Laminar forced convection heat transfer of a non-newtonian fluid in a square duct

Numerical solutions for laminar heat transfer of a non-Newtonian fluid in the thermal entrance region of a square duct are presented for three thermal boundary conditions. The power-law model characterises the non-Newtonian behavior. The numerical results show that for each flow behavior index the Nusselt number decreases from a maximum value at the entry plane to a limiting value when both velocity and temperature profiles are fully developed. The results are compared with the available solutions for Newtonian fluid and excellent agreement is found.     

COMBINED RADIATION AND LAMINAR MIXED CONVECTION IN THE THERMAL ENTRANCE REGION OF HORIZONTAL ISOTHERMAL RECTANGULAR CHANNELS

The interaction of thermal radiation with laminar mixed convection for a gray fluid in the thermal entrance region of a horizontal isothermally heated rectangular channel is numerically investigated. The vorticity-velocity formulation of the Navier-Stokes equation and the integral formulation for radiation solved by finite-element nodal approximation are employed. The effects of radiation and convection on local Nusselt number, the development of bulk temperature, and the friction factor are examined. Secondary flow induced by the buoyancy effects leads to a significant enhancement in heat transfer in the entrance region. The result shows that the existence of secondary flow causes fluctuations in local Nusselt number and this phenomenon is reduced by the effect of thermal radiation and a large aspect ratio.     

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.     

Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid

The Graetz problem for fully developed laminar flow in horizontal rectangular channels with uniform wall heat flux is extended by including buoyancy effects in the analysis for the case of large Prandtl number fluid. A general formulation valid for all Prandtl numbers is presented and the limiting case of large Prandtl number is approached by a numerical method. The typical developments of temperature profile, wall temperature and secondary flow in the thermal entrance region are presented for the case of square channel γ = 1. Local Nusselt number variations are presented for the aspect ratios γ = 0.2, 0.5, 1, 2 and 5 with Rayleigh number as parameter. Due to entry and secondary flow effects, a minimum Nusselt number occurs at some distance from the entrance, depending on the magnitude of Rayleigh number. This behavior is similar to that observed in the thermal entrance region where the transition from laminar to turbulent flow occurs. The effect of Rayleigh number is seen to decrease the thermal entrance length, and the Graetz solution, neglecting buoyancy effects, is found to be applicable only when Rayleigh number is less than about 10³. A study of the practical implications of large Prandtl number on heat transfer results for hydrodynamically and thermally fully developed case reveals that the present heat transfer results are valid for Prandtl number ranging from order 10 to infinity.     

Two-dimensional-numerical investigation on the influence of first rib distance from the entrance of channel on Nusselt number and pressure drop

Enhancing the heat transfer coefficient in heat sinks can be achieved by surface modification techniques. Although the addition of ribs increases heat transfer capacity, it also increases pressure drop, lowering the channel's thermohydraulic performance (THP) factor. Rib research began a decade ago, with the majority of studies focusing on new rib designs or factors such as relative roughness pitch, relative roughness height, channel width, and channel height (geometric optimization) to improve THP. The goal of this study is to investigate the influence of the positioning of the first rib from the channel entrance on the Nusselt number, pressure drop, and THP factor with a simple design that could be manufactured easily. Three distinct rib designs are evaluated with rib positioning from the channel entrance, rib thickness, pitch, and Reynolds number as the parameters. It was found that the fluid starts settling up at the ribs as the ribs are moved closer to the channel entry point, thus increasing the pressure drop and reducing the fluid velocity. For the proposed design and dimensions, the Nusselt number increases by 3%–5%, and the pressure drop lowers by 4%–14% when the first rib is placed away from the channel entrance.     

Effects of viscous dissipation on the heat transfer in a forced pipe flow. Part 2: Thermally developing flow

In this part of the study, consideration is given to thermally developing laminar forced convection in a pipe including viscous dissipation. The axial heat conduction in the fluid is neglected. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Both the wall heating (the fluid is heated) case and the wall cooling (the fluid is cooled) case are considered. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. Results show that the temperature profiles and local Nusselt number are influenced by the Brinkman number (Br) and the thermal boundary condition used for the wall. Significant viscous dissipation effects have been observed for large Br.     

Entrance region heat transfer in a channel downstream of an impinging jet array

An experimental investigation is carried out on the entrance region heat transfer in a parallel plate channel downstream of a jet array located in one of the plates. The jet impingement surface is kept isothermal while the opposing surface, containing the jet array, is adiabatic. The focus of the investigation is the systematic study of the effect of flow rate and array geometric parameters on local Nusselt numbers in the entrance region of the channel immediately downstream of the array. To place these results in context, Nusselt numbers opposite the array and in the fully developed region downstream of the channel entrance are also included. In the entrance region, the ratio of the local to fully developed Nusselt number is independent of the channel Reynolds number, and the effects of some jet array geometric parameters are significant. These effects become negligible within 10 hydraulic diameters from the channel entrance. The entrance length is about 21 hydraulic diameters. The fully developed Nusselt numbers agree well with previous measurements. Empirical correlations are developed to fit the observations.     

Mixed convection with heat and mass transfer in horizontal tubes

This paper presents the influence of the Lewis number on laminar mixed convective heat and mass transfer in a horizontal tube with uniform heat flux and uniform concentration at the fluid–solid interface. The results of this numerical study show that, for these boundary conditions, the effect of the Lewis number on the Sherwood number is most important near the tube inlet. In the case of the Nusselt number and the wall shear stress, this effect is limited to the intermediate region between the entrance and the fully developed regions.     

Analytical solution to the problem of heat transfer in an MHD flow inside a channel with prescribed sinusoidal wall heat flux

An MHD laminar flow through a two dimensional channel subjected to a uniform magnetic field and heated at the walls of the conduit over the whole length with a sinusoidal heat flux of vanishing mean value or not, is studied analytically. General expressions of the temperature distribution and of the local and mean Nusselt numbers are obtained by using the technique of linear operators in the case of negligible Joule and viscous dissipation and by taking into account the axial conduction effect. The principal results show that an increase of the local Nusselt number with Hartmann number is observed, and, far from the inlet section, the average heat transfer between the fluid and the walls shows a significant improvement at all values of Hartmann number used when the frequency of the prescribed sinusoidal wall heat flux is increasing in the case of vanishing mean value of the heat flux and this is true especially at low Peclet numbers.     

NUMERICAL STUDY ON TURBULENT FLOW AND HEAT TRANSFER IN CIRCULAR COUETTE FLOWS

Abstract

A numerical study is performed to investigate heat transfer and fluid flow in the entrance and fully developed regions of an annulus, consisting of a rotating, insulated inner cylinder and a stationary, heated outer cylinder. Several different k-ε turbulence models are employed to determine the turbulent kinetic energy, its dissipation rate, and the heat transfer performance. The governing boundary layer equations are discretized by means of a control volume finite difference technique and numerically solved using the marching procedure. In the entrance region the axial rotation of the inner cylinder induces a thermal development and causes an increase in both the Nusselt number and the turbulent kinetic energy in the inner cylinder wall region. In the fully developed region, an increase in the Taylor number causes an amplification of the turbulent kinetic energy over the whole cross section, resulting in a substantial enhancement in the Nusselt number. These transport phenomena are also affected by the radius ratio and Reynolds number.     

Laminar flow heat transfer from an argon plasma in a circular tube

The laminar flow of a plasma in the entrance region of a circular tube has been analyzed using an implicit finite-difference scheme. The solution is based upon the boundary-layer equations with the plasma radiation term retained in the energy equation, and the transverse convection term retained in both the momentum and energy equations. Numerical results have been obtained for an argon plasma having a linear enthalpy and cubic velocity profile at the tube entrance. At the low temperature limit of the analysis, the friction factor is in agreement with previously published results; and in all but a very small region near the tube entrance the local Nusselt number agrees with the Nusselt number for constant property, fully-developed flow to within approximately 17 per cent.     

Variations in gas properties in laminar micro-convection with entrance effect

The present work investigates the influence of property variations of air in laminar forced convection with entrance effect. Two-dimensional micro-sized geometry (with axisymmetry) with constant wall heat flux boundary condition is considered to predict flow behaviour and thermal development. The continnum-based conservation equations are numerically solved to account for non-rarefaction scaling effects due to variations in fluid properties. At the microscale, results for Nusselt number show significant deviation from conventional theory that does not consider additional mechanisms that surface. The effect of property variation in Graetz problem for low subsonic flow is also studied.     

Convective Heat Transfer and Resistance Characteristics of Nanofluids with Cylindrical Particles

Numerical research on convective heat transfer and resistance characteristics of TiO₂/water nanofluids with cylindrical particles in laminar channel flow are performed by solving the governing equations of fluid flow with the additional term of cylindrical nanoparticles, the equation of probability density functions for cylindrical nanoparticle orientation, and general dynamics equation for nanoparticle volume concentration. The nonuniformity of nanoparticle distribution is considered and the effects of both particle volume concentration and Reynolds number on friction factor and local Nusselt number are mainly analyzed. The results show that the friction factor of nanofluid flow increases with an increase in particle volume concentration. And the friction factor decreases with increasing Reynolds number and is not dependent on the volume concentration at high Reynolds numbers. The Nusselt number declines when the Reynolds number decreases, and finally approaches an asymptotic value after the Reynolds number falls to a certain value. The Nusselt number is higher in the entrance region than at the downstream locations, and will become steady at somewhere downstream when the flow is thermally and hydraulically developed.     

Microtube gas flows with second-order slip flow and temperature jump boundary conditions

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, second-order boundary conditions assuming an effective mean free path model predict a lower slip velocity than a first-order model assuming a hard sphere mean free path model. Heat transfer effects associated with rarefied flow are reduced for the second-order model. The effect of the second-order terms is most significant at the upper limit of the slip regime. For airflow at standard conditions, the maximum second-order change to the Nusselt number is on the order of 15%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.     

Three dimensional laminar non-Newtonian fluid flow and heat transfer in the entrance region of a cross-shaped duct

The Galerkin finite element is used to solve the three dimensional momentum and energy equations for laminar non-Newtonian flow in cross-shaped straight duct. Both flow and heat transfer develop simultaneously from the entrance of the channel. Uniform wall temperature (T) and also constant wall heat flux both axially and peripherally (H2) are used as thermal boundary conditions. The power-law model is chosen to characterize the non-Newtonian behaviour of the fluid. The effect of power-law index and geometric parameter on the apparent friction factor as well as Nusselt number are presented and discussed.     

Effects of entrance region transport processes on free convection slip flow in vertical microchannels with isothermally heated walls

Natural convection gaseous slip flows in vertical microchannels with isothermal wall conditions are numerically investigated, in order to analyze the influence of the entrance (developing) region on the overall heat transfer characteristics. A long channel aspect ratio is considered, so as to achieve both hydrodynamically and thermally fully developed conditions at the channel exit. In other words, the flow-field within the microchannel consists of both developing and fully developed regimes. A wide range of Rayleigh number is covered, so that the cases of very short and relatively large entrance lengths can be analyzed in the same unified mathematical framework. With first order velocity and temperature jump conditions at the microchannel walls, local and average Nusselt number values are computed, by invoking the Navier Stokes equation and the energy conservation equation. It is recognized that the micro-scale effects, being associated with the velocity slip and temperature jump conditions, exhibit enhancements in the rate of heat transfer, as compared to the similar macro-scale geometries. The relative enhancements in the average Nusselt number become more prominent for higher values of Knudsen number, whereas this augmentation effect is found to be somewhat arrested at higher values of Rayleigh number. Contrasting features in the heat transfer rate predictions with and without the considerations of the entrance region effects are also carefully noted.     

Heat transfer in trapezoidal microchannels of various aspect ratios

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7° and 45° are chosen to correspond to etch-resistant planes in the crystal structure of silicon. Local and average Nusselt numbers are reported as a function of dimensionless length and aspect ratio. The effect of Prandtl number upon the thermal entrance condition is explored. The fully developed friction factors are computed and correlated as a function of channel aspect ratio. Correlations are also developed for the local and average Nusselt numbers in the thermal entrance region as a function of a dimensionless axial length variable.     

Conjugate Heat Transfer from Sudden Expansion Using Nanofluid

Conjugate heat transfer from sudden expansion using nanofluid is studied numerically. The governing equations are solved using unsteady stream function-vorticity formulation method. Results are compared with zero nanoparticle fluid to exhibit the role of nanoparticle. The effect of volume fraction of nanoparticles and type of nanoparticles on heat transfer are examined and found to have a significant impact. Local Nusselt number and average Nusselt number are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. Two dimensionality is more pronounced in the solid wall up to recirculation length. Local Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction show significant impact on average Nusselt number. The wall thickness causes larger temperature gradient at the conjugate interface boundary, which leads to larger average Nusselt number.     

Large Eddy Simulation of Turbulent Slot Jet Impingement Heat Transfer at Small Nozzle-to-Plate Spacing

We present fluid flow and heat transfer of a slot jet impingement heat transfer at a small value of the nozzle-to-plate spacing at which a secondary peak in the Nusselt number is observed. Large eddy simulation has been performed with a finite-volume-based computational fluid dynamics code and using a dynamic Smagorinsky model. The optimum domain size and grid for large eddy simulation (LES) have been produced based on LES computations on a coarse mesh and Reynolds-averaged Navier–Stokes-based computations. Two inflow conditions, namely, using the vortex method and no perturbations, were compared. The present LES results, using the vortex method, capture the secondary peak in the Nusselt number better as compared to the case with no perturbations. Results show that mean velocity profile in the stagnation region deviates from the standard law of the wall. Further, large-scale vortical structures were observed near the location of the secondary Nusselt number peak. Increases in both the streamwise and wall normal turbulence fluctuations are observed near the secondary peak in the Nusselt number. The secondary peak in Nusselt number is found to be associated with the combined effect of flow acceleration and an increase in the turbulence kinetic energy.