Transpiration-Induced Buoyancy and Thermal Diffusion-Diffusion Thermo in a Helium-Air Free Convection Boundary Layer

1964 ◽  
Vol 86 (4) ◽  
pp. 508-514 ◽  
Author(s):  
E. M. Sparrow ◽  
W. J. Minkowycz ◽  
E. R. G. Eckert
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Diffusion ◽  
Energy Transport ◽  
Decisive Role ◽  
Stream Temperature ◽  
Horizontal Cylinder ◽  
Appreciable Amount ◽  
Convection Boundary Layer ◽  
Adiabatic Wall

A detailed analytical study has been carried out to examine the effects of buoyancy in a boundary layer where there is mass injection through a porous surface. Specific consideration is given to helium injection into air in the stagnation-point region of a horizontal cylinder. Mass and energy transport by thermal diffusion and diffusion thermo are also included in the analysis. It is found that both the transpiration-induced buoyancy and the diffusional transports play a decisive role in determining the heat transfer when the wall-to-stream temperature ratio (Tw/T∞) is only moderately different from unity. In particular, when Tw/T∞ > 1, the tendency of the transpiration-induced buoyancy to increase the heat transfer is opposed by the action of diffusion thermo. For the condition of the adiabatic wall, the wall temperature may exceed the stream temperature by an appreciable amount; this is due to diffusion thermo. The predictions of the analysis are compared with available experimental data.

The Effect of Diffusion Thermo and Thermal Diffusion for Helium Injection Into Plane and Axisymmetric Stagnation Flow of Air

1964 ◽  
Vol 86 (3) ◽  
pp. 311-319 ◽  
Author(s):  
E. M. Sparrow ◽  
W. J. Minkowycz ◽  
E. R. G. Eckert ◽  
W. E. Ibele
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusion ◽  
Free Stream ◽  
Appreciable Amount ◽  
Stagnation Flow ◽  
Adiabatic Wall ◽  
Helium Concentration ◽  
Aerospace Applications ◽  
Wide Range ◽  
Transfer Flow

An analysis has been carried out with the aim of clarifying the effects of diffusion thermo and thermal diffusion on heat transfer, flow, and mass transfer for the helium-air boundary layer in stagnation flow. To provide information applicable to both laboratory-type situations and aerospace applications, results have been obtained over the range of free-stream temperatures from 500 to 5000 deg R. For ratios of wall-to-stream temperature (Tw/Te) which differ only moderately from unity, it is found that the aforementioned diffusional transport has a decisive effect on heat transfer. For example, the heat transfer may be from the fluid to the wall even if Tw > Te. Further, the diffusion thermo is far more important than the thermal diffusion. When Tw/Te is much less than unity (highly cooled wall), the diffusional effects on heat transfer are small. For the condition of the adiabatic wall, the surface temperature (adiabatic wall temperature) can exceed that of the free stream by an appreciable amount. Once again, it is diffusion thermo which is responsible for this. Numerical results are given over a wide range of blowing rate for the Nusselt number, friction factor, and helium concentration at the wall.

scholarly journals Numerical Study of Viscoelastic Micropolar Heat Transfer from a Vertical Cone for Thermal Polymer Coating

2019 ◽  
Vol 8 (1) ◽  
pp. 449-460 ◽  
Author(s):  
K. Madhavi ◽  
V. Ramachandra Prasad ◽  
A. Subba Rao ◽  
O. Anwar Bég ◽  
A. Kadir
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Angular Velocity ◽  
Numerical Study ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Deborah Number ◽  
Convection Boundary Layer ◽  
Density Parameter ◽  
R Ratio

Abstract A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.

Development of Wall and Free Plumes Above a Heated Vertical Plate

1978 ◽  
Vol 100 (2) ◽  
pp. 184-190 ◽  
Author(s):  
E. M. Sparrow ◽  
S. V. Patankar ◽  
R. M. Abdel-Wahed
Keyword(s):  
Boundary Layer ◽  
Vertical Plate ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Heated Plate ◽  
Adiabatic Wall ◽  
Similarity Type ◽  
Vertical Extension ◽  
Prandtl Numbers ◽  
Wall Plume

An analysis has been made to determine the successive stages of development as the natural convection boundary layer on a steadily heated vertical plate evolves into a plume. Both the wall plume and the free plume are investigated. The wall plume develops along an adiabatic wall which is the vertical extension of the heated plate. The free plume is created as the boundary layer streams away from the upper edge of the plate. Since the plate is heated on only one of its faces, the free plume is initially unsymmetric. The development of these plumes does not admit similarity-type boundary layer solutions, and numerical techniques were, therefore, employed, with results being obtained for Prandtl numbers of 0.7, 2, 5, and 10. It was found that at sufficient downstream distances both plumes attain their respective fully developed behaviors (i.e., similar profiles at successive streamwise stations). For the wall plume, the development for all Prandtl numbers is completed at a position that is about five plate lengths above the leading edge of the heated plate. The development length for the free plume for Pr = 0.7 is about the same as that for the wall plume, but about 30 plate lengths are required for the development of the free plume when Pr = 10. The fully developed free plume is symmetric.

Stagnation-point flow of Jeffrey fluid with melting heat transfer and Soret and Dufour effects

2014 ◽  
Vol 24 (2) ◽  
pp. 402-418 ◽  
Author(s):  
T. Hayat ◽  
Z. Iqbal ◽  
M. Mustafa ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Thermal Diffusion ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Jeffrey Fluid ◽  
Content Type ◽  
Melting Heat ◽  
Layer Flow

Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues. Design/methodology/approach – The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined. Findings – It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction. Practical implications – The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight. Originality/value – Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.

Numerical simulation of crossing-shock-wave/turbulent-boundary-layer interaction using a two-equation model of turbulence

2000 ◽  
Vol 409 ◽  
pp. 121-147 ◽  
Author(s):  
D. KNIGHT ◽  
M. GNEDIN ◽  
R. BECHT ◽  
A. ZHELTOVODOV
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Equation Model ◽  
Adiabatic Wall ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Good Agreement

A crossing-shock-wave/turbulent-boundary-layer interaction is investigated using the k–ε turbulence model with a new low-Reynolds-number model based on the approach of Saffman (1970) and Speziale et al. (1990). The crossing shocks are generated by two wedge-shaped fins with wedge angles α1 and α2 attached normal to a flat plate on which an equilibrium supersonic turbulent boundary layer has developed. Two configurations, corresponding to the experiments of Zheltovodov et al. (1994, 1998a, b), are considered. The free-stream Mach number is 3.9, and the fin angles are (α1, α2) = (7°, 7°) and (7°, 11°). The computed surface pressure displays very good agreement with experiment. The computed surface skin friction lines are in close agreement with experiment for the initial separation, and are in qualitative agreement within the crossing shock interaction region. The computed heat transfer is in good agreement with experiment for the (α1, α2) = (7°, 7°) configuration. For the (α1, α2) = (7°, 11°) configuration, the heat transfer is significantly overpredicted within the three-dimensional interaction. The adiabatic wall temperature is accurately predicted for both configurations.

Radiation effect on natural convection boundary layer flow over a vertical wavy frustum of a cone

2009 ◽  
Vol 223 (7) ◽  
pp. 1605-1614 ◽  
Author(s):  
M M Molla ◽  
M A Hossain ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Boundary Layer Flow ◽  
Average Rate ◽  
Local Heat Transfer ◽  
Convection Boundary Layer ◽  
Local Skin ◽  
Wide Range ◽  
Layer Flow

The effect of thermal radiation on a steady two-dimensional natural convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy frustum of a cone has been investigated. The boundary layer regime when the Grashof number Gr is large is considered. Using appropriate transformations, the basic governing equations are transformed into a dimensionless form and then solved numerically employing two efficient methods, namely: (a) implicit finite difference method together with Keller-box scheme and (b) direct numerical scheme. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid, as well as the local shearing stress in terms of the local skin-friction coefficient, the local heat transfer rate in terms of local Nusselt number, and the average rate of heat transfer for a wide range of the radiation—conduction parameter or Planck number Rd and the surface heating parameter θw.

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