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The present work deals with the laminar natural convection in a cubical cavity filled with a homogenous aqueous solution of carboxymethyl cellulose (CMC) based gold (Au) nanofluid obeying the power-law rheological model. The cavity is heated on the vertical and cooled from the adjacent wall, while the other walls are adiabatic. The governing differential equations were solved with the standard finite-volume method and the hydrodynamic and thermal fields are coupled using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticle volume fraction on the heat-transfer characteristics of CMC-based Au nanofluid over a wide range of the base-fluid Rayleigh number. Accurate numerical results are presented in the form of dimensionless temperature and velocity variations, the mean Nusselt number and the heat-transfer rate. It is shown that adding nanoparticles to the base fluid delays the onset of natural convection. In addition, numerical simulations showed that, just after the onset of natural convection, adding nanoparticles reduces the mean Nusselt number value for any given base-fluid Rayleigh number. Prispevek obravnava naravno konvekcijo v kockastem ohišju, napolnjenem s homogeno nanotekočino karboksimetil celuloza (CMC)-zlato (Au), z reološkim vedenjem, opisanim s potenčnim zakonom. Ohišje je greto na navpični in hlajeno na priležni steni, medtem ko so druge stene adiabatne. Vodilne diferencialne enačbe so bile rešene s standardno metodo končnih prostornin, pri čemer sta hidrodinamično in temperaturno polje sklopljena z Boussinesqovo aproksimacijo. Glavni cilj prispevka je raziskati vpliv prostorninskega deleža nanodelcev na značilnosti prenosa toplote CMC-Au nanotekočine za široko območje vrednosti Rayleighjevega števila nosilne tekočine. Natančni rezultati so predstavljeni v obliki spreminjanja brezdimenzijske temperature in hitrosti, srednje vrednosti Nusseltovega števila in hitrosti prenosa toplote. Pokazano je, da dodajanje nanodelcev v nosilno tekočino zakasni začetek naravne konvekcije. Poleg tega so numerične simulacije pokazale, da takoj za pojavom naravne konvekcije dodajanje nanodelcev zmanjšuje srednjo vrednost Nusseltovega števila za katero koli vrednost Rayleighjevega števila nosilne tekočine.

A numerical analysis is performed to examine the heat transfer of colloidal dispersions of Au nanoparticles in water (Au nanofluids). The analysis used a two-dimensional enclosure under natural convection heat-transfer conditions and has been carried out for the Rayleigh number in the range of 103 < Ra < 105, and for the Au nanoparticles' volume-fraction range of 0 < j < 0.10. We report highly accurate numerical results indicating clearly that the mean Nusselt number is an increasing function of both Rayleigh number and volume fraction of Au nanoparticles. The results also indicate that a heat-transfer enhancement is possible using nanofluids in comparison to conventional fluids. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers. V prispevku smo numerično analizirali prenos toplote v koloidnih disperzijah nanodelcev zlata v vodi (Au-nanotekočine). Pri tem smo obravnavali dvodimenzionalno kotanjo pod pogoji naravne konvekcije za vrednosti Rayleighevega števila 103 < Ra < 105 in volumenske koncentracije Au-nanodelcev 0 < j < 0,10. Rezultati analize kažejo, da je srednje Nusseltovo število naraščajoča funkcija obeh, tako Rayleighevega števila kot volumenskega deleža Au-nanodelcev. Prikazani rezultati nakazujejo, da lahko prenos toplote izboljšamo z uporabo Au-nanotekočin namesto navadnih tekočin. Pri tem pa je pozitivni učinek na prenos toplote izrazitejši pri nižjih vrednostih Rayleighevega števila.

The present work deals with the natural convection in a square cavity filled with a water-based Au nanofluid. The cavity is heated from the lower and cooled from the adjacent wall, while the other two walls are adiabatic. Theg overning differential equations have been solved with the standard finite volume method and the hydrodynamic and thermal fields have been coupled using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticlesć volume fraction on the heat-transfer characteristics of Au nanofluids at a given base-fluid (i.e., water) Rayleigh number Rabf. Accurate results are presented over a wide range of the base-fluid Rayleigh numbers (102 £ Rabf £ 105) and the volume fraction of Au nanoparticles (0 % £ j £ 10 %). It is shown that adding nanoparticles to the base fluid delays the onset of convection. Contrary to what is argued by many authors, we show, with numerical simulations, that the use of nanofluids can reduce the heat transfer instead of increasing it. V prispeveku obravnavamo naravno konvekcijo v kvadratni kotanji, napolnjeni z nanotekočino voda-Au. Kotanja je bila greta s spodnje in hlajena s priležne zgornje stene, preostali dve steni sta bili adiabatni. Vodilne diferencialne enačbe smo reševali s standardno metodo končnih prostornin. Hidrodinamično in temperaturno polje sta bila sklopljena z uporabo Boussinesqove aproksimacije. Glavni cilj prispevka je raziskati vpliv prostorninskega deleža nanodelcev na značilnosti prenosa toplote Au-nanotekočine pri podani vrednosti Rayleighjevega števila nosilne tekočine (vode) Rabf. Natančni rezultati so predstavljeni za široko območje vrednosti Rayleighjevega števila nosilne tekočine (102 £ Rabf £ 105) in prostorninskega deleža Au-nanodelcev (0 % £ j £10 %). Pokazali smo, da dodajanje nanodelcev v nosilno tekočino zakasni začetek naravne konvekcije. V nasprotju s trditvami mnogih avtorjev smo z numeričnimi simulacijami pokazali, da lahko uporaba nanodelcev prenos toplote zmanjša in ne poveča.

The present work deals with the laminar natural convection in a cubical cavity filled with a homogenous aqueous solution of carboxymethyl cellulose (CMC) based gold (Au) nanofluid obeying the power-law rheological model. The cavity is heated on the vertical and cooled from the adjacent wall, while the other walls are adiabatic. The governing differential equations were solved with the standard finite-volume method and the hydrodynamic and thermal fields are coupled using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticle volume fraction on the heat-transfer characteristics of CMC-based Au nanofluid over a wide range of the base-fluid Rayleigh number. Accurate numerical results are presented in the form of dimensionless temperature and velocity variations, the mean Nusselt number and the heat-transfer rate. It is shown that adding nanoparticles to the base fluid delays the onset of natural convection. In addition, numerical simulations showed that, just after the onset of natural convection, adding nanoparticles reduces the mean Nusselt number value for any given base-fluid Rayleigh number. Prispevek obravnava naravno konvekcijo v kockastem ohišju, napolnjenem s homogeno nanotekočino karboksimetil celuloza (CMC)-zlato (Au), z reološkim vedenjem, opisanim s potenčnim zakonom. Ohišje je greto na navpični in hlajeno na priležni steni, medtem ko so druge stene adiabatne. Vodilne diferencialne enačbe so bile rešene s standardno metodo končnih prostornin, pri čemer sta hidrodinamično in temperaturno polje sklopljena z Boussinesqovo aproksimacijo. Glavni cilj prispevka je raziskati vpliv prostorninskega deleža nanodelcev na značilnosti prenosa toplote CMC-Au nanotekočine za široko območje vrednosti Rayleighjevega števila nosilne tekočine. Natančni rezultati so predstavljeni v obliki spreminjanja brezdimenzijske temperature in hitrosti, srednje vrednosti Nusseltovega števila in hitrosti prenosa toplote. Pokazano je, da dodajanje nanodelcev v nosilno tekočino zakasni začetek naravne konvekcije. Poleg tega so numerične simulacije pokazale, da takoj za pojavom naravne konvekcije dodajanje nanodelcev zmanjšuje srednjo vrednost Nusseltovega števila za katero koli vrednost Rayleighjevega števila nosilne tekočine.

The present work deals with the natural convection in a square cavity filled with a water-based Au nanofluid. The cavity is heated from the lower and cooled from the adjacent wall, while the other two walls are adiabatic. Theg overning differential equations have been solved with the standard finite volume method and the hydrodynamic and thermal fields have been coupled using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticlesć volume fraction on the heat-transfer characteristics of Au nanofluids at a given base-fluid (i.e., water) Rayleigh number Rabf. Accurate results are presented over a wide range of the base-fluid Rayleigh numbers (102 L Rabf L 105) and the volume fraction of Au nanoparticles (0 % L j L 10 %). It is shown that adding nanoparticles to the base fluid delays the onset of convection. Contrary to what is argued by many authors, we show, with numerical simulations, that the use of nanofluids can reduce the heat transfer instead of increasing it. V prispeveku obravnavamo naravno konvekcijo v kvadratni kotanji, napolnjeni z nanotekočino voda-Au. Kotanja je bila greta s spodnje in hlajena s priležne zgornje stene, preostali dve steni sta bili adiabatni. Vodilne diferencialne enačbe smo reševali s standardno metodo končnih prostornin. Hidrodinamično in temperaturno polje sta bila sklopljena z uporabo Boussinesqove aproksimacije. Glavni cilj prispevka je raziskati vpliv prostorninskega deleža nanodelcev na značilnosti prenosa toplote Au-nanotekočine pri podani vrednosti Rayleighjevega števila nosilne tekočine (vode) Rabf. Natančni rezultati so predstavljeni za široko območje vrednosti Rayleighjevega števila nosilne tekočine (102 L Rabf L 105) in prostorninskega deleža Au-nanodelcev (0 % L j L10 %). Pokazali smo, da dodajanje nanodelcev v nosilno tekočino zakasni začetek naravne konvekcije. V nasprotju s trditvami mnogih avtorjev smo z numeričnimi simulacijami pokazali, da lahko uporaba nanodelcev prenos toplote zmanjša in ne poveča.

This work presents the possibility of numerical modelling using Computational Fluid Dynamics (CFD) in the field of nano-foils. The governing equations were solved using a Finite Volume Methodology (FVM). The computational domain was discretized using a uniform Cartesian grid with the appropriate mesh size along the x and y directions employing the corresponding number of grid points. The field variables were discretized at the cell centres and the spatial, as well as the time, derivatives were approximated using the second-order accurate numerical scheme. The time-evolution of the temperature and concentration fields, as well as the atomic diffusion coefficient, will be presented for the appropriate Al-Au nano-foil geometry and boundary conditions. V delu je predstavljena možnost numeričnega modeliranja z uporabo računske dinamike fluidov (CFDC) v primeru nanofolij. Ustrezne enačbe so bile rešene z uporabo metodologije končnih prostornin (FVM). Področje izračunov je bilo opredeljeno z uporabo enakomerne kartezijeve mreže s primerno velikostjo vzdolž smeri x in y z ustreznim številom mrežnih točk. Spremenljivke polj so bile opredeljene za središče celic in prostorske ter časovne derivative ter aproksimirane z uporabo numerične sheme z drugim redom velikosti natančnosti. Časovni razvoj temperaturnih in koncentracijskih polj in koeficient atomske difuzije sta predstavljena za ustrezno geometrijo Al-Au-nanofolij in mejne pogoje.

A numerical analysis is performed to examine the heat transfer of colloidal dispersions of Au nanoparticles in water (Au nanofluids). The analysis used a two-dimensional enclosure under natural convection heat-transfer conditions and has been carried out for the Rayleigh number in the range of 103 < Ra < 105, and for the Au nanoparticles' volume-fraction range of 0 < j < 0.10. We report highly accurate numerical results indicating clearly that the mean Nusselt number is an increasing function of both Rayleigh number and volume fraction of Au nanoparticles. The results also indicate that a heat-transfer enhancement is possible using nanofluids in comparison to conventional fluids. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers. V prispevku smo numerično analizirali prenos toplote v koloidnih disperzijah nanodelcev zlata v vodi (Au-nanotekočine). Pri tem smo obravnavali dvodimenzionalno kotanjo pod pogoji naravne konvekcije za vrednosti Rayleighevega števila 103 < Ra < 105 in volumenske koncentracije Au-nanodelcev 0 < j < 0,10. Rezultati analize kažejo, da je srednje Nusseltovo število naraščajoča funkcija obeh, tako Rayleighevega števila kot volumenskega deleža Au-nanodelcev. Prikazani rezultati nakazujejo, da lahko prenos toplote izboljšamo z uporabo Au-nanotekočin namesto navadnih tekočin. Pri tem pa je pozitivni učinek na prenos toplote izrazitejši pri nižjih vrednostih Rayleighevega števila.

This work presents the possibility of numerical modelling using Computational Fluid Dynamics (CFD) in the field of nano-foils. The governing equations were solved using a Finite Volume Methodology (FVM). The computational domain was discretized using a uniform Cartesian grid with the appropriate mesh size along the x and y directions employing the corresponding number of grid points. The field variables were discretized at the cell centres and the spatial, as well as the time, derivatives were approximated using the second-order accurate numerical scheme. The time-evolution of the temperature and concentration fields, as well as the atomic diffusion coefficient, will be presented for the appropriate Al-Au nano-foil geometry and boundary conditions. V delu je predstavljena možnost numeričnega modeliranja z uporabo računske dinamike fluidov (CFDC) v primeru nanofolij. Ustrezne enačbe so bile rešene z uporabo metodologije končnih prostornin (FVM). Področje izračunov je bilo opredeljeno z uporabo enakomerne kartezijeve mreže s primerno velikostjo vzdolž smeri x in y z ustreznim številom mrežnih točk. Spremenljivke polj so bile opredeljene za središče celic in prostorske ter časovne derivative ter aproksimirane z uporabo numerične sheme z drugim redom velikosti natančnosti. Časovni razvoj temperaturnih in koncentracijskih polj in koeficient atomske difuzije sta predstavljena za ustrezno geometrijo Al-Au-nanofolij in mejne pogoje.

This paper deals with the flow analysis around a car in a spray-paint chamber.To solve Navier-Stokes equations for 3D flow of an incompressible and isothermal fluid we used the control-volume method (CFX 5.4). The numerical procedure, the boundary and initial conditions, the methods used for stabilizing the numerical oscillations as well as the other parameters important for the numerical procedure are described in detail. Result for 2D and 3D calculations are presented. The boundary conditions were determined with measurements in a real chamber with and without a car. The filter in the chamber was considered to be porous matter with a quadratic law of resistance,this is in accordance with the manufacturer's data that were verified with pressure-loss measurements. V prispevku smo analizirali tokovne razmere v avtomobilski lakirni komori. Za reševanje Navier-Stokesovih enačb prostorskega toka nestisljive izotermne tekočine smo uporabili metodo nadzornih prostornin (CFX 5.4). Podrobno smo opisali potek izračuna, uporabljene robne in začetne pogoje, uporabljene metode za stabilizacijo numeričnih nihanj ter druge parametre, pomembne za izračun. Predstavili smo rezultate za ravninski in prostorski primer izračuna. Robni pogoji so bili določeni z meritvami na realni komori in to za primer brez avtomobila in z njim. Filter komore je bil upoštevan kot porozna snov s kvadratno funkcijo upora po podatkih proizvajalca, ki smo jih preverili z lastnimi meritvami padca tlakov.

We have analyzed the suitability of the finite-volume method for calculating incompressible, viscous, non-Newtonian fluid flow where the Sisko model was used. In addition, convergence criteria are presented and the convergence depending on the mesh size was analyzed. The method was tested for the driven-cavity case and flow in a channel with a sudden contraction. The numerical solution was compared with the results evailable in the open literature. For the rheological model, parameters obtained from an experiment with a capillary viscometer were used. Analizirali smo primernost metode končnih prostornin za izračun tokovnih razmer v nestisljivi viskozni nenewtonski tekočini ob uporabi Siskovega modela. Prav tako smo analizirali natančnost numeričnih rezultatov v odvisnosti od gostote mreže. Metodo smo testirali na primeru gnanega toka v kotanji in primeru toka v kanalu z nenadno zožitvijo. Numerično dobljene rezultate smo primerjali z vrednostmi iz literature. Za reološki model smo uporabili modelne parametre, dobljene na podlagi preskusa s cevnim viskozimetrom.