Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

2006 ◽  
Vol 129 (4) ◽  
pp. 506-513 ◽  
Author(s):  
A. K. Dhiman ◽  
N. Anjaiah ◽  
R. P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Power Law ◽  
Richardson Number ◽  
Square Cylinder ◽  
Laminar Mixed Convection ◽  
Power Law Fluids ◽  
Power Law Index

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1–30, power-law index: 0.8–1.5, Prandtl number 0.7–100 (Pe⩽3000) for Richardson number 0–0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening (n>1) and shear-thinning (n<1) fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter (Ri⩽0.5) for a fixed Reynolds number in the steady cross-flow regime (Re⩽30).

Mixed Convection Heat Transfer From a Square Cylinder to Power-Law Fluids in Cross-Flow

2006 ◽  
Author(s):  
N. Anjaiah ◽  
A. K. Dhiman ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Steady Flow ◽  
Power Law ◽  
Richardson Number ◽  
Square Cylinder ◽  
Flow And Heat Transfer ◽  
Power Law Fluids

Laminar mixed convection flow and heat transfer to power-law fluids from a square cylinder has been analyzed numerically in the steady flow regime. The full momentum and energy equations along with the Boussinesq approximation have been solved by using a SMAC implicit finite difference method implemented on an uniform staggered grid arrangement for the range of Reynolds number 5 to 40, power-law index 0.6 to 1.4, Prandtl number 1 to 10 and Richardson number 0 to 0.5 in both bounded and unbounded flow configurations. The wall effects have been studied for a fixed blockage ratio of 1/15. The effects of buoyancy on the flow and heat transfer characteristics of power-law fluids have been elucidated. It is found that the mixed convection can initiate an asymmetry in the flow and temperature fields even within the steady flow regime. The variation of drag coefficients, and of the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number and Richardson number for both shear thickening and shear thinning fluids.

Analysis of mixed convection past a heated sphere

2018 ◽  
Vol 233 (3) ◽  
pp. 601-616 ◽  
Author(s):  
Dipjyoti Nath ◽  
Sukumar Pati ◽  
B Hema Sundar Raju
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Drag Coefficient ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Thermal Characteristics ◽  
Sphere Surface ◽  
Critical Richardson Number

The hydrodynamic and thermal characteristics for laminar axisymmetric mixed convection from a heated sphere are analyzed numerically in this work. The governing transport equations of conservation of mass, momentum, and energy have been solved using a higher order compact scheme. The results are presented in terms of the distribution of the streamlines, isotherms, and vorticity contours, and local Nusselt number along the sphere surface together with drag coefficient and average Nusselt number. We identify critical Richardson number above which separation of flow is suppressed. It is revealed that the drag coefficient decreases with an increase in the Reynolds number (Re) and the decrease is more profound for lower range of Re. It is further revealed that the drag coefficient increases monotonically with an increase in the Richardson number, while the same decreases with the increase in the Prandtl number. The average Nusselt number increases monotonically with the increase in Reynolds number, Prandtl number, and Richardson number.

Numerical Analysis of Laminar Mixed Convection in a Lid Driven Square Cavity With an Isothermally Heated Square Internal Blockage

2012 ◽  
Author(s):  
Akand W. Islam ◽  
Muhammad A. R. Sharif ◽  
Eric S. Carlson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Blockage Ratio ◽  
Square Cavity ◽  
Ansys Fluent ◽  
Laminar Mixed Convection

Laminar mixed convection characteristics in a square cavity with an isothermally heated square blockage inside have been investigated numerically using the finite volume method of the ANSYS FLUENT commercial CFD code. Various different blockage sizes and concentric and eccentric placement of the blockage inside the cavity have been considered. The blockage is maintained at a hot temperature, Th, and four surfaces of the cavity (including the lid) are maintained at a cold temperature, Tc, under all circumstances. The physical problem is represented mathematically by sets of governing conservation equations of mass, momentum, and energy. The geometrical and flow parameters for the problem are the blockage ratio (B), the blockage placement eccentricities (εx and εy), the Reynolds number (Re), the Grashof number (Gr), and the Richardson number (Ri). The flow and heat transfer behavior in the cavity for a range of Richardson number (0.01–100) at a fixed Reynolds number (100) and Prandtl number (0.71) is examined comprehensively. The variations of the average and local Nusselt number at the blockage surface at various Richardson numbers for different blockage sizes and placement eccentricities are presented. From the analysis of the mixed convection process, it is found that for any size of the blockage placed anywhere in the cavity, the average Nusselt number does not change significantly with increasing Richardson number until it approaches the value of the order of 1 beyond which the average Nusselt number increases rapidly with the Richardson number. For the central placement of the blockage at any fixed Richardson number, the average Nusselt number decreases with increasing blockage ratio and reaches a minimum at around a blockage ratio of slightly larger than 1/2. For further increase of the blockage ratio, the average Nusselt number increases again and becomes independent of the Richardson number. The most preferable heat transfer (based on the average Nusselt number) is obtained when the blockage is placed around the top left and the bottom right corners of the cavity.

Effect of Driven Sidewalls on Mixed Convection in an Open Trapezoidal Cavity With a Channel

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Muneer A. Ismael ◽  
Ahmed Kadhim Hussein ◽  
Fateh Mebarek-Oudina ◽  
Lioua Kolsi
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Airflow Velocity ◽  
Driven Cavity ◽  
Thermal Fields ◽  
Number Ratio ◽  
The Right

Abstract The mixed convection in an open trapezoidal lid-driven cavity connected with a channel is investigated in the present paper. Four different cases were considered depending on the movement of the cavity sidewalls. For case I, the left sidewall moves downward; for case II, the left sidewall moves downward and the right one moves upward; while for case III, only the right sidewall moves upward. A comparative case (case 0) is accounted when both sidewalls are assumed stationary. The base of the cavity is subjected to a localized heat source of constant temperature Th. The effects of Richardson number Ri and Reynolds number ratio Rer on the flow and thermal fields have been investigated. The results indicated that for cases I and II, the average Nusselt number increases with the increase of the Richardson number and Reynolds number ratio. Moreover, it was found that the maximum average Nusselt number occurs with case I. When the lid-driven speed is three times that of the inlet airflow velocity, the augmentations of the average Nusselt number compared with stationary walls are 163%, 158%, and 96% for cases I, II, and III, respectively.

Numerical Investigation of a Three-Dimensional Laminar Mixed Convection Flows in Lid-Driven Cavity for Very Small Richardson Numbers

2015 ◽  
Author(s):  
M. M. Abo Elazm ◽  
A. I. Shahata ◽  
A. F. Elsafty ◽  
M. A. Teamah
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Three Dimensional ◽  
Lewis Number ◽  
Maximum Error ◽  
Driven Cavity ◽  
Laminar Mixed Convection ◽  
Nusselt Number Distribution ◽  
Volume Method

Laminar mixed convection in a three-dimensional lid driven cavity is numerically investigated. The top lid of the cavity is moving rightwards with a constant speed at a cold temperature. The bottom wall is maintained at an isothermal hot temperature, while the other vertical walls of the cavity are assumed to be insulated. In this study the mass diffusion was not taken into account and the fluid used was air. The flow and heat transfer behavior is studied for various Richardson number ranging from 5 × 10−5 to 3 × 10−4 at a fixed Prandtl number of 0.71 through analyzing the local Nusselt number distribution at different sections inside the cavity. Lewis number Le is assumed to be unity and the buoyancy ratio parameter N is equal to zero. Computations were done using an in-house code based on a finite volume method. The results showed a good agreement with previous two dimensional studies, while the three dimensional study gives different results at different sections inside the cavity. It is observed that, the average Nusselt number “Av Nu” on top and bottom surfaces decreases for all sections inside the cavity with increasing Richardson number. A correlation was formulated for each section on both walls for “Av Nu” as a function of “Ri” with a maximum error of 7.3%.

scholarly journals Numerical Analysis and Entropy Generation of Electrokinetic Flow of Power-Law Fluid in a Microtriangular Prism

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Fehaid Salem Alshammari
Keyword(s):  
Nusselt Number ◽  
Entropy Generation ◽  
Power Law ◽  
Second Law Of Thermodynamics ◽  
Physical Parameters ◽  
Electrokinetic Flow ◽  
Power Law Fluids ◽  
Transfer Equations ◽  
Constant Wall Heat Flux ◽  
Power Law Index

This research aims to study the characteristics of thermal transport and analyse the entropy generation of electroosmotic flow of power-law fluids in a microtriangular prism in the presence of pressure gradient. Considering a fully developed flow subject to constant wall heat flux, the nonlinear electric potential, momentum, and linear heat transfer equations are solved numerically by developing an iterative finite difference method with a nonuniform grid. The thermal efficiency of the model is explored under the light of the second law of thermodynamics. Effect/impact of governing physical parameters on velocity, temperature, Nusselt number, and entropy distributions is studied, and the results are demonstrated graphically; we found that the Nusselt number decreases with the increase of power-law index, and average entropy generation increases with power-law index. We believe that the obtained result in the present study shall be useful for design of energy efficient microsystems which utilize the dual electrokinetic and centrifugal pumping effects.

scholarly journals Numerical analysis of mixed convection in pulsating flow for a horizontal channel with a cavity heated from below

2016 ◽  
Vol 20 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Fatih Selimefendigil
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Amplitude Ratio ◽  
Pulsating Flow ◽  
Pulsation Frequency ◽  
Transfer Enhancement ◽  
Velocity Amplitude

In this study, a channel with a cavity heated from below is numerically investigated for the mixed convection case in pulsating flow for a range of Richardson numbers (Ri=0.1, 1, 10, 100) at Reynolds number of 50 in the laminar flow regime. At the inlet of the channel, pulsating velocity is imposed for Strouhal numbers between 0.1 to 1 and velocity amplitude ratio between 0.3 to 0.9. The effect of the pulsation frequency, amplitude and Richardson number on the heat transfer enhancement is numerically analyzed. The results are presented in terms of streamlines, isotherm plots and averaged Nusselt number plots. FFT plots for the Nusselt number response to single sinusoidal velocity forcing at the inlet and nonlinearity in the response is also provided.

scholarly journals High mixing performances of shear-thinning fluids in two-layer crossing channels micromixer at very low Reynolds numbers

2019 ◽  
Vol 13 (4) ◽  
pp. 5938-5960
Author(s):  
A. Kouadri ◽  
Y. Lasbet ◽  
M. Makhlouf
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Transport Model ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Species Transport ◽  
Industrial Sectors ◽  
Power Law Fluids ◽  
Power Law Index

In a recent study, the Two-Layer Crossing Channels Micromixer (TLCCM) exhibited good mixing capacities in the case of the Newtonian fluids (close to 100%) for all considered Reynolds number values. However, since the majority of the used fluids in the industrial sectors are non-Newtonians, this work details the mixing evolution of power-law fluids in the considered geometry. In this paper, the power-law index ranges from 0.73 to 1 and the generalized Reynolds number is bounded between 0.1 and 50. The conservation equations of momentum, mass and species transport are numerically solved using a CFD code, considering the species transport model. The flow structure at the cross-sectional planes of our micromixer was studied using the dynamic systems theory. The evolutions of the intensity, also the axial, radial and tangential velocity profiles were examined for different values of the Reynolds number and the power-law index. Besides, the pressure drop of the power-law fluids under different Reynolds number was calculated and represented. Furthermore, the mixing efficiency is evaluated by the computation of the mixing index (MI), based on the standard deviation of the mass fraction in different cross-sections. In such geometry, a perfect mixing is achieved with MI closed to 99.47 %, at very small Reynolds number (from the value 0.1) whatever the power-law index and generalized Reynolds numbers taken in this investigation. Consequently, the targeted channel presents a useful tool for pertinent mass transfer improvements, it is highly recommended to include it in various microfluidic systems.

Simulation of Mixed Convection Air Cooling of Protruding Heat Sources Mounted on One Side of a Vertical Channel

2011 ◽  
Author(s):  
Rajat Dhingra ◽  
P. S. Ghoshdastidar
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Regression Analysis ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Vertical Channel ◽  
Separation Distance ◽  
Air Cooling ◽  
Heat Sources

A numerical study of steady, laminar, two-dimensional mixed convection air cooling of identical as well as non-identical rectangular protruding heat sources located on one side of a vertical channel is presented in this paper. The stream function-vorticity-temperature approach with the finite-difference-based methodology implementing higher order upwind scheme has been applied. Three cases have been considered, namely (i) when the number of identical chips is two; (ii) when the number varies from 3 to 10; and finally, (iii) when five chips of different heights but of same width are placed in various orders. For the case of two chips the effects of Re, Gr/Re2 (that is, Richardson number), dimensionless separation distance between the chips (d/H), dimensionless chip height (h/H) and width (w/H) on the average Nusselt number of each chip have been investigated. A correlation based on regression analysis is also presented for each parameter. With increase in Reynolds number the average Nusselt number of both chips increases. Similar trend is seen when the separation distance between two chips is raised. It is also observed that as the number of chips escalates from 2 to 10, the average Nusselt number of downstream chips becomes smaller than that of the upstream chips, the rate of drop being much sharper near the channel inlet. A regression-analysis based composite correlation each for average Nusselt number of Chip 1 (lower chip) and Chip 2 (upper chip) as a function of Reynolds number, Richardson number, separation distance between the chips, chip height and width has been obtained for the 2-chip case. The model also predicts maximum chip temperature in an array of ten chips. Finally, for five non-identical chips having same width but different heights the simulation reveals that the chips placed in increasing order of their heights in the direction of air flow are cooled better as compared to any other pattern of placement of the chips.

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