internal heating and cooling. Finally, results illustrate that under the condition that cylinders rotate in the same direction, the heat transfer rate increases as compared to those that rotate in the opposite direction. Hence rotation direction of cylinders can be used as a desired parameter for controlling heat transfer rate.Originality/valueA comprehensive report of results for the problem of conjugate conduction and mixed convection heat transfer in a circular cylinder containing different shapes of C.C, conducting obstacle and heater and cooler has been presented. An efficient numerical technique has been developed to solve this problem. The achievements of this paper are purely original, and the numerical results were never published by any researcher.

Time-dependent economic risk analysis of the natural gas transmission pipeline system

A methodology to quantify the economic risk of a natural gas transmission pipeline system is developed in this study, and the effect of the line pack is considered. The methodology is based on the risk theory and hydraulic analysis of the transmission pipeline system. In the methodology, the failure probability of the key components in the transmission pipeline system are estimated firstly. Moreover, the transient compressible model for the pipeline system is employed to perform the consequence analysis, and the model is solved by the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm in the process of the consequence analysis. By combining the failure probability estimation with the consequence analysis, the economic risk when an accident happens can be evaluated. A detailed procedure for economic risk evaluation of a natural gas transmission pipeline system is presented, and its feasibility is confirmed with a real transmission pipeline system. Furthermore, impacts of the line pack on the economic risk are investigated, and suggestions to decrease the economy risk are proposed.

Local thermal nonequilibrium effect on nanofluid filled porous cavity subject to mixed convection heat transfer

AbstractIn this study, a numerical study is performed to determine the significance of local thermal nonequilibrium on mixed convection heat transfer of a copper water‐based nanofluid in an inclined porous cavity. By employing the nonequilibrium hypothesis, the governing equations for nanofluid flow in a porous medium are solved by the Semi‐Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. From the obtained results, the nanofluid flow and thermal characteristics are analyzed through streamlines and isothermal plots whereas the heat‐transfer rate of the system is scrutinized via the average Nusselt number.

Exergy Optimization of a Solar Collector in Flat Plate Shape Equipped with Elliptical Pipes Filled with Turbulent Nanofluid Flow: A Study for Thermal Management

In this paper, forced convection of a multiwalled carbon nanotube (MWCNT)–water nanofluid (NF) in a new flat plate solar collector (FPSC) equipped with elliptical pipes instead of circular ones is investigated. The three-dimensional conservation equations were solved in the domain with the finite volume method (FVM) based on the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The laminar-turbulent range of the Reynolds number (Re) and the volume fraction of the NF (ϕ) were 50–12,000 and 0–0.1, respectively. The optimization process was accomplished through the comparison of diverse parameters to attain the optimal case with the highest exergy efficiency. In this study, it was concluded that, in the case of using elliptical pipes instead of circular tubes, the time that the fluid was inside the FPSC increased, which led to an increase in the outlet temperature, while the exergy efficiency of the FPSC increased. Additionally, it was observed that using elliptical pipes enhanced the outlet fluid temperature, energy efficiency, and exergy efficiency. Generally, while the trend of exergy efficiency variation with effective parameters was rising, applying elliptical pipes caused the efficiency to increase. In addition, the exergy efficiency variation decreased when these parameters were changed. The highest value of exergy efficiency was 7.1%. On the other hand, for each specific FPSC, there was a unique mass flow rate at which the exergy efficiency reached its maximum value, and for higher mass flow rates, the efficiency was slightly diminished and then remained unchanged. Finally, the highest exergy efficiency was achieved for ϕ = 0.10%.

Flow structure around two tandem square cylinders close to a free surface

In this study, two dimensional unsteady flow between and in the downstream region of two tandem cylinders close to a free surface was numerically investigated. The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations (SIMPLE). To simulate a free surface, the Volume of Fluid (VOF) method was used. Central differences and Quadratic Upwind Interpolation (QUICK) methods were applied to discretize the viscous and convective terms respectively. Non-uniform grid structures were used in the simulation with denser grids near the free surface, bottom plate, and in the vicinity of the cylinders. The working fluid was water (Fr = 0.3). The degree of submergence of the cylinders (G) ranged from 0.25D to 5.5D, the distance between the cylinders (L) ranged from 1.5D to 4.0D, and the channel depths (H) were 16D, 8D and 4D. The simulations were performed for the Reynolds numbers of 180, 250 and 400. It was shown that the flow characteristics were influenced by the submergence depth, the distance between the cylinders and the depth of the channel as well as by the Reynolds numbers. As the distance to the free surface increased, the vortices in the downstream region were formed at longer distances. As the flow depth decreased, the flow parameters on the cylinders (CDmean, CLmax, and St) increased due to the influence of the boundary layer that was formed on the bottom wall. When the distance between the cylinders was increased (L/D = 4), the cylinders had higher CDmean and CLmax values as the vortex was formed between the cylinders. Increases were observed in all flow parameters as the Re number increased.

Influence of Dimple Height on Turbulent Heat Transfer of Fin Array with Alternate Convex/Concave Dimples

This study analyzes transient turbulent modeling of three-dimensional multiple dimpled fin array using large eddy simulation (LES). The Navier–Stokes equations as well as the energy equation were constructed by the finite volume method and then discretized to form algebraic equations, which were solved by semi-implicit method for pressure-linked equation (SIMPLE). The solutions of temperature and velocity were obtained by iterating computation until it converged within each step. This simulation places nine fins on the bottom surface of a channel and changes the height of the dimple (0.4, 0.8, and 1.2 mm) with three different levels of Reynolds number (Re) (3500, 5000, and 6500) to investigate the temperature and flow field without gravity in forced convection. The results indicate that the dimpled fin array can generate vortices between the convex/concave dimples and the fin base and increase the influences of the height of the dimple on the flow field around the fin array. The averaged time-mean of the Nusselt number (Nu) for the dimple height of 0.8 mm is higher than that of the no-dimple case up to 14.4%, while the averaged time-mean Nu for the dimple height of 1.2 mm is lower than that of the no-dimple case up to 11.6%.

Numerical Study of the Heat Transfer Behavior in Helical Microcoil Tube

This work introduces a numerical study of the convective heat transfer of helical micro coils tube heat exchanger coil. It tested for both circle and elliptical geometry with 18 mm pitch and diameter of copper pipes. It is very difficult and time-consuming if these analyses could be carried out experimentally. Water is used as a working fluid by using 80°C for hot water and 25°C for cold water. The Reynolds number selected in the range of 200 to 1800 for hot water, while specified 5000 for cold water. ANSYS-FLUENT 18.0 has been used to investigate the heat transfer behavior. In computational fluid dynamics (CFD), the partial differential equations was represented by using the finite volume method (FVM) in the form of algebraic equations and the Navier-Stokes equations were solved by using a numerical procedure which is the Semi Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The elementary results observed a proportionality relationship between the heat transfer and the Reynolds number raised values. Also, the circular configuration present maximum heat transfer performance and the maximum values are 5.6, 3.42 for Thermal performance factor and Nuselte number respectively at Reynolds number 1800.

A numerical study of mixed convection heat transfer in a lid-driven cavity using Al2O3-water nanofluid

This study aims a numerical investigation of steady, laminar mixed convection heat transfer in a two-dimensional cavity by employing a finite volume method with a fourth-order approximation of convective terms, when nanoparticles are present. With the aim of solving two-dimensional momentum and energy conservation equations, a finite volume method on a non-uniform staggered grid is utilized. Second-order central differences are utilized to approximate diffusion terms in momentum and energy equations, while the development of a non-uniform four-point fourth-order interpolation (FPFOI) scheme is performed for the convective terms. Continuity and momentum equations are solved using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. In order to evaluate heat transfer enhancement, various viscosity and thermal conductivity models were employed. Numerical solution results were obtained in different models in cases where Gr number is between 103 and 105, Re number is 10-100-1000 and nanoparticle volumetric fraction is 0-5%.