Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

Non-Newtonian Mixed Convection Flow along an Isothermal Horizontal Circular Cylinder

The mixed convective laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is studied along an isothermal horizontal circular cylinder using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively. Here, it is found that heating the cylinder delays separation and if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a very cold cylinder there will not be boundary-layer on the cylinder.     

Mean Flow and Thermal Characteristics of a Turbulent Dual Jet Consisting of a Plane Wall Jet and a Parallel Offset Jet

The standard high-Reynolds number two-equation k ? ? model is used to study the flow and thermal characteristics of a dual jet consisting of a plain wall turbulent jet and a parallel turbulent offset jet (hereafter, dual jet). The flow and thermal characteristics are presented in the form of streamlines, mean velocity vector, turbulent kinetic energy, dissipation of turbulent energy, Reynolds stresses, and isothermal contour plots. The variation in local heat flux and local Nusselt number on the bottom wall is also presented. The finite-volume-method-based SIMPLE algorithm is utilized for understanding the complex nature of flow arising due to a dual jet. The convective flux is discretized using the power-law upwind scheme, while the diffusive term is discretized using the central difference scheme. To study the effect of offset ratio, which is defined as the ratio of height of the jet from the horizontal wall to the width of the jet (nozzle), it is varied between 3 and 15 at an interval of 2. It is noted that the presence of a wall jet in addition to the parallel offset jet has a significant effect on flow and thermal characteristics.     

Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Abstract

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.     

Two-Phase Flow Visualization in Chevron and Bumpy Style Flat Plate Heat Exchangers

Adiabatic flow visualization in a chevron plate, a 1:1 aspect ratio bumpy plate, and a 2:1 aspect ratio bumpy plate heat exchangers were investigated for vertical upward flow with R134a. Qualities ranging from 5% to 90% and mass fluxes of 60, 90, and 125 kg/m²-s were investigated. The flow visualization experiments were conducted at a 10°C inlet temperature. Four flow regimes were observed for the flat plate geometries investigated: bubbly flow, rough annular flow, smooth annular flow, and mist flow. The four flow regimes are mapped out on a mass flux versus quality basis for each geometry. The chevron geometry was seen to undergo flow transitions at lower qualities and mass fluxes than the bumpy plate geometries, and the 2:1 aspect ratio bumpy plate geometry was seen to undergo flow transitions at lower qualities and mass fluxes than the 1:1 aspect ratio bumpy plate geometry.     

Fluid flow and heat transfer in an optical fiber coating process

The optical fiber coating process, using a die and applicator system, was numerically simulated. The coupled partial differential equations, governing the fluid flow and heat transfer, were solved on a transformed, non-uniform, staggered grid. A finite volume method, with conjugate heat transfer, boundary-fitted grid, and variable transport properties, was employed. The pressure was calculated using a SIMPLE-based algorithm. An isothermal case was first modeled, where the effect of the Reynolds number (Re) was studied for different geometries. Different coating fluids were considered. A conjugate boundary condition was employed at the fiber–fluid interface for the non-isothermal flow. A free surface boundary condition was used at the fiber entry into the coating fluid. The meniscus was prescribed on the basis of prior experimental work. Regardless of fiber speed, a circulating flow was observed in the applicator. High shear rates at the dynamic contact point suggest that air can be entrained with a fast moving fiber. It was also found that pressures at the coating fluid inlet did not play a major role, for typical fiber speeds, whereas the thermal conditions that affect the properties of the fluid, such as viscosity, made a significant impact on both the flow and the thermal field. This work could be used to determine the parameters that are critical for improving the quality of the coating, particularly its uniformity, and the production rate.     

The analysis of conjugate problems of conduction and convection for non-Newtonian fluids past a flat plate

In this paper, the conjugate problems of laminar forced convection in non-Newtonian fluid flow and heat conduction inside a heated flat plate is studied. A conjugate parameter ζ is proposed to reflect the characteristics of the conjugate problems. The value of the conjugate parameter lies among 0 and 1 and the two limiting values correspond to the ordinary convection problem with boundary condition of constant wall heat flux (ζ = 0) and constant wall temperature (ζ = 1), respectively. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics, n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of conjugate problems and the whole regime of the non-Newtonian fluids. The effects of the conjugate parameter, the power-law viscosity index and the generalized Prandtl number on the temperature profiles, as well as on the local heat transfer rate are clearly illustrated.     

Mixed convective flow of immiscible viscous fluids in a vertical channel

Combined free and forced convection flow in a parallel‐plate vertical channel is analyzed for immiscible viscous fluids taking into account the effect of viscous dissipation. Three types of thermal boundary conditions are described. These thermal boundary conditions are isothermal‐isothermal, isoflux‐isothermal, and isothermal‐isoflux for the left–right walls of the channel. The coupled nonlinear governing equations are solved analytically using the regular perturbation method. Separate solutions are matched at the interface using suitable matching conditions. The results are represented graphically for various governing parameters such as the ratio of Grashof number to Reynolds number, viscosity ratio, width ratio, and conductivity ratio for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20324     

Influence of Aiding Buoyancy on the Suppression of Flow Separation for Power-Law Fluids Around a Circular Object

Numerical computations are performed to analyze the influence of aiding thermal buoyancy on the phenomenon of suppression of flow separation in power-law fluids around a circular object. The idea has been borrowed from some recent similar works in Newtonian fluids. Owing to the contradictory behavior of shear-thinning and shear-thickening fluids in regard to the separation mechanism, we intend to understand the role of superimposed thermal buoyancy on the suppression phenomena in non-Newtonian power-law fluids, for which a range of power-law indices (0.4 to 1.8) is considered. The Reynolds numbers are kept intentionally low, within 10 to 40, such that the isothermal flow remains steady and separated without imposition of thermal buoyancy. The buoyancy causes a delay in the separation, thereby affecting the suppression phenomena. We determine the critical heating parameter (Richardson number) for the complete suppression of the flow separation and from there we construct a bifurcation diagram to show the typical flow regime evolved due to the complex interplay between the aiding thermal buoyancy and fluid rheology. The Richardson number in the simulation lies in the range 0 to 0.35, keeping the Prandtl number fixed at 50. The heat transfer rates from the object are also obtained and important inferences are drawn in regard to the inhibition/augmentation of heat transfer due to fluid rheology.     

Flow due to a porous stretching/shrinking sheet with thermal radiation and mass transpiration

This study investigates the behavior of carbon nanotubes (CNT) approaching an unsteady flow of a Newtonian fluid over a stagnation point on a stretching surface employing porous media. It flows when the liquid begins to move with the progression of time. Heat exchange with the environment has an impact on the flow. The implicitly limited component technique is used to solve the nondimensional partial differential equation with an associated boundary layer, which is an unstable system. Analytically, the solutions, as well as the required boundary conditions, are obtained. The effects of mass transpiration, volume fraction, and heat radiation on Newtonian fluid flow through porous media are explored. Single- and multi-walled CNTs are used as well as water, as base fluids in the experiment. The impact of thermal radiation and heat source/sink is shown in the energy equation, which is solved under four different cases: uniform heat flux case, constant wall temperature case, general power-law wall heat flux case, and general power-law wall temperature case. By supplying distinct physical characteristics, a theoretical analysis of the existence and nonexistence of unique and dual solutions may be explored. These physical parameters determine the velocity distribution and temperature distribution. Prescribed surface temperature (PST) and prescribed wall heat flux (PHF) heat transfer solutions can be written using confluent hypergeometric equations, and generic power-law PST and PHF situations can also be expressed using confluent hypergeometric equations. The graphical representations assist in the discussion of the current study's findings.     

Two-Phase Flow Distribution to Tubes of Parallel Flow Air-Cooled Heat Exchangers

Abstract

This paper addresses two-phase flow distribution phenomena in multiple header–tube junctions used in heat exchangers. Because of phase separation, it is very difficult to obtain uniform two-phase flow distribution to the branch tubes. The flow distribution is strongly influenced by the header orientation (horizontal or vertical) and the number of branch tubes. Other factors that influence the flow distribution are the flow direction in the header (upflow or downflow), the header shape and tube end projection into the header, and the location and orientation of the inlet and exit connections. The source of maldistribution is the flow in the dividing headers. Work performed by the authors and others (including patents) are discussed. The possibilities for eliminating two-phase flow maldistribution are identified and discussed. This investigation shows that solutions, which provide uniform flow distribution, are very design-specific. Change of the geometry or operating parameters will require modification of the design.     

Forced Convection in Micropolar Fluid Flow through a Wavy-Wall Channel

ABSTRACT

Forced convection of micropolar fluids through a periodic array of wavy-wall channels has been analyzed by using a simple coordinate transformation method and the spline alternating- direction implicit method. The effects of the wavy amplitude, the micropolar parameter, and the Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging-diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and larger wavy amplitudes. For the micropolar fluids, increasing the vortex viscosity causes an increase in the total viscosity of the fluid, thus the skin friction coefficient increases while the Nusselt number decreases. Also, the influence of vortex viscosity on the minimum cross section of the wavy-wall channel and on a tiny change of the maximum cross section is manifest. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, regardless of whether the fluids are Newtonian or micropolar fluids.     

Mixed convection of non-Newtonian fluids along a heated vertical flat plate

Mixed convective heat transfer of non-Newtonian fluids on a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits of zero or infinite viscosity as are encountered in the boundary-layer formulation with traditional models of viscosity for power-law fluids. These unrealistic limits can introduce an irremovable singularity at the leading edge; consequently, the model is physically incorrect. The present modified model matches well with the measurement of viscosity, and does not introduce irremovable singularities. Therefore, the boundary-layer equations can be solved by marching from the leading edge downstream as for Newtonian fluids. The numerical results are presented for a shear-thinning fluid in terms of the velocity and temperature distribution, and for important physical properties, namely the wall shear stress and heat transfer rates.     

Influence of Inlet Premixing on Two-Phase Flow Patterns in a Horizontal Minichannel

Experimental investigations are reported for air–water two-phase flow through a 2.1-mm horizontal circular minichannel. Influence of inlet premixing on two-phase flow is established by constructing various T-junction geometries with cross-flow arrangement of air and water. Six different flow patterns are observed and flow pattern maps are developed. The developed flow pattern maps are then compared for different inlet designs. It is observed that the degree of premixing of the two fluids has significant effect on flow patterns, particularly for surface-tension-dominated regime. The results obtained from these experiments can provide guidelines for selection, design, and control of wide-ranging microfluidic applications. The flow pattern map established in the present study may facilitate prediction of flow regimes in pulsating heat pipes based on the inlet flow rates of the gas and liquid.     

Calculation of the Heat Transfer Coefficient for Laminar Flow in Pipes in Practical Engineering Applications

ABSTRACT

Paper presents an analysis of existing correlations for laminar liquid flow and heat transfer in tubes based on the published theoretical research and experimental data. Considering the relatively large deviation of existing correlations from the experimental data, the novel correlation for laminar heat transfer in tubes is proposed. The new correlation covers large range of tube diameters ranging from micro-scale level 125.4 µm to conventional diameter 20.8 mm, Graetz numbers up to 6500 and fluid to wall viscosity ratio 0.0048–11.7. Correlation ratio of the newly proposed relationship for a total number of 390 experimental runs is 96.6% and standard deviation is 16.2%. Moreover, correlation covers both the hydraulically and thermally undeveloped and developed flows and all cases of boundary conditions that can be met in industrial applications.     

Entropy Generation Due to the Flow of a Non-Newtonian Fluid with Variable Viscosity in a Circular Pipe

The non-Newtonian fluid can be considered as a third-grade fluid with variable viscosity. In this case, the rate of fluid strain can be formulated using the third-grade fluid analogy. In the present study, entropy generation due to non-Newtonian fluid flow in a pipe is investigated. A third-grade fluid with variable viscosity is accommodated in the analysis. Analytical solutions for velocity and temperature distributions are presented, and an entropy generation number is computed for different non-Newtonian parameters, viscosity parameters, and Brinkman numbers. It is found that increasing the non-Newtonian parameter lowers the entropy generation number. This is more pronounced in the region close to the pipe wall. Increasing the viscosity parameter and Brinkman number enhances the entropy generation number, particularly in the vicinity of the pipe wall.     

Laminar Free Convection in Power-law Fluids in a Right Angle Triangular Duct with Heated Base

ABSTRACT

Laminar free convection in power-law fluids in a triangular duct is studied numerically to delineate the effects of the height-to-base ratio of the enclosure (0.2 to 2), power-law index (0.2 to 1.8), Grashof number (10 to 10⁴) and Prandtl number (0.7 to 100). The heat transfer is analyzed for the heated base with the other two walls being cold. Detailed kinematics is characterized by the formation of multiple recirculating zones ranging from two to four cells. Shear rate contours provide additional insights about the variation of the local viscosity in the fluid. Heatlines and the values of the Bejan number over the range of conditions are calculated to delineate the contributions of the entropy generation due to thermal effects and viscous dissipation. At low Grashof and/or Prandtl numbers, conduction dominates the overall heat transfer and this transition between the conduction and convection-dominated regimes is captured in terms of a modified Rayleigh number. The effect of aspect ratio on the Nusselt number is modulated by the values of Grashof and Prandtl numbers and power-law index. The present results have been consolidated via the use of a modified Rayleigh number for estimating the value of average Nusselt number in a new application.     

Analyses of heat and water transport interactions in a proton exchange membrane fuel cell

A two-phase non-isothermal model is developed to explore the interaction between heat and water transport phenomena in a PEM fuel cell. The numerical model is a two-dimensional simulation of the two-phase flow using multiphase mixture formulation in a single-domain approach. For this purpose, a comparison between non-isothermal and isothermal fuel cell models for inlet oxidant streams at different humidity levels is made. Numerical results reveal that the temperature distribution would affect the water transport through liquid saturation amount generated and its location, where at the voltage of 0.55 V, the maximum temperature difference is 3.7 °C. At low relative humidity of cathode, the average liquid saturation is higher and the liquid free space is smaller for the isothermal compared with the non-isothermal model. When the inlet cathode is fully humidified, the phase change will appear at the full face of cathode GDL layer, whereas the maximum liquid saturation is higher for the isothermal model. Also, heat release due to condensation of water vapor and vapor-phase diffusion which provide a mechanism for heat removal from the cell, affect the temperature distribution. Instead in the two-phase zone, water transport via vapor-phase diffusion due to the temperature gradient. The results are in good agreement with the previous theoretical works done, and validated by the available experimental data.     

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.     

Uniform lateral mass flux effect on natural convection of non-Newtonian fluids over a cone in porous media

In this paper, we have investigated a boundary layer analysis for uniform lateral mass flux effect on natural convection of non-Newtonian power-law fluids along an isothermal or isoflux vertical cone embedded in a porous medium. Numerical results for the dimensionless temperature profiles as well as the local Nusselt number are presented for the mass flux parameter, viscosity index n and geometry shape parameter λ. The local surface heat transfer increases for the case withdrawal of fluid, the increase of the value of λ. The local Nusselt number is found to be significantly affected by the surface mass flux than the viscosity index.