Numerical Results Research Articles

A Multilinear HJB-POD Method for the Optimal Control of PDEs on a Tree Structure

Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is via the Dynamic Programming principle. Nevertheless, despite many theoretical results, this method has been applied only to very special cases since it suffers from the curse of dimensionality. Our goal is to mitigate this crucial obstruction developing a version of dynamic programming algorithms based on a tree structure and exploiting the compact representation of the dynamical systems based on tensors notations via a model reduction approach. Here, we want to show how this algorithm can be constructed for general nonlinear control problems and to illustrate its performances on a number of challenging numerical tests introducing novel pruning strategies that improve the efficacy of the method. Our numerical results indicate a large decrease in memory requirements, as well as computational time, for the proposed problems. Moreover, we prove the convergence of the algorithm and give some hints on its implementation.

Magnetization States and Coupled Spin-Wave Modes in Concentric Double Nanorings

Concentric multiple nanorings have previously been fabricated and investigated mainly for their different static magnetization states. Here, we present a theoretical analysis for the magnetization dynamics in double nanorings arranged concentrically, where there is coupling across a nonmagnetic spacer due to the long-range dipole–dipole interactions. We employ a microscopic, or Hamiltonian-based, formalism to study the discrete spin waves that exist in the magnetic states where the individual rings may be in either a vortex or an onion state. Numerical results are shown for the frequencies and the spatial amplitudes (with relative phase included) of the spin-wave modes. Cases are considered in which the magnetic materials of the rings are the same (taken to be permalloy) or two different materials such as permalloy and cobalt. The dependence of these properties on the mean radial position of the spacer were studied, showing, in most cases, the existence of two distinct transition fields. The special cases, where the radial spacer width becomes very small (less than 1 nm) were analyzed to study direct interfaces between dissimilar materials and/or effects of interfacial exchange interactions such as Ruderman–Kittel–Kasuya–Yoshida coupling. These spin-wave properties may be of importance for magnetic switching devices and sensors.

Experimental and numerical investigation of low‐velocity impact behavior and failure mode of shear deficient RC beam strengthened with CFRP strips

AbstractIt is well‐known that shear failure is a collapse mechanism that is the riskiest, fastest, and catastrophic and occurs with no visible signs of damage or prior warning for RC beams. Therefore, to prevent brittle shear failure, the RC beams should include sufficient shear reinforcement, such as stirrups, and be designed to have sufficient shear capacity. However, the RC beams' shear capacity becomes inadequate for various reasons. One of these reasons may be the acting of the impulsive impact load, which is uncommon and disregarded in the design phase on the RC beams. An experimental program was conducted to examine the impact behavior and failure mode of shear‐deficient RC beams in the scope of the present study. Besides, it aims to investigate the effectiveness of the strengthening method using CFRP strips in improving the general behavior, failure mode, and performance of shear‐deficient RC beams exposed to impact load. The time histories of the accelerations, displacements, impact loads, and strains in the CFRP strips were measured. They were interpreted how they are affected by experimental variables examined in the experimental study. Furthermore, the finite element model of the specimens was generated in the LS‐DYNA software, and the experimental and numerical results were compared by performing finite element analysis in terms of failure modes and general behavior.

Composite metastructure with tunable ultra-wide low-frequency three-dimensional band gaps for vibration and noise control

Low-frequency vibration and noise control present enduring engineering challenges that garner extensive research attention. Despite numerous active and passive control solutions, achieving multiple ultra-wide attenuation regions remains elusive. Addressing vibration and noise control across a multidirectional broad low-frequency spectrum, three-dimensional metastructures have emerged as innovative solutions. This study introduces a novel three-dimensional composite metastructure featuring multiple ultra-wide three-dimensional complete band gaps. The research emphasizes the design strategy of elastic ligaments to achieve multiple ultra-wide attenuation regions spanning from 0.7 to 40 kHz. The band structures are elucidated through modal analysis and further substantiated by an analytical model based on a spring-mass chain with an additional resonator. The underlying physical mechanism for the formation of multiple ultra-wide band gaps is revealed through novel vibration modes from finite element analyses. Furthermore, we demonstrate that the distribution and the relative width of the ultra-wide band gaps can be tuned by modifying the geometric parameters of the metastructure. Utilizing additive manufacturing, prototypes are fabricated, and low-amplitude vibration tests are conducted to evaluate real-time vibration attenuation properties. Consistency is observed among theoretical, numerical, and experimental results. The proposed structure shows significant potential for high-performance meta-devices aimed at controlling noise and vibration across an extremely wide low-frequency spectrum.

A-332 Identifying At-Risk Patients Pre-IV Contrast Administration via POCT Creatinine Measurement

Abstract Background The use of intravenous iodinated contrast in computerized tomography studies is associated with a small risk of acute kidney injury. Pre-existing chronic kidney disease is a recognized factor and assessment of renal function prior to contrast administration is essential. This study assessed the ability of the Abbott iSTAT creatinine assay to correctly identify IV-contrast patient risk using lab-based eGFR as the gold standard. Methods This was a retrospective study comparing POCT creatinine (whole blood, Abbott iSTAT enzymatic) and lab creatinine (plasma, Beckman Coulter AU5800 Jaffe) results on simultaneous samples collected in the emergency department. Anonymised data records were extracted from the laboratory database for 2020-2023. IV contrast risk was calculated using eGFR (CKD-EPI 2021) and classified as high risk (HR: eGFR < 30 mL/min/1.73 m2), moderate risk (MR: eGFR 30-59) and low risk (LR: eGFR >=60) as per the Royal Australian and New Zealand College of Radiologists 2018 guidelines, using the Beckman-based eGFR as the gold standard. Results 132 paired samples patients were available for analysis (61% male, average age 69 y (23-98), 70% Chinese, eGFR (iStat) 3-143, eGFR (Beckman) 3-121 mL/min/1.73 m2). The proportions of Beckman-based eGFR HR:MR:LR cases were 53:39:40. The prevalence of HR/MR cases was 70%. The diagnostic performance of the iSTAT-based eGFR to accurately identify HR/MR patients was: sensitivity 93.5%, specificity 95%, PPV 97.7%, NPV 86.4%, accuracy 93.9%. For different Beckman-derived eGFR categories, the mean difference in eGFR (iSTAT - Beckman), 95% lower limit of agreement (LOA) and upper LOA was: <30 mL/min/1.73 m2: -1.0, -3.2, -1.1; 30-60 mL/min/1.73 m2: 0.9, -13.3, 15.1; >60 mL/min/1.73 m2: 1.6, -16.8, 20.1. Linear regression fit (Passing-Bablok): CKD-EPI Beckman = 1.193 + 0.9773 CKD-EPI iSTAT. Correlation coefficient was 0.981. Kappa for the 3 categories of risk classification was 0.814. Conclusions The iSTAT creatinine assay could reliably identify patients at medium/high risk of acute kidney injury following intravenous contrast administration. Performance was best for low and high risk patients with 100% of high risk patients being correctly identified. It is a useful screening test but differences in eGFR of up to 20 mL/min/1.73 m2 may be seen between the Beckman and iSTAT eGFR values at higher levels, meaning numeric eGFR results are not interchangeable.

Improving extensions for the global uniform asymptotic stability of continuous-time nonlinear systems

This paper considers the classical problems of global asymptotic stability (GAS) of nonlinear autonomous (time-invariant) systems and global uniform asymptotic stability (GUAS) of nonlinear non-autonomous (time-varying) systems. By imposing new conditions on the Lyapunov function and its derivative, the state convergence to the origin from any initial condition with bounded norm in the classical setting is extended to the initial conditions with unbounded norms in the present work. The proposed new notions of stability are called extended global asymptotic stability (EGAS) and extended global uniform asymptotic stability (EGUAS) in this paper. The proposed Lyapunov-based criteria yield the global asymptotic stability of the origin and fixed-time/predefined-time attractiveness of any selected neighbourhood of the origin. The result is that the dynamical behaviour of the state trajectories from the convergence time point of view is improved considerably. The relationship between the smoothness and input-to-state stability (ISS) properties is also studied from a quantitative point of view. Under some new sufficient conditions, it is shown that dynamical systems with smaller Lipschitz constants represent smaller ultimate bounds, and as a result, are more robust. The desirable dynamical behaviour and robustness property of the proposed stability notion makes it comparable with the finite/fixed/predefined/prescribed (exact) stable systems that are naturally non-Lipschitz at the origin. Numerical results illustrate the effectiveness of the proposed theoretical results.

A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

Wall effects of an eccentric fluid sphere: Happel's and Kuwabara's models

AbstractIn the limit of very low Reynolds numbers, the steady translation of a fluid sphere situated at a non‐concentric position in a second immiscible fluid bounded by spherical cavity is investigated using boundary collocation technique. The flow inside and outside the fluid sphere is governed by Stokes equations. Boundary conditions at the fluid sphere are continuity of velocity and shear stress. Zero shear stress and zero vorticity are used on spherical cavity. By using superposition principle, a general solution is constructed from the basic solutions in the two spherical coordinate systems based on both the fluid sphere and spherical cavity. The normalized drag force exerted on the fluid sphere contained in a cavity is depended on the ratio of fluid sphere and cavity radii, viscosity ratio of fluid sphere and cavity, relative distance between the centers of fluid sphere and cavity. The results are in good agreement with previously published work in the limiting cases. The numerical results of the drag force are good agreement with the solutions of the translation of the fluid sphere in a concentric cavity and the translation of a solid sphere in a non‐concentric cavity. The drag force is increasing function of the viscosity ratio, volume fraction, and the relative distance. This work is extension of the previous work of Keh and Lee for the fluid sphere using Happel's and Kuwabara's models.

A Finite Element Analysis in Balanced Norms for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations

Abstract In this paper we study approximations of a singularly perturbed system of two coupled reaction-diffusion equations, in one dimension, by using piecewise linear finite elements on graded meshes. When the parameters are of different magnitudes, the solution exhibits in general two distinct but overlapping boundary layers. We prove that, when the mesh grading parameter is appropriately chosen, optimal error estimates in a balanced norm for piecewise linear elements can be obtained. Supporting numerical results are also presented.

B-324 Pilot Study Result of EQA for Fecal Immunochemical Test for Hemoglobin Using a Novel Ready-to-Use Sample Material

Abstract Background The primary screening method for colorectal cancer is fecal immunochemical test (FIT) detecting human hemoglobin (Hb) in feces. There are several tests on the market both for automated analyzers and point-of-care testing (POCT). To ensure high quality results, the tests should be monitored with appropriate quality assessment procedures including participation in external quality assessment (EQA) programs. By participating in an EQA program using a stool-like material, clinical laboratories and POCT sites can fulfil the ISO 15189 requirements of monitoring the complete laboratory process from pre- to postanalytical phases in addition to the quantitative analytical phase of FIT. Here we present the first results of an international EQA pilot study for quantitative FIT using a novel ready-to-use stool-like material, performed by EQA provider Labquality. Methods 40 participants from 8 countries using 9 different FIT reagents were recruited for the pilot study performed in 2023. A set of artificial stool samples containing human hemoglobin uniformly was shipped to the participants at ambient temperature. The sample material is developed by HECTEF (Health Care Technology Foundation, Japan). The participants were instructed to collect the sample with their test specific sample collection kit and perform analysis according to the manufacturer’s instructions as a regular patient sample. Quantitative results (µg Hb/g feces) and qualitative interpretations (positive/negative) were reported in Labquality’s electronic platform LabScala. The quantitative target value was a method group consensus mean. A questionnaire regarding the usability of the sample material was sent to all participants. Results Sample S001 contained no Hb and all participants (40/40) reported a result corresponding to the lower detection limit of their test in use or a low numeric result most likely explained by unspecific background. All reported a negative interpretation. Sample S002 was a high positive sample for Hb. The measured value exceeded the upper detection limit of 4/9 tests (Exdia iFOB, Precision Biosensor; Fecal Occult Blood (iFOB) Neo, Boditech; FOB Test, VedaLab; NADAL FOB Quant test, Nal von Minden). The mean values and CV% were 116 µg/g and 8% for iFOBT, Aidian; 192 ug/g and 4% for Standard iFOB FIA, SD Biosensor; 144 µg/g and 45% for FOB assay kit FOB Gold, Sentinel Diagnostics (different clinical chemistry analyzers used); 91 µg/g and 26% for OC-Sensor FIT, Eiken Chemical. All participants responded a positive qualitative clinical interpretation. The majority of the responders on the feedback questionnaire (26/35) found the samples to be easy to use including comments of the sample being user-friendly and ready-to-use, resembling a patient sample and easy to apply with the test specific sample collection kit. Conclusions The fecal-like sample used in this Labquality’s EQA pilot study evaluates the complete analytical process including the preanalytical, analytical and postanalytical phases. An EQA scheme using this sample material is more compliant to ISO 15189 requirements compared to schemes where liquid or lyophilized samples are used. The new sample material used on this pilot study was positively received by most of the participants and it was compatible with all tests included in the study.

Numerical study of the vortex-induced vibrations of a cantilevered pipe with a concentrated mass end using a wake oscillator model

In this paper, a numerical study based on a wake oscillator model has been carried out to determine the vortex-induced vibration (VIV) response characteristics of a flexible cantilevered pipe with a concentrated mass at the free end. First, a coupled model consisting of a cantilevered pipe and a wake oscillator is established, followed by discretization of the model and an iterative solution using the second-order central difference method. The displacement response and frequency response characteristics for different flow velocities and concentrated end masses have been compared. The numerical results reveal that the maximum value of the structural vibration displacement occurs at the bottom; i.e., free boundary end, for the cantilevered pipe with a concentrated mass at the free end. The dominant vibration mode typically shows a stepwise increase for an increase of the maximum flow velocity. As the vibration mode is transmitted from a lower order to a higher one, the vibration displacement of the structural end decreases fast. As the concentrated end mass increases, the dominant vibration mode shows a stepwise decrease, and as the vibration mode is transmitted from a higher order to a lower one, the vibration displacement of the structural end experiences a sharp increase.

A Bayesian regularization radial basis neural network novel procedure for the fractional economic and environmental system

The motive of current work is to design a novel radial basis Bayesian regularization neural network (RB-BRNN) for solving the nonlinear fractional economic and environmental system (FEES). A radial basis activation function in the hidden layers is applied by taking 20 numbers of neurons. The mathematical FEES is presented in three classes, named as cost of control accomplishment, manufacturing elements competence and technical exclusion’s diagnostics cost. A reference dataset is obtained using the Adams numerical results to reduce the mean square error (MSE) by taking the data for training 70%, while 15% is used for both testing and validation. The negligible absolute error values and comparison of the solutions develop the worth of computing RB-BRNN in order to solve the nonlinear dynamics of the FEES. Error diagrams, regression values, and the MSE performances are implemented to assess the precision of the designed solver.

Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method

Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to ϵ accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as log⁡(1/ϵ). This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.

Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

Numerical simulation of scour dynamics around series of spur dikes using FLOW-3D

Spur dikes are vital structures are used to control erosion and manage flow dynamics. This study evaluates the effectiveness of multiple spur dikes in reducing scour depth around the first dike by adjusting their spacing and length. Numerical simulations were performed using the FLOW-3D-hydro model, incorporating the RNG k-ϵ turbulence model to account for low-intensity flow conditions. Results showed that parallel spur dikes significantly influenced flow direction, reducing scour depth near the first dike. Optimal configurations, with spacing set at twice the length of the dike, reduced scour depth by up to 30%. The numerical model used a nested mesh configuration for precise flow capture. A comparison of experimental and numerical results showed a strong correlation, with an R² of 0.94, RMSE of 0.03, and P-bias of 2.5%. These findings confirm the accuracy of the FLOW-3D model in simulating scour dynamics, offering key insights for hydraulic engineering applications.

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.

Quantitative evaluation of DNA damage repair dynamics to elucidate predictors of autism vs. cancer in individuals with germline PTEN variants.

Persons with germline variants in the tumor suppressor gene phosphatase and tensin homolog, PTEN, are molecularly diagnosed with PTEN hamartoma tumor syndrome (PHTS). PHTS confers high risks of specific malignancies, and up to 23% of the patients are diagnosed with autism spectrum disorder (ASD) and/or developmental delay (DD). The accurate prediction of these two seemingly disparate phenotypes (cancer vs. ASD/DD) for PHTS at the individual level remains elusive despite the available statistical prevalence of specific phenotypes of the syndrome at the population level. The pleiotropy of the syndrome may, in part, be due to the alterations of the key multi-functions of PTEN. Maintenance of genome integrity is one of the key biological functions of PTEN, but no integrative studies have been conducted to quantify the DNA damage response (DDR) in individuals with PHTS and to relate to phenotypes and genotypes. In this study, we used 43 PHTS patient-derived lymphoblastoid cell lines (LCLs) to investigate the associations between DDR and PTEN genotypes and/or clinical phenotypes ASD/DD vs. cancer. The dynamics of DDR of γ-irradiated LCLs were analyzed using the exponential decay mathematical model to fit temporal changes in γH2AX levels which report the degree of DNA damage. We found that PTEN nonsense variants are associated with less efficient DNA damage repair ability resulting in higher DNA damage levels at 24 hours after irradiation compared to PTEN missense variants. Regarding PHTS phenotypes, LCLs from PHTS individuals with ASD/DD showed faster DNA damage repairing rate than those from patients without ASD/DD or cancer. We also applied the reaction-diffusion partial differential equation (PDE) mathematical model, a tumor cell growth model with a DNA damage term, to accurately describe the DDR process in the LCLs. For each LCL, we can derive parameters of the PDE. Then we averaged the numerical results by PHTS phenotypes. By performing simple subtraction of two subgroup average results, we found that PHTS-ASD/DD is associated with higher live cell density at lower DNA damage level but lower cell density level at higher DNA damage level compared to LCLs from individuals with PHTS-cancer and PHTS-neither.

Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase.

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.

Effect of tapered porous ribs on the performance of Proton exchange membrane fuel cells

The conventional trench ridge structure suffers from the difficulty of removing liquid water and poor gas transport performance. The water removal and gas transport performance inside the flow field are enhanced by introducing a tapered porous rib flow field (TPRFF). In order to investigate the performance of TPRFF, a complex three-dimensional, multiphase, non-isothermal agglomeration model was developed using numerical techniques. The numerical results show that the TPRFF exhibits significant improvements in oxygen concentration distribution, oxygen distribution uniformity and water removal compared to a conventional parallel flow field (CPFF). In addition, the dissolved water content remained almost constant while the liquid water saturation was lower. The study also investigated the effect of different cathode exit heights on the performance of the fuel cell using TPRFF. The results showed that the net power density increased by 14.0 %, 11.9 %, 8.7 %, and 1.5 % for outlet heights of 1.3 mm, 1.0 mm, 0.7 mm, and 0.4 mm, respectively, while it decreased by 27 % for an outlet height of 0.1 mm. Finally, the effect of different stoichiometric ratios on cell performance was also investigated in the novel flow field.

Evaluation of thermal and concentration slip effects on heat and mass transmission of nanofluid over a moving wedge surface using Keller box scheme

The current research is based on the impact of thermal and solutal slip in the boundary layer nanofluid flow through a moving accelerating wedge. The present investigation is considered with the influence of Brownian motion and thermophoresis. Thermal insulation, geothermal engineering, crude oil extraction, and heat exchangers are very important applications of nanofluid movement over a wedge surface with thermal and concentration slip. The suggested mathematical analysis is expressed in terms of partial differential equations (PDEs). These PDEs are transformed into ordinary differential equations via similarity transformation. The Keller Box technique is used to integrate the resultant non-similar equations. The set of discretized and first order differential equations is formed with the help of central difference and the Newton–Raphson technique. The graphical and numerical results are extracted with the help of MATLAB. The numerical results with the influence of the Prandtl factor (Pr), constant moving factor (λ), thermal slip factor (S2), and concentration slip parameter (S2) are interpreted visually and numerically. Graphical representations of velocity, thermal, and mass concentration profiles are analyzed in depth. The solution for skin friction coefficient, heat transport rate, and mass transport rate is calculated. The moving velocity function increases as Pr increases. The rate of slip temperature and slip concentration rate is enhanced for a lower Prandtl factor. The maximum slip behavior in temperature function and fluid concentration slip is deduced for each value of thermal-slip and concentration-slip factors. For high Prandtl and Brownian motion factors, the rate of Nusselt number is enhanced significantly.