Increasing Bingham Number Research Articles

Numerical investigation of steady state, laminar, natural convection of Bingham fluids in a trapezoidal enclosure heated from the bottom and cooled from the sides

Laminar, steady-state, natural convection of Bingham fluids in trapezoidal enclosures with a heated bottom wall, cooled inclined sidewalls and an adiabatic top wall has been studied based on numerical simulations for a range of values of nominal Bingham numbers, Rayleigh numbers (i.e., 103 ≤ Ra ≤ 105), and sidewall inclination angles (i.e., 30° ≤ φ ≤ 60°) for a representative nominal Prandtl number (i.e., Pr = 103). It has been found that the mean Nusselt number Nu‾ increases with increasing Rayleigh number Ra due to the strengthening of advective transport. An increase in the sidewall inclination angle φ leads to a decrease in the mean Nusselt number Nu‾ due to an increase in the area for heat loss from the trapezoidal enclosure. The value of the mean Nusselt number Nu‾ was found to decrease with increasing Bingham number Bn. At high values of Bingham number Bn, the fluid flow essentially stops within the enclosure and the heat transfer takes place primarily due to conduction and, accordingly, the mean Nusselt number Nu‾ settles to a constant value, for a given value of sidewall inclination angle φ, irrespective of the value of nominal Rayleigh number Ra. Furthermore, a correlation for the mean Nusselt number Nu‾ in trapezoidal enclosures with a heated bottom wall, an adiabatic top wall, and cooled inclined sidewalls accounting for the range of Rayleigh numbers Ra, Bingham numbers Bn and inclined wall angles φ considered which provides adequate approximation of the corresponding values obtained from the numerical simulations has been identified.

Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel–Bulkley fluids

We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications.

Mixed convective heat transfer analysis for the peristaltic transport of viscoplastic fluid: Perturbation and numerical study

Mixed convective peristaltic flow of incompressible viscoplastic fluid is investigated in a two-dimensional symmetric channel. The rheology of viscoplastic material is characterized by the constitutive equation for Bingham plastic model. The coupling between momentum and energy equations is achieved through Boussinesq approximation. The coupled nonlinear partial differential equations are transformed in wave frame using Galilean transformation and then simplified under realistic assumptions of long wavelength and low Reynolds number. Approximate solution is obtained using regular perturbation method which is restricted to the smaller values of Grashof and Bingham numbers. The validity of approximate solution is established by comparing it with the numerical solution obtained via Matlab built-in routine bvp4c. Based on the numerical solution an extensive analysis is performed in order to analyze the effects of various parameters of interest on flow characteristics, pumping and trapping phenomena. It is found that velocity decreases at the center by increasing Bingham number showing a boundary layer character for large values. However, it increases by increasing Brinkman and Grashof numbers. Moreover, pressure rise per wavelength increases with Bingham number, Brinkman number and Grashof number, in the pumping region. The result further indicate that larger values of Bingham number circumvent bolus growth.

Free Convection from a Heated Vertical Cone in Generalized Newtonian Fluids

In many situations, heat transfer occurs primarily by free convection, such as that in confined and restricted spaces and/or where it is not possible to induce fluid motion by using a pump or impeller. In this work, natural convection from an isothermal cone in power law and Bingham plastic fluids has been investigated numerically by solving the coupled momentum and energy equations over wide ranges of conditions such as the Grashof number (), the Prandtl number (5–100), the Bingham number (1–50), and the power-law index (0.4–1). The structure of the flow and temperature fields is visualized in terms of streamlines and isotherm contours, yielded and unyielded regions, and the variation of the local Nusselt number along the surface of the cone. The location and shape of the yielded and unyielded regions are influenced by the values of the Grashof and Bingham numbers. The size of the unyielded regions progressively decreases with the increasing Bingham number, whereas the Grashof number promotes the growth of fluidlike regions. Shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. On the other hand, the Bingham yield stress has an adverse influence on the overall heat transfer. The present values of the average Nusselt number are correlated in terms of the pertinent dimensionless numbers to enable its prediction in a new application. Finally, a criterion for the onset of convection in Bingham fluid is also reported in terms of ; above which, conduction is the main mode of transport. Thus, the relative magnitudes of the buoyancy and viscous (including the contribution of yield stress) forces determine the degree of deterioration in the rate of heat transfer with reference to that in Newtonian fluids otherwise under identical conditions. This information is valuable: not only in designing heat transfer equipment, but also in the processing of temperature-sensitive materials.

Rayleigh-Bénard convection of Casson fluids

This study aims at investigating numerically the Rayleigh-Bénard Convection (RBC) in viscoplastic fluids. A Casson fluid is considered in a bidimensional square cavity heated from below. The effects of the dimensionless yield stress, the Bingham number Bn, on the heat transfer and motion is investigated in the range 5.103<Ra<105 for the Rayleigh number and Pr=10,100,1000 for the Prandtl number. One shows that the yield stress has a stabilizing effect, reducing the convection intensity. Above a certain value of Bnmax, the convection does not occur and the heat transfer is only due to conduction. For moderate Bn values, truly unyielded regions are located in the center of the cavity; their areas grow with increasing Bingham number and invade the whole cavity at the threshold value Bnmax.

Influences of aspect ratio and wall boundary condition on laminar Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures

PurposeThis paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular enclosures for both constant wall temperature and constant wall heat flux boundary conditions. A nominal Rayleigh number range 103 ≤ Ra ≤ 105 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) has been considered for 1/4 ≤ AR ≤ 4.Design/methodology/approachThe bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt has been found that buoyancy-driven flow strengthens with increasing nominal Rayleigh number Ra, but the convective transport weakens with increasing Bingham number Bn, because of additional flow resistance arising from yield stress in Bingham fluids. The relative contribution of thermal conduction (advection) to the total thermal transport strengthens (diminishes) with increasing AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids for both boundary conditions, and the thermal transport takes place purely because of conduction for tall enclosures.Originality/valueCorrelations for the mean Nusselt number have been proposed for both boundary conditions for both Newtonian and Bingham fluids using scaling arguments, and the correlations have been demonstrated to predict obtained from simulation data for 1/4 ≤ AR ≤ 4, 103 ≤ Ra ≤ 105 and Pr = 500.

Numerical investigation of mixed convection of Bingham fluids in cylindrical enclosures with heated rotating top wall

The steady-state laminar mixed convection of yield stress fluids obeying the Bingham model in a cylindrical enclosure with a heated rotating top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Yield stress effects on heat and momentum transport have been investigated for an aspect ratio (height/radius) of unity (i.e. AR=1) for a range of different values of nominal Prandtl, Richardson and Reynolds numbers given by 10⩽Pr⩽500, 0⩽Ri⩽1 and 100⩽Re⩽3000. The mean Nusselt number Nu‾ has been found to decrease sharply with increasing Bingham number Bn, but subsequently Nu‾ approaches asymptotically to a value of unity, which is indicative of conduction-driven transport. It has also been found that Nu‾ increases with increasing values of Prandtl and Reynolds numbers for both Newtonian (i.e. Bn=0) and Bingham fluids. In contrast, Nu‾ decreases with increasing Ri for both Newtonian and Bingham fluids for small values of Bingham number, whereas Nu‾ remains insensitive to the variation of Ri for large values of Bingham number. The variation of torque coefficient CT, which gives a quantitative measure of power consumption, has also been investigated. The torque coefficient CT has been found to increase with increasing Bn whereas it decreases with increasing Re. It has also been found that CT decreases slightly with increasing Ri for small values of Bn, whereas it becomes insensitive to the variation of Ri for large Bingham numbers. For the fully forced convection (Ri=0) case, Pr does not have a significant influence on CT. However, in the case of mixed convection CT increases with increasing Pr. The simulation data has been used in conjunction with a detailed scaling analysis to propose a correlation for Nu‾ for the range of Re,Ri and Pr considered here.

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

ABSTRACTIn this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 102 to 106, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 105. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number, and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.

Mixed convection from a spheroid in Bingham plastic fluids: Effect of buoyancy-assisted flow

ABSTRACTIn this work, laminar mixed convection from an isothermal spheroidal particle immersed in a Bingham plastic fluid is studied numerically in the buoyancy-assisted regime. The results reported herein encompass the following ranges of conditions: Reynolds number, 0.1 ≤ Re ≤ 100; Prandtl number, 10 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100; Richardson number, 0 ≤ Ri ≤ 8; and aspect ratio of the spheroid, 0.2 ≤ e ≤ 5. In particular, consideration is given to the effect of shape and orientation of the particle on the detailed flow and temperature fields (in terms of streamlines, iso-vorticity, and isotherm contours), morphology of the yielded–unyielded regions, and the local and surface-averaged Nusselt number. All else being equal, the propensity for flow separation is seen to be greater for oblates (e < 1) than that for prolates (e > 1). In both cases, this reduces with the increasing Bingham number and/or the Richardson number. Both drag coefficient and the Nusselt number show a positive dependence on the Bingham number as well as on the Richardson number. Overall, the drag coefficient increases as the particle shape changes from an oblate to prolate, whereas the reverse trend is obtained for the average Nusselt number, which is in line with the general inference that more drag corresponds to more heat transfer. Finally, the average Nusselt number is correlated with the pertinent dimensionless parameters (Re, Pr, Bn, Ri, e) via a simple correlation, thereby enabling its prediction for intermediate values of the parameters and/or in a new application.

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

Laminar natural convection from an isothermal sphere immersed in cold Bingham plastic media has been investigated numerically over wide ranges of the pertinent dimensionless parameters (Rayleigh number, 102 ≤ Ra ≤ 106; Prandtl number, 10 ≤ Pr ≤ 100; and Bingham number, 0 ≤ Bn ≤ 104). Extensive results on the flow and heat-transfer aspects are presented in terms of the streamlines and isotherm contours in the close proximity of the sphere; morphology of the yielded and unyielded regions; and the local and average Nusselt number as functions of the Rayleigh number, Prandtl number, and Bingham number. For a given value of the Rayleigh number, there exists a limiting Bingham number beyond which no convection occurs and heat is transferred from the sphere to the fluid only by conduction. Broadly, fluidlike regions are seen to gradually diminish with the increasing Bingham number, and eventually the flow field is completely frozen, corresponding to the fully plastic limit. Finally, the present numerical results of the average Nusselt number are correlated via a simple expression, thereby enabling the interpolation of the present results for the intermediate values of the parameters.

Effects of aspect ratio on natural convection of Bingham fluids in rectangular enclosures with differentially heated horizontal walls heated from below

Abstract In this analysis the effects of aspect ratio AR (ratio of enclosure height: length) on steady-state natural convection of yield stress fluids obeying the Bingham model within rectangular enclosures has been investigated for 1/4 ⩽ AR ⩽ 4. A nominal Rayleigh number range 103 ⩽ Ra ⩽ 105 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) in a configuration with differentially heated horizontal walls subjected to constant wall temperatures with heated bottom wall has been considered. It has been found that the convective transport strengthens with increasing nominal Rayleigh number Ra for both Newtonian and Bingham fluids but the mean Nusselt number Nu ‾ for Bingham fluids remains smaller than the value obtained for Newtonian fluids for a given set of values of nominal Ra and Pr due to augmented viscous resistance arising from yield stress in Bingham fluids. For Bingham fluids Nu ‾ decreases with increasing Bingham number Bn (non-dimensional yield stress) and thermal transport becomes essentially conduction-driven for large values of Bn. The relative contribution of convection to the overall thermal transport diminishes (strengthens) with increasing (decreasing) AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids. Thus, the thermal transport is principally conduction dominated for tall enclosures. A detailed scaling analysis has been carried out to explain the effects of AR. This scaling analysis, in turn, has been utilised to propose a correlation, which has been demonstrated to predict Nu ‾ obtained from simulation data for 1/4 ⩽ AR ⩽ 4, 103 ⩽ Ra ⩽ 105 and Pr = 500.

Natural convection from a circular cylinder in confined Bingham plastic fluids

Heat transfer by laminar natural convection to Bingham plastic fluids from a heated horizontal circular cylinder in a square cavity has been investigated numerically. The governing partial differential equations describing the fluid flow and heat transfer have been solved (using the finite-element based COMSOL solver) over wide ranges of the pertinent dimensionless parameters, namely, Rayleigh number (103⩽Ra⩽105), Prandtl number (1⩽Pr⩽500) and Bingham number (0⩽Bn⩽Bnmax) for a range of values of the ratio of the cylinder diameter to the size of the square cavity, 0.125⩽B⩽0.5. The detailed flow and temperature fields in the proximity of the heated cylinder are visualized in terms of the streamline and isotherm profiles, respectively. These also facilitate the delineation of the yielded and unyielded regions formed in different parts of the cavity. Further insights are provided in terms of the distribution of the local Nusselt number along the cylinder surface together with its average value. It is found that the average Nusselt number decreases with the increasing Bingham number up to a limiting value of the Bingham number (Bnmax) beyond which the average Nusselt number attains its asymptotic value, close to the pure conduction limit due to the virtually unyielding nature of the fluid. Furthermore, the influence of the aspect ratio, B, on the maximum Bingham number (Bnmax) and the resulting average Nusselt number has been explored extensively. It is found that as the size of the cavity increases with respect to the cylinder diameter, i.e., decreasing value of B, the both maximum Bingham number and average Nusselt number increase. On the other hand, Nusselt number shows a very weak dependence on the Prandtl number beyond that included in the definition of the Rayleigh number.

Laminar Rayleigh-Bénard convection of yield stress fluids in a square enclosure

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated horizontal walls with the bottom wall at higher temperature have been conducted for yield-stress fluids obeying the Bingham model. Heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–105 and a Prandtl number (Pr) range of 0.1–100. The mean Nusselt number Nu¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, weaker convective transport in Bingham fluids leads to smaller values of Nu¯ than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra. The mean Nusselt number Nu¯ decreases with increasing Bingham number in the case of yield stress fluids, and, for large values of Bingham number Bn, the value rapidly approaches to unity (Nu¯=1.0) as thermal conduction dominates the heat transfer. However, this variation in the present configuration is found to be markedly different from the corresponding variation of Nu¯ with Bn for the same nominal values of Ra and Pr in the differentially-heated vertical sidewall configuration. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. Guided by a detailed scaling analysis, new correlations are proposed for the mean Nusselt number Nu¯ for both Newtonian and Bingham fluids which are demonstrated to satisfactorily capture the correct qualitative and quantitative behaviours of Nu¯ for the range of Ra, Pr and Bn considered in this analysis.

BOUNDARY CONDITION EFFECTS ON NATURAL CONVECTION OF BINGHAM FLUIDS IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED HORIZONTAL WALLS

Natural convection of Bingham fluids in square enclosures with differentially heated horizontal walls has been numerically analyzed for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for different values of Bingham number Bn (i.e., nondimensional yield stress) for nominal Rayleigh and Prandtl numbers ranging from 10 to 10 and from 0.1 to 100, respectively. A semi-implicit pressure-based algorithm is used to solve the steady-state governing equations in the context of the finite-volume methodology in two dimensions. It has been found that the mean Nusselt number Nu increases with increasing Rayleigh number, but Nu is found to be smaller in Bingham fluids than in Newtonian fluids (for the same nominal values of Rayleigh and Prandtl numbers) due to augmented flow resistance in Bingham fluids. Moreover, Nu monotonically decreases with increasing Bingham number irrespective of the boundary condition. Bingham fluids exhibit nonmonotonic Prandtl number Pr dependence on Nu and a detailed physical explanation has been provided for this behavior. Although variation of Nu in response to changes in Rayleigh, Prandtl, and Bingham numbers remains qualitatively similar for both CWT and CWHF boundary conditions, Nu for the CWHF boundary condition for high values of Rayleigh number is found to be smaller than the value obtained for the corresponding CWT configuration for a given set of values of Prandtl and Bingham numbers. The physical reasons for the weaker convective effects in the CWHF boundary condition than in the CWT boundary condition, especially for high values of Rayleigh number, have been explained through a detailed scaling analysis. The scaling relations are used to propose correlations for Nu for both CWT and CWHF boundary conditions and the correlations are shown to capture Nu satisfactorily for the range of Rayleigh, Prandtl, and Bingham numbers considered in this analysis.

Laminar Natural Convection of Bingham Fluids in a Square Enclosure with Vertical Walls Subjected to Constant Heat Flux

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with vertical sidewalls subjected to constant heat flux have been carried out, where the enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–106 and a Prandtl number (Pr) range of 0.1–100. It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and for large values of Bingham number Bn, the value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The Nu values for the vertical walls subjected to constant heat flux are smaller than the corresponding values in the same configuration with constant vertical wall temperatures (for identical values of nominal Rayleigh, Prandtl, and Bingham numbers). However, the value of Bingham number at which Nu approaches to unity remains the same for both constant wall temperature and constant wall heat flux configurations. It is demonstrated that for small values of Bingham number Nu increases with increasing Prandtl number, but the opposite behavior occurs for large values of Bingham number. New correlations are proposed for the mean Nusselt number Nu for both Newtonian and Bingham fluids for square enclosures with vertical walls subjected to constant heat flux, which are shown to satisfactorily capture the correct qualitative and quantitative behavior of Nu in response to changes in Ra, Pr, and Bn.

Aspect ratio effects in laminar natural convection of Bingham fluids in rectangular enclosures with differentially heated side walls

In this study, two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated side walls have been conducted for a range of different aspect ratios AR (=H/L where H is the enclosure height and L is the enclosure width). The rectangular enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 104–106 and the aspect ratio range 1/8 to 8 for a single Prandtl number (Pr=7). It is found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu¯ values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu¯ in the case of Bingham fluids is found to decrease with increasing Bingham number, and, for large values of Bingham number Bn, the value of Nu¯ settles to unity (i.e. Nu¯=1.0) as heat transfer takes place principally due to thermal conduction. The effects of aspect ratio AR have also been investigated in detail and it has been found the effects of thermal convection (diffusion) strengthens (weakens) with increasing aspect ratio and vice versa, for a given set of nominal values of Rayleigh number Ra and Prandtl number Pr. It is found that the aspect ratio ARmax at which the maximum mean Nusselt number Nu¯ occurs is found to decrease with increasing Rayleigh number. However, the value of ARmax is shown to increase with increasing Bingham number Bn for a given set of values of Ra and Pr. Detailed physical explanations are provided for the observed phenomena. New correlations are proposed for the mean Nusselt number Nu¯ for Bingham fluids, which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu¯ in response to changes in Ra, AR and Bn.

Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated sidewalls have been carried out where the enclosures are considered to be completely filled with a yield stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number ( Ra) in the range 10 3–10 6 and a Prandtl number ( Pr) range of 0.1–100. It is found that the mean Nusselt number N u ¯ increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, N u ¯ values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number N u ¯ in the case of Bingham fluids is found to decrease with increasing Bingham number, and, for large values of Bingham number Bn, the value settles to unity ( N u ¯ = 1.0 ) as heat transfer takes place principally due to thermal conduction. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. New correlations are proposed for the mean Nusselt number N u ¯ for both Newtonian and Bingham fluids which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of N u ¯ in response to changes in Ra, Pr and Bn.

On the stability of Poiseuille flow of a Bingham fluid

The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.

Application of the concentric annular flow model to blood flow in tapered tubes

This work examines the application of the concentric annular flow model (CAF) to blood flow in small-diameter tapered tubes. An approximate pressure-flow relation is developed and its limitations are discussed. Comparisons between CAF in a tapering vessel and an equivalent cylindrical vessel are presented along with comparisons to pseudohomogeneous flow. The comparisons show that the error in the approximation of a tapered vessel by a cylindrical tube with a radius equal to the mean of the tapered tube increases with increasing radius ratio but decreases with increasing Bingham number. The results also show that for small-diameter tubes, the pressure drop for the CAF model is substantially lower than for the pseudohomogeneous flow model. The resulting pressure-flow relation is used to evaluate resistance ratios for comparison with in vitro perfusion experiments. The results suggest that in some cases, taper can influence the resistance ratio.