Turbulent heat flux

The need for a cleaner environment in urban areas and the high cost of petroleum products which are becoming scarce due to unbalanced relation between supply and demand besides air pollution of sources has led to the research for other fuels to replace fossil fuels. Ethanol from biomass waste is such an alternative to petroleum products. Most studies on optimization of process variables using Response Surface Methodology apply Central Composite Designs yet other designs exist. Optimal designs have fewer trials employed with the aim of obtaining efficient designs for fitting reduced quadratic or higher order models. Coded values of a second order optimal rotatable design in four dimensions constructed using balanced incomplete block designs (BIBD) was fit into experimental data in order to study the effects of four process variables namely; time, PH, temperature and substrate concentration on fermentation of pineapples peels using Saccharomyces cerevisiae for ethanol production. Normal probability plots and Multiple R-squared of 0.9323 and Adjusted R-squared of 0.8944 which measure model fitting reliability indicated aptness of the model. Most values of Probability F were less than 0.05, confirming that the model terms were significant and only 6.8% of the total variation could not be explained by the model ensuring good adjustment of the model to experimental data. Model adequacy was also confirmed by the good agreement between the experimental data and predicted values. The design was found reliable in modeling, and studying the effects of the four factors to the processes of fermentation of pineapples peels as substrate for ethanol production using Saccharomyces cerevisiae

The present work discusses at length the current status of turbulent research in Brazil, After eight introductory sections on the subject, where some general aspects of the problem are presented, and a brief review of some scientific and engineering approaches is given, the paper strolls over four specific sections, analyzing all work carried out in Brazil in the past twenty five years on turbulence. In fact, the present compilation is restricted to the main events sponsored by the Brazilian Society of Mechanical Sciences. The present review quotes 284 references, presents 6 tables and ¡6 figures. The paper contents is: Paper Outline, Some Insights, The Traditional Approaches, Some Basic Working Rules, Turbulence Models, One-Point Turbulence Closure Models, Some Other Aproaches to Turbulence Modelling, Some Major Achievements, A Bit of History, Statistics, A Personal View, Gallery, Final Remarks, Cited Bibliography and Compiled Bibliography.

Abstract. The main goal of this work is to provide a performance analysis of a numerical simulation methodology in solving open-channel turbulent flows with separation of the turbulent boundary layer. To accomplish this, a selected experimental test case was ...

The steady two-dimensional magnetohydrodynamics stagnation point flow of a nanofluid with radiation effect is investigated. Using a similarity transformation, the governing partial differential equations are reduced to ordinary differential equations. The transformed equations are solved numerically for three types of nanoparticles, namely copper (Cu), alumina (Al 2 O 3 ), and titania (TiO 2 ) by using shooting method. The features of the flow with heat and mass transfer characteristics for different values of governing parameters are analyzed and discussed. Comparison with published results is presented and it found to be in good agreement. Key Words: Nanofluid, Heat and Mass Transfer, Thermal Radiation, Stagnation-Point Flow

An investigation of heat transfer was done in a cylindrical enclosure. The effects of varying Reynolds Number, Prandtl number, Froude number, and Euler number on the temperature and velocity was investigated. In the study, the top surface of a vertical cylindrical container was cooled, the bottom surface heated and the vertical cylindrical walls were considered as being adiabatic. The non-linear governing equations subject to Boussinesq approximation were solved using finite difference method. Results were analysed and presented in graphs to understand the fluid flow and temperature profiles at various locations in the enclosure. Results indicated that buoyancy forces due to temperature difference between the bottom and top of the cylinder are important in determining the velocity of air in the enclosure.

Most fluids used in technical applications are of low viscosity; hence, fluid flows encountered in engineering applications are mostly turbulent. Parameters that influence the distribution of the flow field of turbulent flow regimes thus significantly affect the performance of many thermal systems. In this study, we analyze the distribution of the flow field of a Boussinesq buoyancy-driven turbulent airflow for  and , and establish the effect of the Rayleigh number on these distributions. The flow domain comprises of a rectangular enclosure of constant aspect ratio, partially heated on a sidewall and cooled on the opposite wall. Due to the rapid fluctuations in flow properties intrinsic in the turbulent flow regime, we subject the equations governing a viscous incompressible buoyant fluid flow to the Reynolds decomposition and averaging process to obtain equations that describe a turbulent flow field.  We treat turbulence using the  turbulence model coupled with the Boussinesq appro...

In this study we have investigated a turbulent flow of a rotating fluid past a semi-infinite vertical porous plate subjected to a constant heat flux. A variable magnetic field is applied transversely in the direction normal to the plate. An induced electric current known as Hall current exists due to the presence of both electric field and magnetic field. The differential equations governing this problem are solved numerically using a finite difference scheme. Further we have investigated the effects of various parameters on the velocity, temperature, magnetic field and concentration profile. The skin friction the rate of heat transfer and the rate of mass transfer is calculated using Newton's interpolation formula We noted that the Hall current, rotation parameter, Eckert number, injection and Schmidt number affect the velocity, temperature magnetic field and concentration profiles.

Energy transfer mechanism in most technical flows is through turbulent natural convection due to low viscosity of the fluids used in technical applications. Consequently, there is need to establish the parameters that influence the flow field of turbulent flow regime in order to enhance the energy-efficacy of many thermal applications. In order to establish the influence of the geometrical configuration of the flow domain on the flow field, we obtain and analyze the distribution of the velocity and temperature fields of a Boussinesq buoyancy-driven turbulent flow field in a locally heated and cooled enclosure for 0.5 1 AR  while maintaining the Rayleigh number of the flow at 10 5.5 10 . To filter out the enormous turbulent scales inherent in the turbulent flow regime, we decompose the flow variables present in the instantaneous equations governing a viscous Boussinesq buoyant flow and subject the resulting equations to the Reynolds averaging process to obtain equations that governs the turbulent flow field. We resolve the turbulent quantities emanating from this process using the SST k w  turbulence model coupled with the Boussinesq approximation. To ensure the satisfaction of the conservation laws at the discrete level and over the entire solution domain, the non-dimensionalized equations are discretized using the robust finite volume method. The method possesses the ability to adapt a grid structure that captures the local features of the flow domain and imposes the integral form of the governing equations to each finite volume of the discretized solution domain so that the final mathematical formulation has an intimate connection to the actual physical situation. Since the equations are coupled, a segregated pressure-based iterative method is used to obtain the solution. The results revealed that the velocity and temperature fields are non-uniformly distributed in the enclosure and their magnitude and distribution significantly depend on the Aspect ratio of the enclosure. The results are consistent with the experimental results of Markatos and Pericleous (Markatos & Pericleous, 1984).

Most fluids used in technical applications are of low viscosity; hence, fluid flows encountered in engineering applications are mostly turbulent. Parameters that influence the distribution of the flow field of turbulent flow regimes thus significantly affect the performance of many thermal systems. In this study, we analyze the distribution of the flow field of a Boussinesq buoyancy-driven turbulent airflow for 9 11

In this study we have investigated a turbulent flow of a rotating fluid past a semi-infinite vertical porous plate subjected to a constant heat flux. A variable magnetic field is applied transversely in the direction normal to the plate. An induced electric current known as Hall current exists due to the presence of both electric field and magnetic field. The differential equations governing this problem are solved numerically using a finite difference scheme. Further we have investigated the effects of various parameters on the velocity, temperature, magnetic field and concentration profile. The skin friction the rate of heat transfer and the rate of mass transfer is calculated using Newton's interpolation formula We noted that the Hall current, rotation parameter, Eckert number, injection and Schmidt number affect the velocity, temperature magnetic field and concentration profiles.

Transient heat conduction is encountered in metallurgical industries where metals are subjected to different heat treatment processes to enhance their physical and chemical properties (e.g. annealing). The actual heat treatment process involves complex heat transfer processes described andsuch problems are preferentially solved using numerical methods. This work studies the transient cooling of a metal plate using a finite volume-based commercial CFD code. The temperature distribution in the metal plate during the cooling process was well predicted for both the explicit and implicit schemes with the maximum error occurring at the boundary nodes.At the constant heat flux boundary x= 0, the numerical model under predicted the temperatures with a maximum error of-0.08 %. At the convective boundary x = 0.135m , the numerical model over predicted the temperatures with a maximum error of 0 .79%. Furthermore more computational time was required in the explicit scheme in contrast to the implicit scheme that required less time. Using the implicit scheme, the calculated time for the plate to attain steady state was approximately 47,000 s.

An investigation of heat transfer was done in a cylindrical enclosure. The effects of varying Reynolds Number, Prandtl number, Froude number, and Euler number on the temperature and velocity was investigated. In the study, the top surface of a vertical cylindrical container was cooled, the bottom surface heated and the vertical cylindrical walls were considered as being adiabatic. The non-linear governing equations subject to Boussinesq approximation were solved using finite difference method. Results were analysed and presented in graphs to understand the fluid flow and temperature profiles at various locations in the enclosure. Results indicated that buoyancy forces due to temperature difference between the bottom and top of the cylinder are important in determining the velocity of air in the enclosure.

The goal of this work is to propose a new methodology to simulate turbulent thermal wall flows using the classical κ − ε model. The focus of this approach is based on the manner used to implement heat flux boundary conditions on the solid walls. In order to explain and to validate this new algorithm, several test cases are presented, testing a great range of flows in order to analyze the numerical response on different physical aspects of the fluid flow. The proposed approach uses simultaneously a thermal wall law, an analogy between fluid friction and heat transfer and an interpolating polynomial relation that is constructed with a data base generated on experimental research and numerical simulation. The algorithm used to execute the numerical simulations applies the classical κ − ε model with a consolidate Reynolds and Favre averaging process for the turbulent variables. The turbulent inner layer can be modeled by four distinct velocity wall laws and by one temperature wall law. Spacial discretization is done by P1 and P1/isoP2 finite elements and the temporal discretization is implemented using a semi-implicit sequential scheme of finite differences. The pressure-velocity coupling is numerically solved by a variation of Uzawa's algorithm. To filter the numerical noises, originated by the symmetric treatment of the convective fluxes, it is adopted a balance dissipation method. The remaining nonlinearities, due to explicit calculations of boundary conditions by wall laws, are treated by a minimal residual method.

Most fluids used in technical applications are of low viscosity; hence, fluid flows encountered in engineering applications are mostly turbulent. Parameters that influence the distribution of the flow field of turbulent flow regimes thus significantly affect the performance of many thermal systems. In this study, we analyze the distribution of the flow field of a Boussinesq buoyancy-driven turbulent airflow for  and , and establish the effect of the Rayleigh number on these distributions. The flow domain comprises of a rectangular enclosure of constant aspect ratio, partially heated on a sidewall and cooled on the opposite wall. Due to the rapid fluctuations in flow properties intrinsic in the turbulent flow regime, we subject the equations governing a viscous incompressible buoyant fluid flow to the Reynolds decomposition and averaging process to obtain equations that describe a turbulent flow field.  We treat turbulence using the  turbulence model coupled with the Boussinesq appro...

Most fluids used in technical applications are of low viscosity; hence, fluid flows encountered in engineering applications are mostly turbulent. Parameters that influence the distribution of the flow field of turbulent flow regimes thus significantly affect the performance of many thermal systems. In this study, we analyze the distribution of the flow field of a Boussinesq buoyancy-driven turbulent airflow for  and , and establish the effect of the Rayleigh number on these distributions. The flow domain comprises of a rectangular enclosure of constant aspect ratio, partially heated on a sidewall and cooled on the opposite wall. Due to the rapid fluctuations in flow properties intrinsic in the turbulent flow regime, we subject the equations governing a viscous incompressible buoyant fluid flow to the Reynolds decomposition and averaging process to obtain equations that describe a turbulent flow field.  We treat turbulence using the  turbulence model coupled with the Boussinesq appro...

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux-gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt-Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux-gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt-Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions , one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux–gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt–Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.