Calculation of flows with separation, heat transfer, and swirl by means of boundary-layer equations

1993 ◽  
Vol 34 (2) ◽  
pp. 184-189
Author(s):  
V. I. Vasil'ev ◽  
S. V. Khokhlov
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Equations

Spreadsheets Solutions of the Boundary Layer Equations

2004 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Mechanics ◽  
Undergraduate Students ◽  
Classical Problem ◽  
Boundary Layer Equations ◽  
Specialized Software ◽  
Layer Flow ◽  
Basic Course ◽  
The Impact

A classical problem in fluid mechanics and heat transfer is boundary layer flow over a flat plate. This problem is used to demonstrate a number of important concepts in fluid mechanics and heat transfer. Typically, in a basic course, the equations are derived and the solutions are presented in tabular or chart from. Obtaining the actual solutions is mathematically and numerically too involved to be covered in basic courses. In this paper, it is shown that the similarity solution and the solution to boundary layer equations in the primitive variables can easily be obtained using spreadsheets. Without needing much programming skills, or needing to learn specialized software, undergraduate students can use this approach and obtain the solution and study the impact of different parameters.

Second-Law Analysis of Heat Transfer in Swirling Flow Through a Cylindrical Duct

1987 ◽  
Vol 109 (2) ◽  
pp. 308-313 ◽  
Author(s):  
P. Mukherjee ◽  
G. Biswas ◽  
P. K. Nag
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Swirling Flow ◽  
Tangential Velocity ◽  
Merit Function ◽  
Second Law ◽  
Constant Wall Temperature ◽  
Boundary Layer Equations ◽  
Second Law Analysis ◽  
Cylindrical Duct

A second-law analysis is made on a swirling flow in a cylindrical duct with constant wall temperature. A purely tangential entry of the fluid is considered and a simplified model, consisting of a central air core enclosed by a potential, free vortex region and a boundary layer, is assumed. The approximate hydrodynamic boundary layer equations, and the continuity equation, are set up and solved numerically for the velocity gradients in the boundary layer. Similarly, the temperature gradients within the thermal boundary layer are obtained from the energy equation. The local Nusselt number and rate of entropy generation are calculated and used to evaluate the rate of heat transfer and loss of available energy, respectively. A merit function, defined as the ratio of exergy transferred to the sum of exergy transferred and exergy destroyed, is evaluated for various values of Reynolds number, based on the inlet tangential velocity, and conclusions are drawn about the influence of inlet swirl on irreversibility.

Free Convection Effects on the Developing Laminar Flow in Vertical Concentric Annuli

1980 ◽  
Vol 102 (4) ◽  
pp. 617-622 ◽  
Author(s):  
M. A. I. El-Shaarawi ◽  
A. Sarhan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Conditions ◽  
The Other ◽  
Axial Distance ◽  
Heat Transfer Characteristics ◽  
Boundary Layer Equations ◽  
Energy And Momentum ◽  
Laminar Convection ◽  
Momentum Boundary Layer

Coupled energy and momentum boundary layer equations have been numerically solved for the problem of combined forced-free laminar convection in the entrance region of vertical concentric annuli. Both upflow and downflow of a fluid with Pr = 0.7 are considered under the thermal conditions of one wall being isothermal and the other adiabatic. Results for the development of velocity profiles, axial distance at which the axial velocity gradient normal to the wall vanishes, pressure drop, and heat transfer characteristics are presented at various values of the parameter Gr/Re ranged from −700 to 1500.

scholarly journals Comparison of k-ε Models in Predicting Heat Transfer and Skin Friction Under High Free Stream Turbulence

1996 ◽  
Author(s):  
Ganesh R. Iyer ◽  
Savash Yavuzkurt
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Skin Friction Coefficient ◽  
Empirical Correlations ◽  
Free Stream Turbulence ◽  
Boundary Layer Equations

Calculations of the effects of high free stream turbulence (FST) on heat transfer and skin friction in a flat plate turbulent boundary layer using different k-ε models (Launder-Sharma, K-Y Chien, Lam-Bremhorsi and Jones-Launder) are presented. This study was carried out in order to investigate the prediction capabilities of these models under high FST conditions. In doing so, TEXSTAN, a partial differential equation solver which is based on the ideas of Patankar and Spalding and solves steady-flow boundary layer equations, was used. Firstly, these models were compared as to how they predicted very low FST (≤ 1% turbulence intensity) cases. These baseline cases were tested by comparing predictions with both experimental data and empirical correlations. Then, these models were used in order to determine the effect of high FST (>5% turbulence intensity) on heat transfer and skin friction and compared with experimental data. Predictions for heat transfer and skin friction coefficient for all the turbulence intensities tested by all the models agreed well (within 1–8%) with experimental data. However, all these models predicted poorly the dissipation of turbulent kinetic energy (TKE) in the free stream and TKE profiles. Physical reasoning as to why the aforementioned models differ in their predictions and the probable cause of poor prediction of free-stream TKE and TKE profiles are given.

Characterization of magnetized CNT-based hybrid nanofluid subjected to convective phenomenon

2021 ◽  
Author(s):  
T. Hayat ◽  
W. A. Khan ◽  
Aqsa ◽  
M. Waqas ◽  
S. Z. Abbas ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Dynamic Properties ◽  
Hybrid Nanofluid ◽  
Nonlinear System Of Equations ◽  
Boundary Layer Equations ◽  
Suitable Form ◽  
Hybrid Nanofluids ◽  
Convective Phenomenon

Hybrid nanofluid gains attention of scientists due to its dynamic properties in various fields, and thus, hybrid nanofluids can be taken as an innovative form of nanofluids. Even though analysts acquire tremendous results in the field of hybrid nanofluids but yet no study has been carried out to predict magnetohydrodynamic effects in such fluid models. In this present analysis, influence of MHD has been investigated for the micro hybrid nanofluid over a stretched surface under convective conditions. Combine boundary layer equations for the flow have been altered into a suitable form via boundary layer approximations. Further, complete nonlinear system of equations has been numerically solved via BVP-4C method. Interesting results have been demonstrated for an exponentially stretched surface and expressed in the form of shear stress and rate of heat transfer. Results have also been visualized in the form of streamlines and isotherms. This study reveals after observing the numeric values of skin friction and Nusselt number that micropolar hybrid nanofluid models have greater heat transfer rate as compared to nanofluids.

The solution of heat transfer problems by the Wiener-Hopf technique. I. Leading edge of a hot film

1973 ◽  
Vol 333 (1594) ◽  
pp. 347-362 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Half Plane ◽  
Leading Edge ◽  
Infinite Plane ◽  
Longitudinal Diffusion ◽  
Boundary Layer Equations ◽  
Leading Term ◽  
Hot Film

An incompressible fluid of constant thermal diffusivity flows with velocity Sy in the x -direction over the infinite plane wall y = 0. The half-plane y = 0, x > 0 is maintained at a uniform temperature T 1 greater than the temperature T 0 of the oncoming fluid. The adiabatic boundary condition T y = 0 is imposed on the half-plane y = 0, x < 0. An exact solution for the dimensionless heat transfer from the heated half-plane x > 0, incorporating longitudinal diffusion, is obtained by the Wiener-Hopf technique, and is reduced to a single convergent real integral which is evaluated numerically. An asymptotic expansion is made in inverse powers of x , whose leading term is Lévêque’s (1928) boundary-layer solution. Subsequent terms in the expansion lead to a determination of the coefficients of the eigenfunctions of the boundary-layer equations which would remain arbitrary in a direct asymptotic expansion of the governing equation.

scholarly journals The Effects of Upstream Mass Injection on Downstream Heat Transfer

1970 ◽  
Vol 92 (3) ◽  
pp. 385-392 ◽  
Author(s):  
W. R. Wolfram ◽  
W. F. Walker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Flat Plates ◽  
Transfer Rates ◽  
Boundary Layer Equations ◽  
Mass Injection ◽  
Complete Set ◽  
Injection Region ◽  
Body Heat

The present study was performed in order to determine the effects of upstream mass injection on downstream heat transfer in a reacting laminar boundary layer. The study differs from numerous previous investigations in that no similarity assumptions have been made. The complete set of coupled reacting laminar boundary layer equations with discontinuous mass injection was solved for this problem using an integral-matrix technique. The effects of mass injection on heat transfer to both sharp and blunt-nosed isothermal flat plates were studied for a Mach 2 freestream. The amount of injection and the length of the injected region were varied for each body. Heat transfer rates were found to decrease markedly in the injected region. A sharp rise in heat transfer was found immediately downstream of the region of injection followed by an asymptotic approach to the heat transfer rates calculated for the case of no injection. An insulating effect was found to persist for a considerable distance downstream from the injection region. The distance required for this insulating effect to die out was found to depend on the length of the injection region as well as the rate of injection.

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