TRANSVERSE LAMINAR FLOW OF NON-NEWTONIAN FLUIDS OVER A BANK OF LONG CYLINDERS

The creeping transverse flow of incompressible Carreau model fluids past an array of infinitely long cylinders has been analysed theoretically. The hydrodynamic interactions between cylinders have been simulated using a simple cylinder-in-cylinder free surface cell model. In this formalism, the overall mean porosity characterises an array of cylinders without any assumption regarding the actual geometrical arrangement of the individual cylinders. The resulting non-linear field equations have been solved approximately by employing the well known velocity and stress variational principles. The resulting upper and lower bounds are non-coincident and diverge increasingly with the rising extent of non-Newtonian behaviour of the liquid medium. However, the mean value of the drag coefficient deviates from the individual bounds by no more than 22% and therefore, the use of the arithmetic mean of the upper and lower bounds is suggested. The theoretical predictions reported herein encompass wide ranges of physical and kinematic conditions as follows: 1 ≥ n ≥ 0.2; 0.9 ≥ ε ≥ 0.3 and ∧ ≤ 500. The paper is concluded by presenting comparisons between the present predictions and the scant experimental results for two limiting cases, namely, for the flow of Newtonian fluids (n = 1) through assemblages of solid rods and random fibrous beds, and for the flow of power law liquids (i.e., for large values of ∧) through banks of rods. The correspondence is found to be satisfactory.     

NUMERICAL STUDY OF DEVELOPED LAMINAR MIXED CONVECTION OF Al2O3/WATER NANOFLUID IN AN ANNULUS

This work aims to study the combined free and forced convection of an Al₂O₃/water nanofluid flowing throughout an annulus. A set of three-dimensional elliptic governing equations were solved numerically using the finite volume technique. The effect of the volume fraction of the nanoparticles and the Richardson number on the thermal and hydrodynamic parameters was extensively investigated. The distribution of the axial velocity and temperature at different cross sections is shown. The axial variation of the frictional and heat transfer coefficients is presented. Results indicate that the Richardson number does not influence the frictional coefficient, while the heat transfer coefficient directly depends on the Ri number. The dimensional axial velocity continually increases with greater volume fraction of nanoparticles at the upper and lower sides of the annulus, while this behavior for dimensionless axial velocity is not continuous. The results indicate that any increase in the volume fraction results in secondary flow enhancement and, therefore, a delay in the occurrence of the maximum heat transfer coefficient.     

HEAT TRANSFER TO NON-NEWTONIAN LIQUIDS FLOWING THROUGH HORIZONTAL TUBES

Experimental and analytical investigation of heat transfer to single phase flow of pseudoplastic fluids under constant heat flux condition was carried out. Experimental data for laminar flow heat transfer in the thermally developing region over a wide range of rheological properties ( n from 0.54 to 0.84 and K from 0.07 to 2.41 Nsⁿ/m²) in 0.028 and 0.057 m diameter pipes were collected. Enhancement in heat transfer rate due to natural convection and temperature dependent rheotogy was observed. The temperature dependent viscosity effect is a function of flow behavior index and it contributes more towards heat transfer enhancement than natural convection does. A correlation (confidence level ±15%) for the entire set of data is also presented.     

FLOW OF A NON-NEWTONIAN FLUID WITH HEAT TRANSFER ABOVE A ROTATING DISK CONSIDERING THE ION SLIP

The steady flow and heat transfer of a conducting non-Newtonian fluid due to the rotation of an infinite nonconducting disk in the presence of an axial uniform steady magnetic field are studied considering the ion slip. The governing nonlinear equations are solved numerically using finite differences, and the solution shows that the ion slip and the non-Newtonian fluid characteristics give some interesting results.     

FLOW OF A NON-NEWTONIAN FLUID WITH HEAT TRANSFER ABOVE A ROTATING DISK CONSIDERING THE ION SLIP

The steady flow and heat transfer of a conducting non-Newtonian fluid due to the rotation of an infinite nonconducting disk in the presence of an axial uniform steady magnetic field are studied considering the ion slip. The governing nonlinear equations are solved numerically using finite differences, and the solution shows that the ion slip and the non-Newtonian fluid characteristics give some interesting results.     

MASS TRANSFER FROM FLAT PLATES TO POWER-LAW FLUIDS IN LAMINAR FLOW

Mass transfer from vertical flat plates to water and 0.5 to 1.5% aqueous CMC solutions is measured in the Reynolds number range of 10^{- 2}to 6.0 x 10₃. Blasius analysis has been found to be valid only up to a Reynolds number of 100, below which Graetz-Leveque solution is more appropriate.     

EXPERIMENTAL STUDY OF GRAVITY-DRIVEN FILM FLOW OF NON-NEWTONIAN FLUIDS

In this research the problem of a thin layer of a power law liquid falling down an inclined plate was studied experimentally. Three different carboxymethyl cellulose (CMC) solution concentrations (1.1%, 1.5%, and 2%), which are extensively used in industry, have been selected as the operating fluid, and their rheology, surface tension, and contact angle have been determined. Dynamics of the falling film has been studied by image acquisition techniques, and by using image processing methods the velocity of falling film, film thickness, and the shape of the falling film have been investigated. The inclined plate with different inclination angles φ (0 < φ < π/2), and nonidentical surfaces (ceramic, aluminum, and glass) were used to study the effect of inclination, rheological properties, and contact angle on the vital parameters mentioned earlier. These variables are embedded in dimensionless groups, Weber (We), Reynolds (Re), and Froude (Fr) numbers, and some correlations were devised to relate dimensionless velocity distribution parameters and film thickness to these dimensionless groups.     

MASS AND MOMENTUM TRANSFER WITH NON-NEWTONIAN FLUIDS IN FLUIDIZED BEDS

A new model for non-Newtonian fluid flows through fluidized beds is developed by extending the Richardson-Zaki concept. In the proposed model, the existing correlations for an isolated single sphere are simply extended to those for a fluidized bed by incorporating a voidage function. The model is found to be in a good agreement with other correlations for flows of a non-Newtonian fluid through multi-particle systems. The model is also applied to interpret mass transfer in fluidized beds.     

MASS AND MOMENTUM TRANSFER WITH NON-NEWTONIAN FLUIDS IN FLUIDIZED BEDS

A new model for non-Newtonian fluid flows through fluidized beds is developed by extending the Richardson-Zaki concept. In the proposed model, the existing correlations for an isolated single sphere are simply extended to those for a fluidized bed by incorporating a voidage function. The model is found to be in a good agreement with other correlations for flows of a non-Newtonian fluid through multi-particle systems. The model is also applied to interpret mass transfer in fluidized beds.     

环隙内流动沸腾传热的计算

提出环隙内流动沸腾传热计算的数学模型和计算方法。将传热系数K与流动沸腾传热系数hb的计算结果与实测数据加以比较。对环隙与空管两种结构的流动沸腾传热性能也进行了分析对比。     

FINITE ELEMENT ANALYSIS FOR LAMINAR FLOW AND HEAT TRANSFER IN FINITE ROD BUNDLES

This investigation deals with the application of finite element method to solve the thermohydraulic problem of laminar fully developed flow in the interior and wall sub-channels of finite fuel rod bundles. A variational principle has been used for the solution of the momentum and energy equations. Wall shear stress and temperature distributions, ?Re and Nusselt numbers are obtained for the sub-channels of different configurations. The results are compared with solutions generated by collocation and finite difference methods.     

FINITE ELEMENT ANALYSIS FOR LAMINAR FLOW AND HEAT TRANSFER IN FINITE ROD BUNDLES

This investigation deals with the application of finite element method to solve the thermohydraulic problem of laminar fully developed flow in the interior and wall sub-channels of finite fuel rod bundles. A variational principle has been used for the solution of the momentum and energy equations. Wall shear stress and temperature distributions, ƒRe and Nusselt numbers are obtained for the sub-channels of different configurations. The results are compared with solutions generated by collocation and finite difference methods.     

LAMINAR BOUNDARY LAYER HEAT TRANSFER TO POWER-LAW FLUIDS

The heat transfer for the steady two-dimensional incompressible laminar boundary layer of power-law non-Newtonian fluids past a semi-infinite static or moving flat plate is studied by local similarity method. Four cases are considered: static plate with prescribed wall temperature and heat flux; and moving plate with prescribed wall temperature and heat flux. The effescts of the flow index, streamwise distance and modified Prandtl number on the temperature distribution and heat transfer rate are discussed in detail.     

LAMINAR BOUNDARY LAYER HEAT TRANSFER TO POWER-LAW FLUIDS

The heat transfer for the steady two-dimensional incompressible laminar boundary layer of power-law non-Newtonian fluids past a semi-infinite static or moving flat plate is studied by local similarity method. Four cases are considered: static plate with prescribed wall temperature and heat flux; and moving plate with prescribed wall temperature and heat flux. The effescts of the flow index, streamwise distance and modified Prandtl number on the temperature distribution and heat transfer rate are discussed in detail.     

HEAT TRANSFER IN THREE-PHASE FLUIDIZED BEDS WITH NON-NEWTONIAN PSEUDOPLASTIC SOLUTIONS

Heat transfer experiments have been conducted in three-phase fluidized beds (TPFB) of 3 and 5 mm glass spheres. To assess the effect of non-Newtonian flow behavior, concentrated pseudoplastic xanthan solutions were employed. The gas and liquid superficial velocities range from 0.81 to 14.4 cm/s and 1.27 to 9.0 cm/s respectively. The impact of these parameters as well as the effect of the effective liquid viscosity, and the solid size on heat transfer in TPFB are discussed. All heat transfer coefficients can be discribed satisfactorily by a new correlation which predicts the Nu-values in TPFB with pseudoplastic solutions with ±9.13% average standard deviation.     

A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD

The thermoconvective boundary layer flow of a generalized third-grade viscoelastic power-law non-Newtonian fluid over a porous wedge is studied theoretically. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. A similarity transformation is applied to reduce the governing partial differential equations for mass, momentum, and energy conservation to dimensionless, nonlinear, coupled, ordinary differential equations. The homotopy analysis method (HAM) is employed to generate approximate analytical solutions for the transformed nonlinear equations under the prescribed boundary conditions. The HAM solutions, in comparison with numerical solutions (fourth-order Runge-Kutta shooting quadrature), admit excellent accuracy. The residual errors for dimensionless velocity and dimensionless temperature are also computed. The influence of the “power-law” index on flow characteristics is also studied. The mathematical model finds important applications in polymeric processing and biotechnological manufacture. HAM holds significant promise as an analytical tool for chemical engineering fluid dynamics researchers, providing a robust benchmark for conventional numerical methods.     

DISPERSED FLOW HEAT TRANSFER IN CIRCULAR BENDS

This paper presents an experimental study of dispersed flow heat transfer in 90-degree circular bends. From extensive measurements, two different heat transfer patterns are identified, i.e. heat transfer without and with rewetting. Their intrinsic mechanisms are analysed, based on the present experimental evidence and our previous theoretical studies. Effects of mass flow rate, wall heat flux, system pressure and curvature ratio on heat transfer are also investigated. An empirical criterion is developed to identify the heat transfer pattern in the bend.     

CONTRIBUTION TO HEAT TRANSFER IN AIR-LIFT AND BUBBLE COLUMN FERMENTORS WITH NEWTONIAN AND NON-NEWTONIAN SOLUTIONS

Heat transfer in five air-lift and bubble column bioreactors has been investigated. Water (Newtonian) and xanthan solutions (non-Newtonian) were used. The effects of superficial gas velocity, liquid-phase viscosity and riser-to-downcomer cross-section area ratio have been studied. In air-lift slightly higher heat transfer coefficients were observed than in bubble column reactors. The superficial gas velocity and the effective liquid-phase viscosity influence strongly the heat transfer performance in all systems studied. Following the surface renewal concept, general correlations for heat transfer in Newtonian and non-Newtonian fermentation broth were developed. They describe precisely heat transfer coefficients in a wide range of operating and geometrical conditions.     

DISPERSED FLOW HEAT TRANSFER IN CIRCULAR BENDS

This paper presents an experimental study of dispersed flow heat transfer in 90-degree circular bends. From extensive measurements, two different heat transfer patterns are identified, i.e. heat transfer without and with rewetting. Their intrinsic mechanisms are analysed, based on the present experimental evidence and our previous theoretical studies. Effects of mass flow rate, wall heat flux, system pressure and curvature ratio on heat transfer are also investigated. An empirical criterion is developed to identify the heat transfer pattern in the bend.     

CONJUGATE HEAT TRANSFER WITH TURBULENT FLOW IN A CIRCULAR TUBE

A steady heat transfer problem has been analyzed as a conjugate problem with turbulent flow in a circular tube. The three kinds of thermal boundary conditions considered here are specified as constant temperature, constant heat flux and constant heat transfer coefficient at the outer surface of the wall.

From the results of numerical calculation for Prandtl numbers in the range 0.01 ≤ Pr ≤ 10 and for Reynolds numbers in the range 10⁴ ≤ Re ≤ 10⁵, it was confirmed that the dimensionless parameter R_c could have significant effects on the heat transfer and the temperature field in the fluid adjacent to the wall.