scholarly journals Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

2021 ◽  
Vol 63 (1) ◽  
Author(s):  
Thomas Schaub ◽  
Frederik Arbeiter ◽  
Wolfgang Hering ◽  
Robert Stieglitz
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Permanent Magnet ◽  
Local Nusselt Number ◽  
Velocity Profiles ◽  
Thermal Boundary Condition ◽  
Backward Facing Step ◽  
Heating Plate

Abstract In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments. Graphical Abstract

Effect of Pr on the Development of Upward Laminar Mixed Convection in the Entrance Region of Vertical Quarter Circle Ducts

2007 ◽  
Author(s):  
Yousef M. F. El Hasadi
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Local Nusselt Number ◽  
Entrance Region ◽  
Wall Friction ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Wide Range

Upward laminar mixed convection in the entrance region for vertical quarter circle ducts is investigated theoretically. The governing momentum and energy equations are solved numerically using a marching technique with finite control volume approach following the SIMPLER algorithm. Results are obtained for the thermal boundary condition of uniform heat input axially with uniform wall temperature circumferentially at any cross section (H1 boundary condition) with Pr = 7.0 and 0.7 which corresponds to water and air respectively, Re = 500 and wide range of Grashof numbers. These results include the velocity and temperature distributions, at different axial locations, axial distribution of local Nusselt number and local average wall friction factor. It is found that the local Nusselt number follows the expected behavior of monotonic decrease along the developing region down to the fully developed region. However, the axial development of the local friction factor follows a different trend than that of local Nusselt number. The effect of Grashof number is to increase the values of local Nusselt number and friction factor in the developing and fully developed regions. The effect of Pr is mainly in the entrance region where the values of Nusselt number and friction factor corresponding to air are higher than those of water; however, the flow in the fully developed region is independent of Pr.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

Mixed Convection Adjacent to 3-D Backward-Facing Step

2000 ◽  
Author(s):  
A. Li ◽  
B. F. Armaly
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Buoyancy Force ◽  
Three Dimensional ◽  
The Other ◽  
Convection Flow ◽  
Backward Facing Step ◽  
Grashof Number ◽  
Recirculating Flow

Abstract Results from three-dimensional numerical simulation of laminar, buoyancy assisting, mixed convection airflow adjacent to a backward-facing step in a vertical rectangular duct are presented. The Reynolds number, and duct geometry were kept constant at Re = 200, AR = 8, ER = 2, and S = 1 cm. Heat flux at the wall downstream from the step was kept uniform, but its magnitude was varied to cover a Grashof number (Gr) range between 0.0 to 4000. All the other walls in the duct were kept at adiabatic condition. The flow, upstream of the step, is treated as fully developed and isothermal. The relatively small aspect ratio of the channel is selected specifically to focus on the developments of the three-dimensional mixed convection flow in the separated and reattached flow regions downstream from the step. The presented results focus on the effects of increasing the buoyancy force, by increasing the uniform wall heat flux, on the three-dimensional flow and heat transfer characteristics. The flow and thermal fields are symmetric about the duct’s centerline. Vortex generated near the sidewall, is the major contributor to the three dimensional behavior in the flow domain, and that feature increases as the Grashof number increases. Increasing the Grashof number results in an increase in the Nusselt number, the size of the secondary recirculating flow region, the size of the sidewall vortex, and the spanwise flow from the sidewall toward the center of the channel. On the other hand, the size of the primary reattachment region decreases with increasing the Grashof number. That region lifts away and partially detaches from the downstream wall at high Grashof number flow. The maximum Nusselt number occurs near the sidewalls and not at the center of the channel. The effects of the buoyancy force on the distributions of the three-velocity components, temperature, reattachment region, friction coefficient, and Nusselt number are presented, and compared with 2-D results.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Laminar Mixed Convection Adjacent to Three-Dimensional Backward-Facing Step

2001 ◽  
Vol 124 (1) ◽  
pp. 209-213 ◽  
Author(s):  
A. Li and ◽  
B. F. Armaly
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Region ◽  
The Other ◽  
Backward Facing Step ◽  
Number Range ◽  
Grashof Number ◽  
Recirculation Flow

Simulations of three-dimensional laminar buoyancy-assisting mixed convection adjacent to a backward-facing step in a vertical rectangular duct are presented to demonstrate the influence of Grashof number on the distributions of the Nusselt number, and the reverse flow regions that develop adjacent to the duct’s walls. The Reynolds number, and duct’s geometry are kept constant: heat flux at the wall downstream from the step is kept uniform but its magnitude varied to cover a Grashof number range of 0–4000; all the other walls in the duct are kept at adiabatic condition; and the flow, upstream of the step, is treated as fully developed and isothermal. Increasing the Grashof number results in increasing the Nusselt number; the size of the secondary recirculation flow region adjacent to the stepped wall; the size of the reverse flow region adjacent to the sidewall and the flat wall; and the spanwise flow from the sidewall toward the center of the duct. On the other hand, the size of the primary recirculation flow region adjacent to the stepped wall decreases and detaches partially from the heated stepped wall as the Grashof number increases. Details are presented and discussed.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

scholarly journals On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient

2017 ◽  
Vol 21 (suppl. 3) ◽  
pp. 585-596 ◽  
Author(s):  
Sergio Hoyas ◽  
Andrea Ianiro ◽  
María Perez-Quiles ◽  
Pablo Fajardo
Keyword(s):  
Boundary Condition ◽  
Prandtl Number ◽  
Marangoni Number ◽  
Outer Wall ◽  
Bond Number ◽  
Thermal Boundary Condition ◽  
Annular Domain ◽  
Aspect Ratios ◽  
High Prandtl Number ◽  
Lateral Walls

This manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. The effects of several parameters in the flow are evaluated. Three different values for the ratio of the momentum diffusivity and thermal diffusivity are considered: relatively low Prandtl number (Pr = 1), intermediate Prandtl number (Pr = 5) and high Prandtl number (ideally Pr ? ? , namely Pr = 50). The thermal boundary condition on the top surface is changed by imposing different values of the Biot number, Bi. The influence of the aspect ratio (?) is assessed for through by studying several aspect ratios, ?. The study has been performed for two values of the Bond number (namely Bo = 5 and 50), estimating the perturbation given by thermocapillarity effects on buoyancy effects. Different kinds of competing solutions appear on localized zones of the ?-Bi plane. The boundaries of these zones are made up of co-dimension two points. Co-dimension two points are found to be function of Bond number, Marangoni number and boundary conditions but to be independent on the Prandtl number.

MHD Stagnation-Point Flow of a Nanofluid Past a Stretching Sheet with a Convective Boundary Condition and Radiation Effects

2019 ◽  
Vol 892 ◽  
pp. 168-176 ◽  
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Mohd Ishak ◽  
Ioan Pop
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary

In this paper, the investigation of magnetohydrodynamic (MHD) stagnation point flow of a nanofluid past a stretching sheet with a convective boundary condition and radiation effects is carried out numerically. Similarity transformation is used to reduce the governing partial differential equations into third and second order non-linear ordinary differential equations. These equations are then being solved numerically using a problem solver built in the MATLAB software. The numerical solutions for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for different values of the physical parameters are presented graphically and discussed further. The results indicate that the velocity and the temperature are influenced by the magnetic parameter M, Brownian motion parameter Nb and radiation parameter Nr. The local Nusselt number and the skin friction coefficient are affected significantly in the presence of suction at the boundary.

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