Patel's Model Research Articles

Social norms and the dynamics of observers' education

The paper presents a dynamical extension of the well­known Bernheim— Cartwright—Patel model of conformism. In this model the signaling equilibrium is a result of the optimal choice of an individual when he/she maximizes his/ her utility by choosing a donation in the amount x. In doing this the individual takes into account the intrinsic utility based on the generosity type t, and social attitude expressed by two types of observers: rational and naïve. Such an attitude significantly depends on social norms in this society and affects the esteem of the individual. Social attitude toward generosity varies within the broad range and at its endpoints leads to either neglect of the society (I do not care what people think of me) or an ideal conformism when a person chooses the same x as the rest of the public. Cartwright and Patel have shown that the presence of the inexperienced observers greatly affects equilibrium. This paper explores the dynamics of the naïve observers when they are informed by the rational ones. The dynamic law in the form of the differential equation was set and the stable steady­state solutions were found. Besides, while working on the dynamic law some clarifications of the preceding results of the original model were done.

Thermal analysis of magnetized [formula omitted] nanolubricant flow in a Darcy-Forchheimer porous medium with nonlinear heat generation

The nanolubricant ZnO−SAE50 is widely used in automobiles and heat exchange systems to minimize friction and resist corrosion and scrape between moving parts. It also improves system's performance and durability and cuts fuel consumption. In this work, the flow of magnetized ZnO−SAE50 nanolubricant is analyzed over a flat plate with variable temperature immersed in a Darcy-Forchheimer medium. The thermal analysis is carried out in the occurrence of nonlinear heat generation and thermal radiation. Furthermore, the influences of viscous dissipation and Joule heating have also been deliberated. A micro-nano convection model named as Patel model of thermal conductivity has been used in view of rise in thermal conductivity. The governing PDEs are altered to ODEs with the incorporation of similarity transformations and then numerically treated by using an eminent MATLAB's built-in bvp4c method. The influences of different physical parameters on velocity, temperature and Nusselt number are discussed and analyzed graphically and in tabular form. The velocity profile diminishes under the impacts of inertia coefficient and magnetic field. The temperature and exponential dependent heat generation parameters considerably enhance temperature of the nanolubricant ZnO−SAE50. The temperature power coefficient tends to reduce the temperature profile. The enhancing strength of thermal radiations and nonlinear heat generation significantly enhance the value of Nusselt number. Furthermore, an increase in the value of temperature dependent heat generation parameter from 0.2 to 0.6 tends 12.37% increment in the value of Nusselt number in conventional SAE50oil, whereas the nanolubricant ZnO−SAE50 experiences a more significant 26.72% increment in the value of Nusselt number. Thus, better heat transmission rate can be achieved by using ZnO−SAE50 nanolubricant rather than conventional SAE50 oil.

Rheological behavior of magnetized ZnO – SAE50 nanolubricant over Riga plate: A theoretical study

[Formula: see text] nanolubricant is one of the most important nanolubricants having widespread uses in heat exchange systems and automobiles. It minimizes friction between moving parts and prevents them from corrosion and scrape, improves durability and performance of the system and also minimizes the consumption of fuel. This work investigates the rheological behavior of magnetized [Formula: see text] nanolubricant over moving/stationary Riga plate with viscous dissipation and nonlinear heat generation. The novel features of the current work are the use of [Formula: see text] nanolubricant as a flow fluid across a Riga plate and the application of the Patel model to boost the thermal conductivity of the nanolubricant. The governing system of equations is transformed to nonlinear ODEs and then treated analytically by using HAM. The augmentation in the velocity of nanolubricant [Formula: see text] is observed due to increasing values of Grashof number. The higher values of nonlinear thermal radiation and nonlinear heat generation parameters upsurge the temperature profile. The value of skin friction increases by increasing modified Hartman number and velocity slip parameter while reverse trend is observed by enhancing magnetic parameter. The radiation parameter, temperature dependent heat source parameter and solid volume fraction tend to augment Nusselt number at the Riga surface.

NUMERICAL SOLUTION ON MIXED CONVECTION FLOW OF NANOFLUID AROUND A FINNED ANGULAR SECTOR OF HEAT SINK

The aim of this study is to investigate mixed convection flow of nanofluid around a three-dimensional (3D) finned angular sector of heat sink by means of numerical simulations. The finite-volume method is used to solve the governing equations of mass, momentum, and energy conservation. The Brownian motion of the nanoparticles in the base fluid is explicitly taken into account in the thermal conductivity model (Patel model). A parametric study is carried out to examine the effects of several key parameters on the rate of heat transfer; the angular sector apex angle, the volume fraction of suspended nanoparticles (0 ≤ φ ≤ 0.09), the Richardson number (<i>Ri</i> = <i>Gr/Re</i><sup>2</sup>), and the size of the nanoparticles diameter (5, 20, 60, and 100 nm). It is shown that for a fixed low Richardson number <i>Ri</i>, the rate of heat transfer increases with the volume fraction of the nanoparticles, as forced convection mechanism is dominated. The heat-transfer enhancement is obtained for the nanofluid water/TiO<sub>2</sub> rather than the water/Cu at higher nanoparticles volume concentration and highest Richardson number. Moreover, the Maxwell thermal conductivity model resulted in a maximum enhancement in the case of nanofluid water/TiO<sub>2</sub> than that of water/Cu, whereas the nanofluid water/ Cu gives better heat-transfer enhancement at small particles than that of water/TiO<sub>2</sub>. It is observed too that the nanoparticles' diameter does not have a significant effect on the temperature field.

Thermo‐mechanical properties of flexible and rigid polyurethane (PU)/Cu composites

AbstractIn this article, flexible and rigid polyurethane (PU)/copper (Cu) composites are prepared via a simple and cost‐effective solution casting process. The filler dispersion and chemical bonding of composites are investigated by SEM and FTIR techniques. The results showed the homogeneous dispersion of Cu microparticles. Furthermore, thermal properties are investigated using DMA, DSC, and thermal conductivity measurements. The maximum improvement in thermal conductivity for flexible and rigid PU composites is 24%, and 48%, respectively, as compared to their pure counterparts. The obtained thermal conductivity values are also compared and analyzed with the mechanical property model (Corans and Patel model) and found in good agreement with the output of the model. DMA results showed enhancement in the storage modulus with filler loading while the DSC results revealed the endothermic temperature did not significantly change with adding Cu filler in both flexible and rigid PU matrices. The mechanical properties of composites were studied using tensile and hardness (Shore A and Shore D) test. For flexible PU composites an improvement in tensile strength (43%), Young's modulus (111%), Shore A hardness (6%), Shore D hardness (27%) as compared to pure flexible PU. For rigid PU composites a reduction in tensile strength (23%), Young's modulus (32%), and an increase in Shore A hardness (3%), Shore D hardness (5%) as compared to pure rigid PU. As a result of the current study, TC of rigid PU is found doubly enhanced compared to flexible PU at the same filler concentration. Copper microparticles can act as active filler in both flexible and rigid PU matrices.

Association between postnatal growth and neurodevelopmental impairment by sex at 2 years of corrected age in a multi-national cohort of very preterm children

Extra-uterine growth restriction (EUGR) is common among very preterm (VPT) infants and has been associated with impaired neurodevelopment. Some research suggests that adverse effects of EUGR may be more severe in boys. We investigated EUGR and neurodevelopment at 2 years of corrected age (CA) by sex in a VPT birth cohort. Data come from a population-based cohort of children born <32 weeks' gestation from 11 European countries and followed up at 2 years CA. Postnatal growth during the neonatal hospitalization was measured with: (1) birthweight and discharge-weight Z-score differences using Fenton charts (2) weight-gain velocity using Patel's model. Published cut-offs were used to define EUGR as none, moderate or severe. Neurodevelopmental impairment was assessed using a parent-report questionnaire, with standardized questions/instruments on motor function, vision, hearing and non-verbal cognition. We estimated relative risks (RR) adjusting for maternal and neonatal characteristics overall and by sex. Among 4197 infants, the prevalence of moderate to severe impairment at 2 years CA was 17.7%. Severe EUGR was associated with neurodevelopmental impairment in the overall sample and the interaction with sex was significant. For boys, adjusted RR were 1.57 (95% Confidence Intervals (CI): 1.18-2.09) for Fenton's delta Z-score and 1.50 (95% CI: 1.12-2.01) for Patel's weight-gain velocity, while for girls they were 0.97 (0.76-1.22) and 1.12 (0.90-1.40) respectively. EUGR was associated with poor neurodevelopment at 2 years among VPT boys but not girls. Understanding why boys are more susceptible to the effects of poor growth is needed to develop appropriate healthcare strategies.

Entropy minimization in mixed convective Falkner-Skan flow of ZnO-SAE50 nanolubricant over stationary/moving Riga plate

The present investigation imparts the mixed convection non-linear Falkner-Skan flow and heat flux analysis of ZnO-SAE50 nanolubricant over a stationary/moving Riga-plate in presence of thermal radiation. Additionally, velocity and thermal slip boundary conditions are considered. In the current study, a micro-convection model (Patel model) is considered. The present model has great influence in significant enrichment of heat transport capability of the nanoliquids. The similar transformed nonlinear coupled governing expressions are examined numerically by the Runge-Kutta-Fehlberg integration scheme. The important outcome of the present study is that the augmented pressure gradient impedes the motion of nano-lubricant while reverse trend is attained due to the amplification of modified Hartmann number and velocity slip at the boundary. Further, the growth of thermal slip peters out the heat transfer rate from the Riga plate.

Lattice Boltzmann simulation of magneto-hydrodynamic double-diffusive natural convection in an enclosure with internal heat and solute source using nanofluids

Magneto-hydrodynamic double-diffusive natural convection in a cavity is numerically investigated in the present work. Al2O3, Cu, and Ag based nanofluids in a square cavity with a thermal and solute source in the center, and uniform magnetic field are considered. The Patel model is employed to estimate the thermal conductivity of applied nanofluids, and the numerical calculation is based on the implementation of the lattice Boltzmann method and utilizing the standard $$D_{2} Q_{9}$$ model to study the heat transfer, and also species concentration. A parametric study is carried out to observe the influence of the type, the volume fraction of nanoparticle ( $$\phi = 0 - 5\%$$ ), Rayleigh ( $$Ra = 10^{4} - 10^{5} - 10^{6} )$$ , Lewis $$\left( {0.1 - 2 - 10} \right)$$ , and Hartmann number $$\left( {10 - 20 - 100} \right)$$ on average Nusselt and Sherwood numbers, flow fields, temperature, and concentration distribution. The results show that an augment in nanoparticle volume fraction and Rayleigh number increased the average Nusselt and Sherwood numbers. Lewis number showed a significant impact on mass transfer rate. However, it did not affect the heat transfer rate remarkably. Applying a magnetic field caused a reduction in flow circulation which resulted in a decline in heat and mass transfer. A comparison of the simulation outcome with the available data shows that the generated code perfectly captures the fluid flow behavior and heat transfer process as a function of the affecting parameters.

HHR impact on 3D radiative stretched flow of Cu-H2O nanofluid influenced by variable magnetic field and convective boundary condition

In an attempt to the influence of homogenous and heterogeneous reactions, variable magnetic field and thermal radiation on three-dimensional flow of an incompressible nanofluid over an exponential stretching sheet subject to convective boundary condition has been analyzed. In view of enhancement of heat transfer capability of nanofluids, effective implementation of Patel model is carried in the current study. The transformed governing differential equations are solved using fourth-order Runge-Kutta method along with shooting technique and secant method is employed for better approximation. The significant outcome of the present computational study is that the magnetic field interaction impedes the fluid motion leading to diminution of the wall shear stresses (axial as well as transverse) and homogenous and heterogeneous parameters belittle the fluid concentration appreciably.

Magnetohydrodynamic flow and heat transfer impact on ZnO-SAE50 nanolubricant flow over an inclined rotating disk

The present article has been fine-tuned with the investigation of mixed convection Darcy-Forchheimer flow of ZnO-SAE50 oil nanolubricant over an inclined rotating disk under the influence of uniform applied magnetic field applied to various industries. The current study has been enriched with additional consideration of slip flow, thermal radiation, viscous dissipation, Joulian dissipation and internal heating. In view of augmentation of thermal conductivity of nanolubricant, a new micro-nano-convection model namely Patel model has been invoked. The specialty of this model involves the effects of specific surface area and nano-convection due to Brownian motion of nanoparticles, kinetic theory based micro-convection, liquid layering and particle concentration. Suitably transformed governing equations have been solved numerically by using Runge-Kutta-Fehlberg scheme. An analysis of the present study has shown that applied magnetic field, porosity of the medium, velocity slip and inertia coefficient account for the slowing down of radial as well as tangential flow of ZnO-SAE50 oil nanolubricant, thereby leading to an improvement in velocity and thermal boundary layers.

Rheological behaviour of various metal-based nano-fluids between rotating discs: a new insight

Abstract In this study, nanofluid flow and heat transfer between two contracting and rotating disks are investigated. Brownian motion is considered to simulate viscosity of nanofluid and Patel model is used to predict the behavior of thermal conductivity of nanofluid. The governing equations are solved via the fourthorder Runge–Kutta method. Different kinds of nanoparticles are examined. Effects of active parameters such as nanoparticle volume fraction, rotational Reynolds number, injection Reynolds number, and expansion ratio are considered. Results indicate that Nusselt number is a decreasing function of expansion ratio while it is increasing function of other parameters such as nanoparticle volume fraction, rotational Reynolds number, and injection Reynolds number. Also, it can be found that maximum value of heat transfer enhancement is obtained by selecting the silver (Ag) as nanoparticle.

Combined effects of slip and convective boundary condition on MHD 3D stretched flow of nanofluid through porous media inspired by non-linear thermal radiation

In the present study, the main concern is to investigate the magnetohydrodynamic nanofluid flow subject to porous matrix and convective heating past a permeable linear stretching sheet. In addition, the influence of velocity slip, viscous dissipation, Joule heating and non-linear thermal radiation are considered. A new micro-convection model known as the Patel model is implemented for considerable enhancement of the thermal conductivity and hence, the heat transfer capability of nanofluids. Moreover, a convective heat transfer model is introduced where the bottom surface of the sheet gets heated due to a convection mechanism from a hot fluid of particular temperature. The numerical results of the transformed governing differential equations have been obtained by using fourth-order Runge–Kutta method along with shooting approach and secant method is used for better approximation. In the present analysis, base fluids such as water and Ethylene glycol and Copper, Silver and Aluminum oxide nanoparticles are considered. Results of the present investigation show that inclusion of porous matrix contributes to slow down the fluid velocity and diminution of wall shear stress (axial as well as transverse). Drag force due to magnetic field strength, velocity slip and imposed fluid suction impede the fluid motion and upsurge the heat transfer rate from the surface. In addition, rise in viscous dissipation widens the thermal boundary layer.

3D free convective MHD flow of nanofluid over permeable linear stretching sheet with thermal radiation

This paper mainly focuses on the influence of transverse magnetic field as well as thermal radiation on three-dimensional free convective flow of nanofluid over a linear stretching sheet. One remarkable aspect of this study is that a new micro-convection model namely Patel model has been introduced in view of enhancement of thermal conductivity and hence more heat transfer capability of nanofluid. The non-linear partial differential equations have been converted into strong non-linear ordinary differential equations by employing suitable transformations and these transformed equations are solved by Runga-Kutta method of fourth order along with Shooting technique as well as Secant method for better approximation. From this study, it is found that the presence of magnetic field slows down the fluid motion while it enhances the fluid temperature leading to a reduction in heat transfer rate from the surface. It is also found that enhancing thermal radiation parameter causes a reduction in heat transfer rate.

Flow and heat transfer over a rotating porous disk in a nanofluid

The steady flow of an incompressible viscous fluid due to a rotating disk in a nanofluid is studied. The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction parameter φ and suction/injection parameter h0. Two models for the effective thermal conductivity of the nanofluid, namely the Maxwell–Garnett model and the Patel model, are considered. It is found that for the Patel model, the heat transfer rate at the surface increases for both suction and injection, whereas different behaviors are observed for the Maxwell–Garnett model, i.e. increasing the values of φ leads to a decrease in the heat transfer rate at the surface for suction, but increases for injection. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.

Modified polyacrylonitrile blends with cellulose acetate: blend properties

Polyacrylonitrile (PAN) was modified by copolymerizing with methyl acrylate (MA) and 2-acrylamido-2-methyl propane sulfonic acid (AMPS abbreviated as AP), and blended with cellulose acetate (CA) in dimethyl formamide. Scanning electron microscopy (SEM) showed much finer domain morphology for MA–PAN blends than AP–PAN blends. Dynamic mechanical property measurements showed an inward migration of the two glass transition temperatures (Tg) viz., Tg’s of PAN and CA, however the migration of PAN Tg was more pronounced in AP–PAN blends, the result agreed well with the conjugate phase calculation. The phase inversion composition, calculated using Coran–Patel model agreed well with SEM morphology.

Deconfinement transition and flux-string models

Flux-string models can be used to study the deconfining phase transition. In this note, we study the models proposed by Patel. We also study the large N_c limits of Patel's model. To discuss the validity of the mean field theory results, the one-loop Coleman-Weinberg effective potential is calculated for N_c=3. We argue that the quantum corrections vanish at large N_c when the energy of the so-called baryonic vertices scale with N_c.

A new model for the performance evaluation of synchronous circuit switched multistage interconnection networks

Patel (1981) proposed a probabilistic approach to analyze the performance of synchronous multistage interconnection networks (MINs) based on a uniform reference model and the assumption of independent requests. Patel's model and analytical results have been widely adopted by numerous researchers as a basis to investigate various aspects of MINs. We study in detail the effects of the independence assumption on the accuracy of system performance and point out the factors which cause an inaccuracy. A new queueing model is then proposed and is shown to be very accurate. Since only six states are needed, independent of the size of MINs, this new model is very efficient computationally.

TWO-LAYER-MODEL PREDICTIONS OF HEAT TRANSFER INSIDE ENHANCED TUBES

ABSTRACT Turbulent flow in axisymmetric enhanced tubes with repeated transverse rectangular disruptions was simulated using the two-layer turbulence model of Chen and Patel 111. The predictions were in good agreement with experimental data for friction factors and both local and average Nusselt numbers. The low-Reynolds-number two-equation model of Lam and Bremhorst 121 was considered, and the predicted results were also compared with local heat transfer measurements. This model overestimated the local Nusselt numbers at some locations by about a factor of 2. Results from the two turbulence models were also compared for a sudden pipe-expansion geometry. The Lam and Bremhorst model yielded acceptable local Nusselt number predictions, while the Chen and Patel model underpredicted the local Nusselt numbers and predicted the location of the heat transfer maximum further upstream.

Modeling a circuit switched multiprocessor interconnect

Abstract : This study began as an attempt to understand discrepancies between Patel's classic model of a circuit-switched interconnection network and simulations as part of the MIT ALEWIFE Multiprocessor project. After a careful analysis of Patel's model, we developed a model with fewer approximations that produced results generally closer to detailed simulation. The major source of inaccuracy in patel's model is the unit-request approximation, which treats a t- cycle request as t l-cycle requests producing significant inaccuracies for networks with many switching levels and for small packet sizes. Our model followed the behavior of the network more closely, explicitly modeling the effects of switch size, network depth, packet size and memory latency, thereby alleviating some inaccuracies in Patel's model. However, despite the slightly lower accuracy of Patel's model, we believe that its simplicity makes it the practical choice for most applications. Thus, our main contribution was to understand the causes of inaccuracies in both models, allowing us to predict the quality of the estimations they yielded. Another research result is validating a complicated simulator using relatively simple models, not a common use for a model. We found that some of the original discrepancies between patel's model and the simulator were due to hidden inconsistancies between parameters used by the model and those used by the simulator, and that others were duet to bugs in the simulator code.