Development and Validation of Nusselt Number Correlations for Mixed Convection in an Arc-Shape Cavity

The analytical study has been performed to investigate the combined effects of lid movement and buoyancy force parameter on mixed convective flow in an arc-shape cavity. The dimensional analysis based on Buckingham π-Theorem is used in the present study. It results in correlations for Nusselt number in terms of non dimensionalized parameters, viz. Re, Pr, Gr, θ etc. The correlations developed are validated against the experimental data of horizontal arc- shape cavity and numerical data of inclined arc-shape cavity obtained from open literature. The correlation developed in the present study for horizontal arcshape cavity is valid for wide ranges of Re varying from 30 to 1500 and Gr from 0 to 107. In inclined arc-shape cavity it is valid for Re varying from 30 to 1500, Gr from105 to 107 and inclination angle from 150to 600.The close agreement in the comparison between predicted results by correlation developed in the present study and reported Nu correlation shows the validity of the correlation.

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Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows

Journal of Heat Transfer ◽

10.1115/1.4033378 ◽

2016 ◽

Vol 138 (10) ◽

Cited By ~ 9

Author(s):

G. Lorenzini ◽

B. S. Machado ◽

L. A. Isoldi ◽

E. D. dos Santos ◽

L. A. O. Rocha

Keyword(s):

Nusselt Number ◽

Aspect Ratio ◽

Convective Flow ◽

Numerical Study ◽

Reynolds Numbers ◽

Lower Surface ◽

Driven Cavity ◽

Constructal Design ◽

Mixed Convective Flow ◽

Forced Convective Flow

The present work shows a numerical study of laminar, steady, and mixed convective flow inside lid-driven square cavity with intruded rectangular fin in its lower surface. The main purpose here is to maximize the heat transfer between the rectangular fin and the surrounding mixed convective flow inside a lid-driven cavity by means of constructal design. The problem is subject to two constraints, the lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (ϕ = 0.05). The investigated geometry has one degree-of-freedom (DOF), the fin aspect ratio (H1/L1), which is varied in the range 0.1 ≤ H1/L1 ≤ 10. The aspect ratio of the cavity is maintained fixed (H/L = 1.0). The effect of the fin geometry over the Nusselt number is investigated for several Rayleigh (RaH = 103, 104, 105 and 106) and Reynolds numbers (ReH = 10, 102, 3.0 × 102, 5.0 × 102, 7.0 × 102 and 103). For all simulations, the Prantdl number is fixed (Pr = 0.71). The conservation equations of mass, momentum, and energy are numerically solved with the finite volume method. Results showed that fin geometry (H1/L1) has strong influence over the Nusselt number in the fin. It was also observed that the effect of H1/L1 over Nusselt number changes considerably for different Rayleigh numbers and for the lowest magnitudes of Reynolds numbers, for example, differences of nearly 770% between RaH = 106 and forced convective flow were observed for the lowest Reynolds number studied (ReH = 10).

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An asymptotic model of two-dimensional convection in the limit of low Prandtl number

Journal of Fluid Mechanics ◽

10.1017/s0022112081002541 ◽

1981 ◽

Vol 102 ◽

pp. 75-83 ◽

Cited By ~ 36

Author(s):

F. H. Busse ◽

R. M. Clever

Keyword(s):

Nusselt Number ◽

Prandtl Number ◽

Buoyancy Force ◽

Close Agreement ◽

Preceding Paper ◽

Critical Value ◽

Temperature Fields ◽

Asymptotic Model ◽

Two Dimensional ◽

Velocity And Temperature Fields

An approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms. The results indicate that inertial convection becomes possible when the Rayleigh number exceeds a critical value of about 7 × 103. Beyond this value the velocity and temperature fields become independent of the Prandtl number except in thin boundary layers. The convective heat transport approaches the law Nu = 0·175 R¼ for the Nusselt number Nu. These results are in reasonably close agreement with the numerical results described in the preceding paper by Clever & Busse (1980).

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Analytical Study of Heat and Mass Transfer in Porous Sheets During Contact Drying Process

Heat Transfer: Volume 3 ◽

10.1115/ht2008-56460 ◽

2008 ◽

Author(s):

Mohammad R. Izadpanah ◽

Amir R. Ansari Dezfooli

Keyword(s):

Mass Transfer ◽

Temperature Distribution ◽

Moisture Content ◽

Close Agreement ◽

Analytical Study ◽

Numerical Data ◽

Drying Process ◽

Governing Equations ◽

Sturm Liouville ◽

Contact Drying

Contact drying process has gained wide application in different industries including paper, ceramics and construction industries. Suitable control over temperature distribution will result in required moisture content and its distribution. In the present study, governing equations for a porous sheet are derived using Luikov equation. These equations are then converted into sturm-liouville equations and solved simultaneously. Comparison of temperature and moisture distributions with numerical data shows a close agreement.

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Impact of partial slip on mixed convective flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-06-2018-0258 ◽

2019 ◽

Vol 29 (5) ◽

pp. 1647-1662 ◽

Cited By ~ 11

Author(s):

Aurang Zaib ◽

Rizwan Ul Haq ◽

Ali J. Chamkha ◽

Mohammad Mehdi Rashidi

Keyword(s):

Boundary Layer ◽

Nusselt Number ◽

Convective Flow ◽

Design Methodology ◽

Volume Fraction ◽

Partial Slip ◽

Content Type ◽

Water Based ◽

Riga Plate ◽

Mixed Convective Flow

Purpose The purpose of this paper is to present an inclusive study of the mixed convective flow involving micropolar fluid holding kerosene/water-based TiO2 nanoparticle towards a vertical Riga surface with partial slip. The outcomes are confined for opposing and assisting flows. Design/methodology/approach Similarity equations are acquired and then worked out numerically by the Keller box technique. Findings Impacts of significant parameters on microrotation velocity, temperature distribution, velocity profile together with the Nusselt number and the skin friction are argued with the help of graphs. Two solutions are achieved in opposing flow, while the solution is unique in assisting flow. It is also monitored that the separation of boundary layer delays because of micropolar parameter and accelerates because of volume fraction. Originality/value The authors trust that all these results are new and significant for researchers.

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Measurements in Buoyancy-Assisting Separated Flow Behind a Vertical Backward-Facing Step

Journal of Heat Transfer ◽

10.1115/1.2910692 ◽

1993 ◽

Vol 115 (2) ◽

pp. 403-408 ◽

Cited By ~ 33

Author(s):

B. J. Baek ◽

B. F. Armaly ◽

T. S. Chen

Keyword(s):

Nusselt Number ◽

Buoyancy Force ◽

Heated Wall ◽

Laser Doppler Velocimeter ◽

Force Parameter ◽

Reattachment Length ◽

Reattachment Point ◽

Backward Facing Step ◽

Temperature Distributions ◽

Laminar Mixed Convection

Measurements of velocity and temperature distributions in buoyancy-assisting laminar mixed convection boundary-layer flow over a vertical, two-dimensional backward-facing step are reported. The leading surface upstream of the step and the step itself were adiabatic, and the surface downstream of the step was heated and maintained at a uniform temperature. A laser-Doppler velocimeter and a cold-wire anemometer were utilized to measure simultaneously the velocity and the temperature distributions in the recirculation and the reattached region downstream of the step. Flow visualization was used to study the flow and to measure the reattachment length for different free-stream velocities (0.37 m/s ≤ u0 ≤ 0.72 m/s), wall temperature differences (10°C ≤ ΔT ≤ 30°C), and step heights (0.38 cm ≤ s ≤ 1 cm). Results show that for a given step height the reattachment length decreases as the buoyancy force parameter, Grs/Res2, increases. The Nusselt number at the heated wall downstream of the step increases and the location of its maximum value moves closer to the step as the buoyancy force parameter increases. For the present experimental range, it is found that the location of the maximum Nusselt number occurs downstream of the reattachment point and the distance between the reattachment point and the location of the maximum Nusselt number increases as the buoyancy force parameter increases. Predicted behavior agrees favorably with the measured results.

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Entropy Optimization in Nonlinear Mixed Convective Flow of Nanomaterials Through Porous Space

Journal of Non-Equilibrium Thermodynamics ◽

10.1515/jnet-2019-0048 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Tasawar Hayat ◽

Ikram Ullah ◽

Ahmad Alsaedi ◽

Shaher Momani

Keyword(s):

Convective Flow ◽

Second Law Of Thermodynamics ◽

Second Law ◽

Porous Space ◽

Arrhenius Activation Energy ◽

Suction Parameter ◽

Electrically Conducting ◽

Entropy Optimization ◽

Dimensionless Variables ◽

Mixed Convective Flow

Abstract Our intention in this article is to investigate entropy optimization in nonlinear mixed convective unsteady magnetohydrodynamic flow of nanomaterials in porous space. An exponentially stretched sheet creates the liquid flow. Nanomaterial is considered electrically conducting. The concentration and energy expressions comprise viscous dissipation, Joule heating, thermophoresis and Brownian motion aspects. Arrhenius activation energy is considered. Computation of entropy generation based upon the second law of thermodynamics is made. Nonlinear partial expressions are obtained via suitable dimensionless variables. Resultant expressions are tackled by the OHAM technique. Features of numerous variables on entropy, temperature, velocity and concentration are graphically visualized. Skin friction and the temperature gradient at the surface are also elaborated. Comparative analysis is deliberated in tabulated form to validate the previously published outcomes. Velocity is reduced significantly via the suction parameter. The entropy rate increases for higher values of Brinkman, Biot and Hartmann numbers.

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