Effect of Sinusoidally Varying Flow of Yield Stress Fluid On Heat Transfer From a Cylinder

2021 ◽  
Author(s):  
Sanjay Gupta ◽  
Swati Patel ◽  
Raj P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Process Intensification ◽  
Simple Expression ◽  
Pulsation Frequency ◽  
Mean Velocity ◽  
Bingham Plastic ◽  
Bingham Number

Abstract The effect of pulsating laminar flow of a Bingham plastic fluid on heat transfer from a constant temperaturre cylinder is studied numerically over wide ranges of conditions as: Reynolds number (0.1 = Re = 40) and Bingham number (0.01 = Bn = 50) based the on mean velocity, Prandtl number (10 = Pr = 100), pulsation frequency (0 = w* = Pi) and amplitude (0 = A = 0.8). Results are visualized in terms of instantaneous streamlines, isotherms, apparent yield surfaces at different instants of time during a pulsation cycle. The overall behavior is discussed in terms of the instantaneous and time averaged values of the drag coefficient and Nusselt number. The size of the yielded zone is nearly in phase with the pulsating velocity whereas the phase shift has been observed in both drag coefficient and Nusselt number. The maximum augmentation ( ~30 %) in Nusselt number occurs at Bn = 1, Re = 40, Pr = 100, w* = Pi and A = 0.8 with respect to that for uniform flow. However, the increasing yield stress tends to suppress the potential for heat transfer enhancement. Conversely, this technique of process intensification is best suited for Newtonian fluids in the limit of Bn ~ 0. Finally, a simple expression consolidates the numerical values of the time-average of the Nusselt number as a function of the pertinent dimensionless parameters which is consistent with the widely accepted scaling of the Nusselt number with ~Pe1/3 under these conditions.

Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe With Uniform Wall Heat Flux: The Graetz Problem Extended

1999 ◽  
Vol 121 (3) ◽  
pp. 556-563 ◽  
Author(s):  
T. Min ◽  
J. Y. Yoo
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Yield Stress ◽  
Wall Heat Flux ◽  
Circular Pipe ◽  
Bingham Plastic ◽  
Graetz Problem ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

Thermally developing laminar flow of a Bingham plastic in a circular pipe with uniform wall heat flux has been studied analytically. Expressions for the fully developed temperature and Nusselt number are presented in terms of the yield stress, Peclet number, and Brinkman number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet, and Brinkman numbers on the Nusselt number are discussed. In particular, it is shown that the heat transfer characteristics in the entrance region are significantly affected by the yield stress with the inclusion of viscous dissipation.

Combined Effects of Fluid Yield Stress and Geometrical Arrangement on Natural Convection in a Square Duct From Two Differentially Heated Horizontal Cylinders

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Lubhani Mishra ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Duct ◽  
Bingham Plastic ◽  
Square Enclosure ◽  
Bingham Number ◽  
Heated Cylinder

Abstract Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders arranged either one above the other or along the diagonal of the square enclosure. The coupled momentum and energy equations have been solved to elucidate the effect of Rayleigh number (104–106), Prandtl number (10–100), Bingham number (0.01 to Bnmax), and the gap between the two cylinders in terms of the geometric parameters (0 to −0.25 for vertical alignment and 0.15 to 0.35 for diagonal alignment) on the detailed structure of the flow field and the overall heat transfer characteristics of the system. New extensive results are visualized in terms of streamlines, isotherm contours, and variation of the local Nusselt number along various surfaces. Additional insights are developed by examining the shear-rate contours and the yield surfaces delineating the fluid-like and solid-like regions in the flow domain. At high values of the Bingham number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which promotes heat transfer. The augmentation in heat transfer depends on the volume of fluid participating in the buoyancy-induced flow. For the vertical arrangement, the average Nusselt number (for the heated cylinder) decreases a little as these are moved slightly away from the center of the enclosure, followed by an increase as the two cylinders approach one of the sidewalls; this is so even in the conduction limit. In contrast, when the two cylinders are arranged along the diagonal, the Nusselt number progressively decreases as the gap between the two cylinders increases. Finally, predictive correlations have been developed for the average Nusselt number and the limiting Bingham number thereby enabling their estimation in a new application.

Natural Convection of Viscoplastic Fluids in a Square Enclosure

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Average Nusselt Number ◽  
Critical Value ◽  
Square Enclosure ◽  
Bingham Number ◽  
Viscoplastic Fluids

Viscoplastic fluids are special kind of non-Newtonian materials which deform or flow only when applied stresses are more than a critical value known as yield stress. In this work, a numerical investigation of natural convection in a square enclosure filled with viscoplastic fluids has been reported. The enclosure has been partially heated from the bottom wall by a heating source and symmetrically cooled from both the side walls. The rheology of the viscoplastic fluids has been modeled with Bingham fluid model. A scaling analysis has been presented to establish the gross dependence of heat transfer on different values of operating parameters of the problem. The effects of yield stress of the fluid on heat and fluid transport inside the enclosure have been investigated for different values of temperature difference, across the hot and cold surfaces and also for different fluids. The effects of different lengths of heated zone on the flow phenomena and heat transfer characteristics have been investigated for three different values of the heated zones. All the important results have been expressed in terms of Bingham number (Bn), Rayleigh number (Ra), and Prandtl number (Pr). It has been observed that with the increase in Bingham number, the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Bingham number for which the heat transfer inside the enclosure takes place solely by conduction mode. This critical value increases with the increase in Rayleigh number. For fixed value of Bingham number, i.e., fixed value of yield stress, the effects of Rayleigh number and heated length on heat transfer have been observed similar to the case of natural convection in Newtonian fluid. It has been also observed that at high Bingham number the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Bingham number. Using the present numerical results, a correlation of average Nusselt number as a function of other nondimensional numbers has been established.

Forced convection heat transfer study of a blunt-headed cylinder in non-Newtonian power-law fluids

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jaspinder Kaur ◽  
Roderick Melnik ◽  
Anurag Kumar Tiwari
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Power Law ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Total Drag ◽  
Shear Thinning Fluids ◽  
Power Law Fluids

Abstract In this present work, forced convection heat transfer from a heated blunt-headed cylinder in power-law fluids has been investigated numerically over the range of parameters, namely, Reynolds number (Re): 1–40, Prandtl number (Pr): 10–100 and power-law index (n): 0.3–1.8. The results are expressed in terms of local parameters, like streamline, isotherm, pressure coefficient, and local Nusselt number and global parameters, like wake length, drag coefficient, and average Nusselt number. The length of the recirculation zone on the rear side of the cylinder increases with the increasing value of Re and n. The effect of the total drag coefficient acting on the cylinder is seen to be higher at the low value of Re and its effect significant in shear-thinning fluids (n < 1). On the heat transfer aspect, the rate of heat transfer in fluids is increased by increasing the value of Re and Pr. The effect of heat transfer is enhanced in shear-thinning fluids up to ∼ 40% and it impedes it’s to ∼20% shear-thickening fluids. In the end, the numerical results of the total drag coefficient and average Nusselt number (in terms of J H −factor) have been correlated by simple expression to estimate the intermediate value for the new application.

Forced Convective Flow of Bingham Plastic Fluids in a Branching Channel With the Effect of T-Channel Branching Angle

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Anamika Maurya ◽  
Naveen Tiwari ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Length Variation ◽  
Heat Transfer Characteristics ◽  
Local Pressure ◽  
Bingham Plastic ◽  
Transfer Characteristics ◽  
Wide Range ◽  
Branching Angle ◽  
Plastic Fluids

Abstract This work aims to explore the T-channel momentum and heat transfer characteristics with the combined effect of Bingham plastic fluids (0.01 ≤ Bn ≤ 20) behavior and geometrical variation in terms of branching angle (30 deg ≤ α ≤ 90 deg). The problem has been solved over a wide range of Reynolds number (50 ≤ Re ≤ 300) and Prandtl number (10 ≤ Pr ≤ 50). For the momentum flow, qualitative and quantitative features are analyzed in terms of streamlines, structure of yielded/unyielded regions, shear rate contours, plug width and length variation, and local pressure coefficient. These features have been represented in terms of isotherm patterns, temperature profile, Nusselt number, and its asymptotic value for heat transfer characteristics. The recirculating flows have been presented here in the vicinity of T-junction, which promote mixing and heat transfer. Broadly, the size of this zone bears a positive dependence on Re and α. However, fluid yield stress tends to suppress it. The critical Reynolds and Bingham numbers were found to be strong functions of the pertinent parameters like α. The inclination angle exerts only a weak effect on the yielded/unyielded regions and on the recirculation length of main branch. Results show a strong relationship of the plug width and length with key parameters and branches. The Nusselt number exhibits a positive relationship with α, Bn, and Re but for lower Pr in the T-junction vicinity for both branches. Such length indicates the required optimum channel length for thermal mixing.

Heat Transfer, Fluid Flow, and Pressure Measurements Inside a Rotating Two-Pass Duct With Detached 90-Deg Ribs

2003 ◽  
Vol 125 (3) ◽  
pp. 565-574 ◽  
Author(s):  
Tong-Miin Liou ◽  
Meng-Yu Chen ◽  
Yu-Ming Wang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Rotation Number ◽  
Pressure Coefficient ◽  
Heat Transfer Fluid ◽  
Laser Doppler Velocimeter ◽  
Height Ratio ◽  
Mean Velocity ◽  
Transfer Velocity

Transient thermochromic liquid crystal thermography, a laser-Doppler velocimeter, and pressure transducers have been used to measure the local heat transfer, velocity, and wall static-pressure distributions, respectively, in a rotating two-pass square duct with 90-deg ribs detached from the leading and trailing walls. The ribs were square in cross-section and their detached-distance/height ratio was 0.38. The rib-height/duct-height ratio and the pitch/rib-height ratio were 0.136 and 10, respectively. The duct Reynolds number was 1×104 and rotation number ranged from 0 to 0.2. Results are compared with attached rib cases in terms of regional averaged Nusselt number, transverse mean velocity component, pressure coefficient distributions and variation of friction factor with rotation number. The competition between convection effect of the wall jet and downwash effect of the rib-top separated shear layer on the heat transfer augmentation is addressed in detail. Discussion on local Nusselt number distribution, mean velocity components, and turbulent kinetic energy is included. Simple expressions are obtained to correlate friction factor with rotation number. Rib detachment is found to enhance heat transfer on the leading wall of the first outward pass and on the trailing wall of the second inward pass over as compared to the attached rib case. The trend is reversed on the other two walls. Nevertheless, detached ribs create more uniform heat transfer distributions on the leading and trailing walls than attached ribs.

scholarly journals Heat Transfer and Fluid Flow in a Square Duct With 12 Different Shaped Vortex Generators

1999 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chung-Chu Chen ◽  
Tzi-Wei Tsai
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Secondary Flow ◽  
Fluid Dynamic ◽  
Vortex Generator ◽  
Flow Patterns ◽  
Hydraulic Diameter ◽  
Longitudinal Vortex ◽  
Mean Velocity

Detailed local Nusselt number distributions, streamwise mean flow patterns and cross-sectional secondary flow patterns, and friction factors in the first pass of a sharp turn two-pass square channel with various configurations of longitudinal vortex generator arranged on one wall were measured using transient liquid crystal thermography, laser-Doppler velocimetry, and pressure transducer probing, respectively. The Reynolds number, based on channel hydraulic diameter and bulk mean velocity, was fixed at 1.2 × 104. The vortex generator height-to-hydraulic diameter ratio and pitch-to-height ratio were 0.12 and 10, respectively. Comparisons in terms of heat transfer augmentation and uniformity and friction loss are first performed on 12 configurations of longitudinal vortex generator. The fluid dynamic mechanisms and wall confinement relevant to heat transfer enhancement are then documented for three-selected vortex generator models. In addition, the differences in fluid flow and heat transfer characteristics between a single vortex generator and a vortex generator array are addressed for the delta wing 1 U and 45° V U models which provide better thermal performance. The direction and strength of the secondary flow with respect to the heat transfer wall are found to be the most important fluid dynamic factors affecting the heat transfer promotion through the channel wall, followed by the convective mean velocity, and then the turbulent kinetic energy. Furthermore, the effects of the two-dimensional heat conduction near the vortex generator edge and unseen heat transfer areas on the Nusselt number estimation are documented in detail.

Heat transfer to pulsating turbulent flow in an abrupt pipe expansion

2003 ◽  
Vol 13 (3) ◽  
pp. 286-308 ◽  
Author(s):  
S.A.M. Said ◽  
M.A. Habib ◽  
M.O. Iqbal
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Pulsation Frequency ◽  
Pipe Expansion ◽  
Cent Increase ◽  
The Mean ◽  
Mean Time

A numerical investigation aimed at understanding the flow and heat transfer characteristics of pulsating turbulent flow in an abrupt pipe expansion was carried out. The flow patterns are classified by four parameters; the Reynolds number, the Prandtl number, the abrupt expansion ratio and the pulsation frequency. The influence of these parameters on the flow was studied in the range 104<Re<5×104, 0.7<Pr<7.0, 0.2<d/D<0.6 and 5<f<35. It was found that the influence of pulsation on the mean time‐averaged Nusselt number is insignificant (around 10 per cent increase) for fluids having a Prandtl number less than unity. This effect is appreciable (around 30 per cent increase) for fluids having Prandtl number greater than unity. For all pulsation frequencies, the variation in the mean time‐averaged Nusselt number, maximum Nusselt number and its location with Reynolds number and diameter ratio exhibit similar characteristics to steady flows.

Analysis of Unsteady Hydrodynamics Related to Vortex Induced Vibrations on Bluff-Bodied Offshore Structure

2017 ◽  
Author(s):  
Mandar Tabib ◽  
Adil Rasheed ◽  
Franz Georg Fuchs
Keyword(s):  
Drag Coefficient ◽  
Vortex Shedding ◽  
Pulsation Frequency ◽  
Offshore Structure ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Vortex Induced Vibrations ◽  
Shedding Frequency ◽  
Lock In ◽  
Inflow Conditions

Flows around a fixed cylinder with uniform and pulsating inflow conditions at different Reynolds numbers are simulated using Large Eddy Simulation (LES). For pulsating inflow, a sinusoidal profile, with an amplitude ΔU and a pulsation frequency fe, is superimposed onto the mean velocity U∞ at the inlet plane. The current study reveals that the pulsation can influence flow-physics in three possible ways as compared to uniform inflow conditions: (a) The vortex shedding pattern is seen to be more asymmetric for pulsating inflow than for uniform inflow. This needs to be validated with an experimental campaign devoted to the study of flow-asymmetricity due to pulsatile and uniform flow condition. (b) The dominant shedding frequency fd gets locked with respect to the frequency of the pulsating inflow fe, (for both the turbulent and transition regime) at a ratio of fe/fs0 equivalent to 0.65 – 0.75 (where fs0 is the vortex shedding frequency for uniform inflow) and ε = ΔU / (2πfeD) ≈ 0.2, where D is the diameter of the cylinder. This numerical observation is validated using the experimentally observed turbulent vortex regime work ( [1])in this range. For conditions with fe/fs0 > 0.75 the lock-in may happen at fe/2. (c) Compared to uniform inflow, the pulsating inflow leads to a larger drag coefficient. The drag coefficient is influenced by the ratios fe/fs0 and ΔU / U∞.

scholarly journals Laminar Free Convection From a Heated Square Cylinder in Bingham Plastic Fluids

2021 ◽  
Author(s):  
Bairi Levi Rakshith
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Cylinder Surface ◽  
Square Cylinder ◽  
Governing Equations ◽  
Bingham Plastic ◽  
Bingham Number ◽  
Wide Range ◽  
Nusselt Number Distribution ◽  
Plastic Fluids

The free convection phenomenon from a heated square cylinder submerged in Bingham Plastic fluids is numerically investigated. The governing equations are solved for a wide range of physical dimensionless parameters, such as Rayleigh number (10^2 ≤ Ra ≤ 10^5), Prandtl number (10 ≤ Pr ≤ 100) and Bingham number (0 ≤ Bn ≤ 10^7). The heat transfer characteristics are investigated in terms of local Nusselt number distribution over the surface of the cylinder surface average Nusselt number. Streamlines, isothermal contours, yielded and unyielded regions are visualized in detail.

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