Exponential Heat Research Articles

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Impact of Exponential Heat Source and Thermal Radiation on the flow of Hybrid Nanofluid across a Bi-Directional Stretching Surface with Activation Energy

The study focuses on how activation energy and exponential heat source affects the radiative motion of a hybrid nanofluid (EG + ZnO + TiO 2) over a bidirectional elongating sheet. Convective boundary condition is assumed. The bvp4c, an inherent function in MATLAB, is used to unravel the altered system deduced from those equations which describe the current work in the two scenarios, i.e., binary (EG + ZnO + TiO 2) and mono (EG + ZnO) nanofluids. Added a little quantitative discussion regarding engineering parameters including Sherwood number. The most notable findings from this study are mentioned here. Enhanced volume fraction of ZnO lessens the fluid velocity and increasing heat source parameter step-up the fluid temperature. It was noticed that with a raise in magnetic field and the volume fraction of ZnO lessens the friction factor. The rate of mass transfer is lowered with the enhanced activation energy parameter and the same enhances as the reaction rate parameter is amplified. The increment quantities in the Sherwood number against the reaction rate parameter (Γ) are 0.35151 (EG + ZnO + TiO 2) and 0.35125 (EG + ZnO), when Γ is set to 0 ≤ Γ ≤ 0.9. Furthermore, the decrement rates in mass transfer rate against the activation parameter (En ) are observed as 0.02681 (EG + ZnO + TiO 2) and 0.02687 (EG + ZnO), when En is set to 0 ≤ En ≤ 2.5. It is detected that there is an amelioration in the heat transmission rate with the raise in Biot number (Bi). It has been noticed that, when Bi fixed to be 0 ≤ Bi ≤ 0.8, Nusselt number is lowered by 0.736332 (EG + ZnO + TiO 2) and 0.621826 (EG + ZnO). Our findings are checked against previous findings for validity. A reasonable compromise has been uncovered.

Magnetohydrodynamics tangent hyperbolic nanofluid flow across a vertical stretching surface using Levengberg-Marquardt back propagation artificial neural networks

This analysis uses the Levenberg-Marquardt back propagation artificial neural networks (LM-BP-ANNs) approach to demonstrate the mathematical strategy of neural networks for the simulation of MHD Tangent hyperbolic nanofluid (THNF) flow consisting of motile microorganisms through a vertically extending surface. The fluid flow is being investigated in terms of exponential heat source/sink, thermal radiation, and magnetic field. The modeled equations are relegated to the ordinary system of differential equations by substituting similarity variables. The ND-solve approach is applied for the modeled equations to numerically handle and generate a dataset. Several activities, including testing, verification, and training, are performed by creating a scheme for various fluid problems using reference data sets. The precision of LM-BP-ANNs is evaluated using mean square error, curve fitting error histogram, and the regression analysis plot. Furthermore, graphs are used to analyze flow parameters for concentration, momentum, and energy profiles. It has been observed that the velocity field declines as the magnetic field grows stronger. The THNF model for energy, mass, and momentum equations is tested, authenticated, and trained within an average of 10−9. The LM-BP-ANNs accomplish the highest accuracy, with a target date and absolute error reference values in the 10−4 to 10−5 range.

Lie group analysis on EMHD Jeffrey nanofluid flow with exponential heat source: Heat transfer optimization using RSM

The present research examines the behavior of a Jeffrey nanofluid flow across a stretching sheet under the effect of electric and magnetic fields. It comprises the Buongiorno model as well as an exponential heat source. The impact of chemical reaction has also been taken into consideration. While assuming no mass flux, the study considers boundary conditions for thermal convection and velocity slip. Lie group transformations are employed to transform the set of governing equations into a dimensionless system and later simulated using the finite difference scheme. It is found that the velocity profile rises as the Deborah number is enhanced whereas the ratio of relaxation to retardation time parameter has an inverse effect on the velocity profile. It is noted that per unit change in the Deborah number descends the drag coefficient by 31.29%. In this study, the response surface methodology and sensitivity analysis have been conducted by choosing heat transport as the dependent variable and the electric-field parameter ( 0.01 ≤ E ≤ 0.03 ) , exponential heat source parameter ( 0.02 ≤ Qe ≤ 0.06 ) , and Biot number ( 0.15 ≤ Bi ≤ 0.25 ) as the independent variables. The Nusselt number escalates when the Bi number is increased and drops as the E values are raised. In the instance of the Biot number, the Nusselt number exhibits the maximum sensitivity.

Darcy Forchhiemer imposed exponential heat source-sink and activation energy with the effects of bioconvection over radially stretching disc

The Darcy–Forchheimer model is a commonly used and accurate method for simulating flow in porous media, proving beneficial for fluid separation, heat exchange, subsurface fluid transfer, filtration, and purification. The current study aims to describe heat and mass transfer in ternary nanofluid flow on a radially stretched sheet with activation energy. The velocity equation includes Darcy–Fochheimer porous media effects. The novelty of this study is enhanced by incorporating gyrotactic microorganisms which are versatile and in nanofluid can greatly improve the thermal conductivity and heat transfer properties of the base fluid, resulting in more efficient heat transfer systems. Furthermore, the governing PDEs are reduced to ODEs via appropriate similarity transformations. The influence of numerous parameters is expanded and physically depicted through the graphical illustration. As the Forchheimer number escalates, so do the medium's porosity and drag coefficient, resulting in more resistive forces and, as a result, lowering fluid velocity. It has been discovered that increasing the exponential heat source/sink causes convective flows that are deficient to transport heat away efficiently, resulting in a slower heat transfer rate. The concentration profile accumulates when the activation energy is large, resulting in a drop in the mass transfer rate. It is observed that the density of motile microorganisms increases with a rise in the Peclet number. Further, the results of the major engineering coefficients Skin-friction, Nusselt number, Sherwood number, and Microorganism density number are numerically examined and tabulated. Also, the numerical outcomes were found to be identical to the previous study.

Transient MHD Darcy-Forchheimer of Williamson-Casson flow with CCS: Application of wastewater treatment

With regards to the Cattaneo-Christoph (CCS) speculation, the thermal and mass transfer of a MHD Williamson-Casson ferrofluid flow through a permeable medium obeying the Darcy-Forchmeier law through an extended chamber or slab is carefully considered. The chemical reaction and Buongiorno nanofluid model were modified in the model to describe the nanoscale properties of liquid particles. Heat sources can be divided into two categories: linear and exponential space-dependent convection heat sources. The entire governing equations are changed to common differential terms, using a reasonable similarity change. These equations and their associated boundary conditions are calculated numerically via the fourth-order Runge-Kutta method. Comparison was made with the analytical solution in a special case, and very good agreement was reached. Economic success with deeper water purification can be attained by developing models for wastewater treatment facilities, conducting experiments and calculations on them, and making predictions for their nature in order to improve their cleaning efficiency, Prevent issues from arising during construction, operation, and reconstruction. The structural parameters of the quencher were physically modeled using mathematical modeling; It is possible to establish a cost-effective and effective filter model for industry and small settlements using the calculations and vertical filter model created in the article. Furthermore, it will be feasible to produce. Our mathematical procedure assure that: the deposit’s mass will be diminished through treated water under attractive field impacts; The magnetic field openness with nanometer-sized particles modifies the physical and synthetic properties of water particles bringing about exceptional characteristics; the water concentration will be decreased with the increase in the bending modulus; This means that in wastewater treatment the sediment mass will decrease.

Numerical investigation of MHD hybrid nanofluid flow with heat transfer subject to thermal radiation across two coaxial cylinders

Numerically the hybrid nanofluid (HNF) flow comprised of aluminum alloys (AA7072 and AA7075) across to coaxial cylinders is reported in the current analysis. The fluid flow has been examined under the significances of viscous dissipation, thermal radiation, and exponential heat source/sink. The HNF is produced by the addition of AA7072 and AA7075 nanoparticles (NPs) in water. Aluminum alloys are mostly used for the electric module wrapping, electronic machinery, automotive body, solar and wind energy controlling, and energy generation. The flow has been modeled in the form of momentum, continuity, and energy equations. Numerical approach parametric continuation method (PCM) is used to solve the modeled equations. The consequences of flow and energy parameters on the temperature, velocity, skin friction, and Nusselt number have been revealed through figures. It has been noticed that the fluid velocity drops, whereas the energy curve develops with the escalating influence of magnetic field. Furthermore, the rising numbers of AA7072 and AA7075 NPs in the water diminish the fluid velocity and temperature profile. Energy curve accelerates with the growing values of Brinkman number. It can be observed that the energy transmission rate upsurges up to 13.17% by the addition of AA7072 and AA7075 NPs in the water.

Analytical simulation of Darcy–Forchheimer flow of hybrid nanofluid through cone with nonlinear heat source and chemical reaction

This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH3OH), nanoparticles of titanium oxide (TiO2) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases.

Irreversibility scrutiny of SWCNT and MWCNT nanofluid convective flow using Darcy-Forchheimer rule in an upright microchannel with variable thermal conductivity and Brownian motion and thermophoresis

Carbon nanotubes are used to attain greater thermal transfer rates in a various of enormous applications in the field of microsystem, emission, conductive polymers, fibers, and fabrics. Hence the aim of this article is to explore the entropy generation analysis of single wall carbon nanotubes and multiwall carbon nanotubes flow in an upright micro channel with variable thermal conductivity. The exponential heat source and non-linear thermal radiation were considered. The micro channel retains the no slip and convective boundary conditions. The Buongiorno model was used in this study, which emphasizes the light on Brownian motion and thermophoresis phenomena that occur during the fluid flow. Darcy- Forchheimer model is also taken into account. The governing equation numerically solved by employing Runge-Kutta Fehlberg's fourth-fifth order. The repercussion of this study upholds that the inflates of variable thermal conductivity magnify the thermal field. Entropy production inflates at right wall of the channel with augmented Brownian parameter and exhibits exactly opposite behavior at left wall of the channel. One of the important tasks of the investigation was to compare SWCNT and MWCNT. The findings confirmed that multiwall carbon nanotubes exhibit more magnificent heat and mass transfer than single wall carbon nanotubes.

Time-dependent stagnation point flow of nano Casson fluid with Joule heating over an elongated surface subjected to viscous heating and exponential space-based heat source/sink: Boungiorno model

The unsteady two-directional flow of a non-Newtonian magneto-Casson nanoliquid flow over an elongated flat surface with the porous matrix is investigated. The flow is subjected to space-based exponential heat generation/absorption (ESHS), thermophoresis, Brownian motion of nanoparticles, and transverse magnetic field. Within the base fluid, the diffusion of chemically reactive nanoparticles is assumed to be highly significant; hence considered. The governing equations of the flow model admit self-similar equations and are numerically solved by employing the Runge-Kutta-based shooting technique (RKSM). The significance of key parameters on the temperature, velocity, friction factor at the surface, heat transfer rate, and mass transfer rate distributions is analyzed. The use of high-Prandtl number base fluid and nanoparticles of high thermal conductivity could be of practical use to increase the heat transfer rate and avoid nanoparticle accumulation. The occurrence of nanoparticles in the operating liquids reduces the shearing stress at the plate surface to avoid backflow.

Significance of Inclined MHD on Hybrid Nanoliquid Flow in an Annulus Using Modified Buongiorno Model in the Presence of Two Different Heat Sources: Response Surface Methodology

In this modern fluid field technology, hybrid nanoliquid are of great interest to researchers because of their thermal properties which provide superior heat transfer improvements compared to nanoliquid. Thus, in this study, the heat and mass transport characteristics in a horizontal annular duct filled with the water-based Cu–Al2O3 hybrid nanoliquid is analyzed using the modified Buongiorno model (two-phase model). The two different heat sources namely, temperature-related heat source (THS) and exponential space-related heat source (ESHS) are analyzed in thermal analysis. An inclined magnetism and viscous dissipation aspects are also taken into account. The correlation for effective thermal conductivity and viscosity are modeled by utilizing the experimental work of Corcione. The coupled nonlinear equations were solved numerically using the finite difference method. Further, the heat transport rate is optimized using the response surface methodology (RSM). The significance of effective parameters on the flow structure, thermal pattern, concentration field, heat and mass transport rate are visualized through two-dimensional (2D) and three-dimensional (3D) surface plots. It is noticed that the chaotic motion of nanoparticles advances the thickness of the thermal and solutal boundaries. The velocity field has an inverse association with the applied magnetic field and its angle of inclination. The consequence of the Reynolds number is favorable for the velocity and temperature fields. The heat transport is more dominated by the Reynolds number compared to the chaotic motion of nanoparticles and thermophoretic aspect. Furthermore, the sensitivity of the Nusselt number to the Reynolds number, chaotic motion of nanoparticles and thermophoretic aspect are always negative.

Illustration of activation energy and exponential heat source on the conducting viscous fluid through an expanding surface

In the current scenario, this investigation deal with the illustration of the advanced heat source properties influenced by exponential distribution for the inclusion of activation energy in the flow of viscous conducting fluid over an expanding surface. The flow through porous matrix is also characterized by the heat dissipation formulated due to viscous, Joule, and Darcy effects. Due to the consideration of the transverse magnetic field, and porous matrix, the effect of Joule and Darcy dissipations cannot be neglected. However, the novelty arises for the investigation that characterizes its key role to optimize the transport properties in numerous industrial application that be governed by the external heat source, which is beneficial for the better shape of the product and size of the manufacturing products. The dimensionless form of the proposed model associated with various flow properties is solved numerically employing shooting based “ Runge-Kutta fourth-order.” The illustration of the features of the various components associated in the present profiles is deployed graphically and the numerical computation of shear rate vis-a-vis other rate coefficients are presented in the tabular form. Finally, the important outcomes of the study deployed as; the velocity profile augments with the increasing thermal buoyancy as well as the ratio of the volumetric coefficient and the enhanced Lewis number combined with the reaction coefficient augments the solutal rate.

Darcy-Forchheimer hybrid nanofluid flow in an asymmetric channel with an exponential heat source, variable thermal conductivity, and activation energy

Background Heat transfer in nanofluid flows plays a vital role in many industrial, medical, and manufacturing industries. Hybrid nanofluid (HNF) has a significant potential to enhance the thermal characteristics of several fluids employed in a wide range of thermal systems and thus uses reduced energy and provides increased sustainability. Also, the thermal conductivity of nanofluid depends on the mobility of nanoparticles and that can be improved by activation energy (AE) besides the latent micro convection. Literature reveals that the research works available on the enhanced heat transfer due to the appropriate combination of nanoparticles along with AE in an asymmetric channel is very limited. Aim This study aims to explore the impact of the AE and the variable thermal conductivity (VTC) on the HNF flow in an asymmetric channel with permeable walls. The effects of radiation, thermal conductivity, and exponential heat sources are also considered. Method An effective similarity transformation is used to convert the governing equations into a system of nonlinear ordinary differential equations (ODEs). The nonlinear ODEs with appropriate boundary conditions are solved numerically by a shooting method. Results The consequences of the physical parameters on the axial velocity, temperature, and species concentration are explained and are presented through graphs. In comparison to viscous fluid, the dual nanofluids have a 5.8% higher heat transfer rate with VTC parameter at the lower wall. However, the species concentration rate of HNF is 20.0% higher than that of viscous fluid with AE parameter.

NUMERICAL SIMULATION OF 3D DARCY-FORCHHEIMER HYBRID NANOFLUID FLOW WITH HEAT SOURCE/SINK AND PARTIAL SLIP EFFECT ACROSS A SPINNING DISC

The current study explains the numerical simulation for the Darcy-Forchheimer (DF) hybrid nanofluid (HNF) flow across a permeable rotating disc. The HNF is prepared with the addition of AA7072 and AA7075 (aluminum alloys) nanoparticles (NPs) in water. Aluminum alloys are frequently used in aircraft parts like fuselages and wing flaps due to their lightweight and durability. Additionally, making M16 rifles for the American military is another intriguing application of aluminum alloys. The fluid flow has been estimated with the significances of thermal radiation, DF effect, viscous dissipation, thermal slip condition, and exponential heat source/sink. The modeled equations are simplified to an ordinary system of differential equations (ODEs) by substituting similarity variables. The obtained set of equations is solved using the parametric continuation method (PCM). It has been noticed that with the HNF, both the radial and axial velocity diminishes with the upshot of the porosity parameter and DF term. The velocity and temperature fields reduce with the rising numbers of aluminum alloys (AA7072 and AA7075).

Overview of solar thermal applications of heat exchangers with thermophysical features of hybrid nanomaterials.

With their notable thermal characteristics, fluids incorporating nanoparticles have significant importance in industrial processes. Due to the higher proficiency of hybrid nanofluid, this study is organized to observe the flow phenomenon and thermal characteristics of kerosene-oil-based hybrid ferrofluid in relation to the modified versions of two imperative Yamada-Ota and Xue models. A performance-based comparison is conducted for an incompressible hybrid ferrofluid in relation to the upgraded Yamada-Ota and Xue models. The magnetized flow mechanism in two dimensions is explored over a stretchable, curved sheet. With the ordinary kerosene oil liquid, the ferroparticles, namely cobalt ferrite and magnetite, are merged to form (CoFe2O4-Fe3O4/kerosene oil) hybrid ferrofluid. Mass and heat transport mechanisms are scrutinized with the execution of activation energy, convective constraints, Joule heating, exponential heat sources, and thermal radiation. Suitable ansatzes are utilized to achieve the dimensionless pattern of the equations that regulate the problem. To numerically explore the dimensionless equations, a powerful bvp4c strategy is implemented. On behalf of both considered models, the characteristics of hybrid ferrofluid relative to pertinent parameters are graphically investigated and comparatively analyzed. This study ensures that the improved Yamada-Ota model yields more proficient outcomes in comparison to the Xue model. Moreover, the concentration field demonstrates an escalating trend with the enhanced activation energy parameter.

Heat Transfer Augmentation for Impingement of Steady Air Jet under Exponential Heat Flux Boundary Condition

Heat Transfer Augmentation for Impingement of Steady Air Jet under Exponential Heat Flux Boundary Condition

Numerical Study of Nonlinear Convective Heat Transfer Flow of Metal Oxide Nanoparticle TiO<sub>2</sub>-Enhanced Fluid between Two Concentric Cylinders with Aggregation of Nanoparticles

The utilization of nanofluid is one of the most used techniques for improving heat transfer in applications like heat exchangers, heat storage systems, mining and nuclear power plants. Because of high thermal conditions, the density relation of the working fluids may not be linear, therefore, an analysis is conducted on the quadratic convection of nanofluid flow in a porous annulus region considering an inclination. The phenomenon of temperature-dependent viscosity on the flow, kinematics of nanoparticle aggregation, and heat transport phenomenon with Exponential Space-Related Heat Source (ESHS) and a Temperature-Related Heat Source (THS) are considered. The governing equations are solved numerically. The influence of key parameters is analyzed using 2D and 3D graphs.

Significance of heat passage in four-phase Oldroyd-B nanofluid with solar thermal radiations through a cone: A study of entropy analysis

The studies of non-Newtonian fluids are extremely important because of their unlimited and extensive usage and applications in different mechanisms and processes. The current work carried out the visualization of thermal energy in the Oldroyd-B fluid model by inserting different types of nanoparticles, which are used to promote thermal performance. The flow is assumed to be passed through a cone with electro-magneto-hydrodynamic effect and thermal radiation and exponential external heat source. The modeled problem appears in the form of coupled nonlinear PDEs, which are transformed into corresponding ODEs by engaging the appropriate transformation. The solution of these transformed equations is calculated by using the finite element procedure. The utilization of tetra-hybrid nanoparticles improves the thermal performance and it is recorded that by inserting these particles fluid temperature increases significantly. It is worth mentioning that a finite element scheme is an authentic procedure to tackle highly nonlinear problems. The influence of multiple parameters such as M,E*,γ1,γ2 are examined and discussed in detail across the velocity profile whilst parameters behavior namely M,Ec,E* and Qs is observed graphically across the temperature profile. It was noticed through computed results that the velocity profile depicts enhanced behavior for E*,γ1,γ2 whereas, it illustrates reduced demeanor. Moreover, the Temperature profile illustrates accelerated behavior for M,Ec,E* and Qs. Moreover, skin friction and Nusselt number impact under distinct parameters are also presented graphically and show excellent agreement.

Energy transmission through radiative ternary nanofluid flow with exponential heat source/sink across an inclined permeable cylinder/plate: numerical computing

The steady two-dimension (2D) ternary nanofluid (TNF) flow across an inclined permeable cylinder/plate is analyzed in the present study. The TNF flow has been examined under the consequences of heat source/sink, permeable medium and mixed convection. For the preparation of TNF, the magnesium oxide (MgO), cobalt ferrite (CoFe2O4) and titanium dioxide (TiO2) are dispersed in water. The rising need for highly efficient cooling mechanisms in several sectors and energy-related processes ultimately inspired the current work. The fluid flow and energy propagation is mathematically described in the form of coupled PDEs. The system of PDEs is reduced into non-dimensional forms of ODEs, which are further numerically handled through the Matlab package (bvp4c). It has been observed that the results display that the porosity factor advances the thermal curve, whereas drops the fluid velocity. The effect of heat source/sink raises the energy field. Furthermore, the plate surface illustrates a leading behavior of energy transport over cylinder geometry versus the variation of ternary nanoparticles (NPs). The energy dissemination rate in the cylinder enhances from 4.73 to 11.421%, whereas for the plate, the energy distribution rate boosts from 6.37 to 13.91% as the porosity factor varies from 0.3 to 0.9.

Heat transfer optimization and rheological features of Buongiorno nanofluid in a convectively heated inclined annulus with nonlinear thermal radiation

The theoretical analysis of the mixed convective Buongiorno nanofluid flow in an inclined annular microchannel with convectively heated walls subjected to the effects of nonlinear thermal radiation, exponential heat source (EHS), thermal dependent heat source (THS) is carried out. The description of the Buongiorno nanofluid is implemented to analyze the Brownian diffusion and thermo-migration mechanisms. The general boundary conditions for the velocity, thermal, and nanoparticle volume fraction (NVF) are considered. Numerical solutions for fully developed governing equations are obtained using bvp5c solver and verified with FEM. The optimization of heat transport rates is made by using the Box-Behnken design-based response surface method. It is found that the Lorentz force and the inclination angle of the annulus significantly affect the rheological characteristics of the nanofluid. Nanoparticles increase thermal energy in the system through Brownian diffusion and thermophoresis, resulting in increased temperature field. Internal heat sources would serve as an important tool for modulating the thermal field in microchannel, as they are directly associated. At low-level values of the thermal Biot number, the exponential heat source, and the thermal radiation parameter, it is possible to attain the maximum Nusselt number on both walls of the annulus.