Unsteady Mixed Convection Near the Stagnation Point in Three-Dimensional Flow

1982 ◽  
Vol 104 (1) ◽  
pp. 132-138 ◽  
Author(s):  
M. Kumari ◽  
G. Nath
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Skin Friction ◽  
Stagnation Point ◽  
Wall Temperature ◽  
Buoyancy Force ◽  
Three Dimensional ◽  
Forced Flow ◽  
Unsteady Mixed Convection ◽  
Similar Solutions

The combined effect of forced and free convection on the unsteady laminar incompressible boundary-layer flow with mass transfer at the stagnation point of a three-dimensional body with time dependent wall temperature has been studied. Both semisimilar and self-similar solutions have been obtained. The governing equations have been solved numerically using an implicit finite-difference scheme. The results indicate that the buoyancy force strongly affects the skin friction whereas its effect on the heat transfer is comparatively less. However, the heat transfer is significantly changed due to the wall temperature which varies with time, but the skin friction is little affected by it. The mass transfer and Prandtl number affect both the skin friction and heat transfer. The buoyancy force which assists the forced flow causes an overshoot in both the velocity components.

Unsteady Incompressible Three-Dimensional Asymmetric Stagnation-Point Boundary Layers

1980 ◽  
Vol 47 (2) ◽  
pp. 241-246 ◽  
Author(s):  
M. Kumari ◽  
G. Nath
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Stagnation Point ◽  
Wall Temperature ◽  
Three Dimensional ◽  
Stream Velocity ◽  
Symmetric Flow ◽  
Maximum Heat ◽  
Maximum Heat Transfer

The unsteady laminar incompressible boundary-layer flow near the three-dimensional asymmetric stagnation point has been studied under the assumptions that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. It is found that in contrast with the symmetric flow, the maximum heat transfer occurs away from the stagnation point due to the decrease in the boundary-layer thickness. The effect of the variation of the wall temperature with time on heat transfer is strong. The skin friction and heat transfer due to asymmetric flow only are comparatively less affected by the mass transfer as compared to those of symmetric flow.

Unsteady mixed convection flow at a three-dimensional stagnation point

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Unsteady Mixed Convection

Purpose This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

The Effect of Mass Transfer on Free Convection

1960 ◽  
Vol 82 (3) ◽  
pp. 260-263 ◽  
Author(s):  
R. Eichhorn
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Free Convection ◽  
Skin Friction ◽  
Leading Edge ◽  
Temperature Profiles ◽  
Constant Wall Temperature ◽  
Constant Property ◽  
Boundary Layer Equations ◽  
Similar Solutions

Consideration is given to the constant property laminar boundary layer equations with free convection and mass transfer. It is shown that similar solutions are possible for blowing rate distributions varying as the distance from the leading edge raised to the power (n − 1)/4 where n is the exponent in a power law surface temperature distribution. Solutions to the equations in the form of skin friction and heat-transfer parameters, and velocity and temperature profiles are presented for the constant wall temperature case for a fluid with Pr = 0.73. The cases considered range from strong suction to strong blowing. Mass transfer has a pronounced effect on the heat transfer but only a slight effect on the skin friction. In light of the solutions presented, these effects are shown to be physically rational.

Mass Transfer Cooling in a Boundary Layer

1961 ◽  
Vol 12 (2) ◽  
pp. 165-188 ◽  
Author(s):  
D. G. Hurley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Stagnation Point ◽  
Theoretical Work ◽  
Absolute Temperature ◽  
Analogue Computer ◽  
Constant Wall Temperature ◽  
Dimensional Boundary ◽  
Similar Solutions

SummaryPrevious theoretical work on mass transfer cooling is reviewed and it is shown that this may be complemented by similar solutions that occur when the velocity outside a two-dimensional boundary layer varies as some power of the distance from the front stagnation point. The case of stagnation point flow with constant wall temperature is investigated in some detail, under the assumption that the temperature differences are everywhere small compared with the absolute temperature. Calculations on an analogue computer, supplemented by an investigation of the asymptotic behaviour, are used to determine the boundary layer development and heat transfer rates when the coolant is hydrogen, helium, steam or carbon dioxide. It is found that, on a mass flow basis, hydrogen reduces the heat transfer rate most and that steam is the next most effective of the substances investigated.

Effects of hydromagnetic and chemical reaction over a stagnation point flow of horizontal stretching/shrinking cylinder in Ag-CuO/water hybrid nanofluid

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Adilah Liyana Aladdin ◽  
Norfifah Bachok
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mass Transfer ◽  
Skin Friction ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type

Purpose This paper aims to explore on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder by adding the effect of chemical reaction, B together with the magnetic field, M. Design/methodology/approach A set of reduced ordinary differential equations from the governing equations of partial differential equations is obtained through similarities requirements. The resulting equations are solved using bvp4c in MATLAB2019a. The impact of various physical parameters such as curvature parameter, ϒ, chemical reaction rate, B, magnetic field, M and Schmidt numbers, Sc on shear stress, f′′0 local heat flux, -θ′(0) and mass transfer, -∅′(0) also for velocity, f′(η), temperature, θ(η) and concentration, ∅(η) profiles have been plotted and briefly discussed. In this work, some vital characteristics such as local skin friction, Cf, local Nusselt number, Nux and local Sherwood number, Shx are chosen for physical and numerical analysis. Findings The findings expose that the duality of solutions appears in a shrinking region ( ε < 0). The value of skin friction, heat transfer rate and mass transfer rate reduction for existing of M, but in contrary result obtain for larger ϒ, B and Sc. Furthermore, the hybrid nanofluid demonstrates better heat transfer compared to nanofluid. Practical implications The hybrid nanofluid has widened its applications such as in electronic cooling, manufacturing, automotive, heat exchanger, solar energy, heat pipes and biomedical, as their efficiency in the heat transfer field is better compared to nanofluid. Originality/value The findings on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder with the effect of chemical reaction, B and magnetic field, M is new and the originality is preserved for the benefits of future researchers.

scholarly journals Unsteady MHD Mixed Convection Flow in Hybrid Nanofluid at Three-Dimensional Stagnation Point

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 549
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

There has been significant interest in exploring a stagnation point flow due to its numerous potential uses in engineering applications such as cooling of nuclear reactors. Hence, this study proposed a numerical analysis on the unsteady magnetohydrodynamic (MHD) mixed convection at three-dimensional stagnation point flow in Al2O3–Cu/H2O hybrid nanofluid over a permeable sheet. The ordinary differential equations are accomplished by simplifying the governing partial differential equations through suitable similarity transformation. The numerical computation is established by the MATLAB system software using the bvp4c technique. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The influence of certain functioning parameters is inspected, and notable results exposed that the rate of heat transfer is exaggerated along with the skin friction coefficient while the suction/injection and magnetic parameters are intensified. The results also signified that the rise in the volume fraction of the nanoparticle and the decline of the unsteadiness parameter demonstrates a downward attribution towards the heat transfer performance and skin friction coefficient. Conclusively, the observations are confirmed to have multiple solutions, which eventually contribute to an investigation of the analysis of the solution stability, thereby justifying the viability of the first solution.

scholarly journals Radiation Effect on Unsteady Mixed Convection Boundary Layer Flow, Heat and Mass Transfer over a Wedge

2016 ◽  
Vol 64 (1) ◽  
pp. 59-64 ◽  
Author(s):  
NC Roy ◽  
MN Firoza ◽  
AK Halder
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Unsteady Mixed Convection ◽  
Flow Heat ◽  
Layer Flow

This paper concerns the unsteady mixed convection laminar boundary layer flow past a vertical wedge in the presence of thermal radiation. The governing equations have been solved by the straightforward finite difference method for the entire frequency range. We observe that the Richardson’s number, Ri, strongly affects the skin friction, heat transfer and mass transfer. The effect of the Schmidt number, Sc, on the mass transfer is significant, whereas the skin friction and the heat transfer are almost unaffected by it. Also the heat transfer is considerably dependent on the conduction-radiation parameter, Rd, but the influence of this parameter on the skin friction and the mass transfer is rather weak.Dhaka Univ. J. Sci. 64(1): 59-64, 2016 (January)

scholarly journals Mixed Convection Flow of Powell–Eyring Nanofluid near a Stagnation Point along a Vertical Stretching Sheet

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 364
Author(s):  
Nadhirah Abdul Halim ◽  
Noor Fadiya Mohd Noor
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stagnation Point ◽  
Buoyancy Force ◽  
Skin Friction Coefficient ◽  
Transfer Rates

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

Swirl Flow Investigations on the Enhancement of Heat Transfer Processes in Cyclone Cooling Ducts

2012 ◽  
Author(s):  
Florian Wassermann ◽  
Sven Grundmann ◽  
Michael Kloss ◽  
Heinz-Peter Schiffer
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Complex Structure ◽  
Three Dimensional ◽  
Swirl Flow ◽  
Flow Structures ◽  
Stable Complex ◽  
Reynolds Analogy ◽  
Transfer Processes ◽  
Cooling Ducts

Cyclone cooling is a promising method to enhance heat-transfer processes in future internal turbine-blade leading-edge cooling-ducts. The basic component of such cooling channels is the swirl generator, which induces a swirling movement of the coolant. The angular momentum generates stable, complex and three-dimensional flow structures of helical shape with alternating axial flow directions. Full three-dimensional and three-component velocity measurements using magnetic resonance velocimetry (3D3C-MRV) were conducted, with the aim to understand the complex structure of pipe flows with strong swirl. In order to mimic the effect of different installation concepts of the cyclone-cooling ducts an idealized bend-duct swirl-tube configuration with variable exit orifices has been investigated. Pronounced helical flow structures and distinct velocity zones could be found in this swirl flow. One substantial result is the identification of stationary helix-shaped streaks of high axial velocity in the direct vicinity of the wall. These findings are in good agreement with mass-transfer measurements that also show helix-shaped structures with increased mass transfer at the inner surface of the tube. According to the Reynolds analogy between heat and mass transfer, augmented heat-transfer processes in these areas are to be expected.

A Study of Three-Dimensional Mixed Convective Heat Transfer From Short Vertical Cylinders in a Horizontal Forced Flow

2000 ◽  
Author(s):  
David A. Scott ◽  
P. H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Three Dimensional ◽  
Forced Flow ◽  
Low Velocity ◽  
Buoyancy Forces ◽  
The Mean ◽  
Mixed Convective Flow ◽  
Comparison Of The Results

Abstract Heat transfer from relatively short vertical isothermal cylinders in a horizontal forced fluid flow has been considered. The flow conditions are such that the buoyancy forces resulting from the temperature differences in the flow are in general significant despite of the presence of a horizontal forced flow of air, that is, mixed convective flow exists. Because the cylinders are short and the buoyancy forces act normal to the forced flow, three-dimensional flow exists. The experiments were performed in a low velocity, open jet wind tunnel. The study involved the experimental determination of the mean heat transfer coefficient and a comparison of the results with a previous numerical analysis. Mean heat transfer rates were determined using the ‘lumped capacity’ method. The mean Nusselt number has the Reynolds number, Grashof number and the height to diameter ratio of the cylinders as parameters. The results have been used to determine the conditions under which the flow departs from purely forced convection and enters the mixed convection regime, i.e., determining the conditions for which the buoyancy effects should be included in convective heat transfer calculations for short cylinders.

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