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.

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.

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).

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.

Effects of moving wall on the flow of micropolar fluid inside a right angle triangular cavity

2018 ◽  
Vol 28 (10) ◽  
pp. 2404-2422 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
T. Javed
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Micropolar Fluid ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Content Type ◽  
Moving Wall ◽  
Flow And Heat Transfer

Purpose The main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid. Design/methodology/approach It is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number. Findings The results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters. Research limitations/implications The present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work. Originality/value This work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.

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.

scholarly journals Mixed convection of functionalized DWCNT-water nanofluid in baffled lid-driven cavities

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2503-2514 ◽  
Author(s):  
Esfe Hemmat ◽  
Arani Abbasian ◽  
Wei-Mon Yan ◽  
Alireza Aghaie ◽  
Masoud Afrand ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Minimum Length ◽  
Convection Flow ◽  
Flow And Heat Transfer ◽  
Inclination Angles ◽  
Nanoparticles Volume Fraction

The present study aims to evaluate the mixed convection flow and heat transfer of functionalized DWCNT/water nanofluids with variable properties in a cavity having hot baffles. The investigation is performed at different nanoparticles volume fraction including 0, 0.0002, 0.001, 0.002, and 0.004, Richardson numbers ranging from 0.01 to 100, inclination angles ranging from 0 to 60? and at constant Grashof number of 104. The results presented as streamlines and isotherms plot and Nusselt number diagrams. According to the finding with increasing nanoparticles volume fraction and distance between the left hot baffles of nanoparticles average Nusselt number enhances for all considered Richardson numbers and cavity inclination angles. Also with increasing Richardson number, the rate of changes of average Nusselt number increase with increasing distance between the left hot baffles. For example, at Richardson number of 0.01, by increasing L1 from 0.4 to 0.6, the average Nusselt number increases 7%; while for similar situation at Richardson number of 0.1, 1.0, and 10, the average Nusselt number increases, respectively, 17%, 24%, and 26%. At all Richardson numbers, the maximum value of average Nusselt number is achieved for a minimum length of left baffles. <br><br><font color="red"><b> This article has been corrected. Link to the correction <u><a href="http://dx.doi.org/10.2298/TSCI190203032E">10.2298/TSCI190203032E</a><u></b></font>

An Area-Average Correlation for Oil-Jet Cooling of Automotive Pistons

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
J. Easter ◽  
C. Jarrett ◽  
C. Pespisa ◽  
Y. C. Liu ◽  
A. C. Alkidas ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Average Nusselt Number ◽  
Laboratory Tests ◽  
Average Correlation ◽  
Cooling Rates ◽  
Number Range ◽  
Jet Cooling ◽  
Oil Jet

Laboratory tests were performed to measure cooling rates of an impinging oil-jet on the underside of an automotive piston as functions of oil nozzle-to-piston surface spacing, oil pressure, oil temperature, and piston temperature. Based on these results, area-average Nusselt number correlations were derived for a Reynolds number range of 100–4500, a Prandtl number range of 90–750, and a nozzle-to-piston surface spacing range over 73–160 mm, which are within the ranges expected for oil-jet cooling of automotive pistons.

Laminar Mixed Convection of Non-Newtonian Nanofluids Flowing Vertically Upward Across a Confined Circular Cylinder

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Abhipsit Kumar Singh ◽  
Nanda Kishore
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Numerical Results ◽  
Total Drag ◽  
Drag Coefficients

Numerical results on laminar mixed convective heat transfer phenomenon between a confined circular cylinder and shear-thinning type nanofluids are presented. The cylinder is placed horizontally in a confined channel through which nanofluids flow vertically upward. The effect of buoyancy is same as the direction of the flow. Because of existence of mixed convection, governing continuity, momentum, and energy equations are simultaneously solved within the limitations of Boussinesq approximation. The ranges of parameters considered are: volume fraction of nanoparticles, ϕ = 0.005–0.045; Reynolds number, Re = 1–40; Richardson number, Ri = 0–40; and confinement ratio of circular cylinder, λ = 0.0625–0.5. Finally, the effects of these parameters on the streamlines, isotherm contours, individual and total drag coefficients, and local and average Nusselt numbers are thoroughly delineated. The individual and total drag coefficients decrease with the increasing both ϕ and Re; and/or with the decreasing both Ri and λ. The rate of heat transfer increases with the increasing Re, ϕ, Ri, and λ; however, at Re = 30–40, when ϕ > 0.005 and Ri < 2, the average Nusselt number decreases with the increasing Richardson number. Finally, correlations for the total drag coefficient and average Nusselt number are proposed as functions of pertinent dimensionless parameters on the basis of present numerical results.

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 Heat transfer from a rotating circular cylinder in the steady regime: Effects of Prandtl number

2012 ◽  
Vol 16 (1) ◽  
pp. 79-91 ◽  
Author(s):  
Varun Sharma ◽  
Kumar Dhiman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Rotation Rate ◽  
Average Nusselt Number ◽  
Steady Regime ◽  
Rotating Circular Cylinder ◽  
Prandtl Numbers

In this work, effects of Prandtl number on the heat transfer characteristics of an unconfined rotating circular cylinder are investigated for varying rotation rate (? = 0 - 5) in the Reynolds number range 1 - 35 and Prandtl numbers range 0.7 - 100 in the steady flow regime. The numerical calculations are carried out by using a finite volume method based commercial CFD solver FLUENT. The isotherm patterns are presented for varying values of Prandtl number and rotation rate in the steady regime. The variation of the local and the average Nusselt numbers with Reynolds number, Prandtl number and rotation rate are presented for the above range of conditions. The average Nusselt number is found to decrease with increasing value of the rotation rate for the fixed value of the Reynolds and Prandtl numbers. With increasing value of the Prandtl number, the average Nusselt number increases for the fixed value of the rotation rate and the Reynolds number; however, the larger values of the Prandtl numbers show a large reduction in the value of the average Nusselt number with increasing rotation rate.

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