Efficiency Comparison Between Circular and Semicircular Fins Circumscribing Circular Pipes

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
R. Chakraborty ◽  
A. Sirkar
Keyword(s):  
Temperature Distribution ◽  
Thermal Performance ◽  
Numerical Results ◽  
Circular Pipe ◽  
Two Dimensional ◽  
Governing Equations ◽  
Degree Polynomial ◽  
Circular Pipes ◽  
Efficiency Comparison ◽  
Detailed Derivation

A new design of fin has been conceived, which is in the shape of a semicircular strip. A step-by-step straightforward detailed derivation of the governing equations for two-dimensional temperature distribution in a semicircular fin has been presented, assuming a third degree polynomial. Numerical results are presented to illustrate the effects of pipe size and the number of semicircular fins on the thermal performance of the fin. It has been shown mathematically that the efficiency of a semicircular fin can be greater than that of a circular fin, having same total volume of fin material when employed over the circumference of a circular pipe.

Solutions for supersonic rotational flow around a corner using a new co-ordinate system

1968 ◽  
Vol 34 (4) ◽  
pp. 735-758 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Similarity Solution ◽  
Inviscid Flow ◽  
Numerical Results ◽  
Rotational Flow ◽  
Incoming Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
Perfect Gas ◽  
Convex Corner

A co-ordinate system consisting of the left-running characteristics (α = const.) and the streamlines (ϕ = const.) is used. The governing equations are derived in terms of α and ϕ for a two-dimensional steady supersonic rotational inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel supersonic rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic (case 1) or sonic (case 2). For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner, are found for the Mach angle and flow deflexion angle in terms of their values on the leading characteristic and at the corner. In case 2, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results.

LIFT AND DRAG OF A TWO-DIMENSIONAL PAD SLIDING UPON A POROUS SURFACE

1996 ◽  
Vol 20 (4) ◽  
pp. 349-363
Author(s):  
André Desseaux ◽  
Jean-Luc Menet
Keyword(s):  
Approximate Solution ◽  
Vertical Velocity ◽  
Similarity Solution ◽  
Numerical Results ◽  
Porous Surface ◽  
Quasilinearization Method ◽  
Two Dimensional ◽  
Governing Equations ◽  
Lift And Drag ◽  
Asymptotic Formulation

We consider the influence of withdrawal or injection of a fluid through a porous surface on the flow limited by a long parallel slider. Due to the no-slip conditions, the flow lacks of symmetry. But, a choice for a vertical velocity independent on the gap between the two surfaces is equivalent to a classical similarity solution. Then, the governing equations are reduced to a set of three ordinary differential equations. The quasilinearization method is a powerful tool to resolve these equations as soon as a first approximate solution is known. In both cases of small and large values for Re, we present an asymptotic formulation and use these first solutions for the scheme. A comparison with our numerical results shows that, respectively, these two approximations can be used until Re<5 for the first one and if Re>25 for the second. The different numerical results (velocity profiles, pressure, lift and drag) as functions of Re are analysed and compared with other published values.

Prediction of Temperature Distribution in a Food Self-Heating System

2010 ◽  
Author(s):  
Son H. Ho ◽  
Muhammad M. Rahman ◽  
Aydin K. Sunol
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Thermal Performance ◽  
Exothermic Reaction ◽  
Heating System ◽  
Food Tray ◽  
Governing Equations ◽  
Heating Unit ◽  
Self Heating ◽  
Heating Profiles

This paper presents a numerical modeling and simulation of heat transfer in a food self-heating unit for group meals. A model of a water-activated heater based on an exothermic reaction was developed. The resulting governing equations of heat conduction and chemical reaction were solved for an analytical approximate solution, to which experimental data found from literature were compared and curve fitted. Then a model of a complete food-heating unit, which includes a stack of four sets of food tray, heating tray, and heater sandwiched between them, as well as the cardboard container, was developed. A system of governing equations for heat transfer in the composite medium for the complete model was solved. Numerical solution of temperature distribution within the food-heating unit is presented. The responses in thermal performance of the heating system to the parameters that influence heating profiles of the heater such as decay constant and heat generation were studied in order to improve the thermal performance of the heating system. The results are useful for designing and optimizing self-heating systems for food served to groups of many people.

Theoretical considerations of the temperature distribution in a channel bounded by two co-axial circular pipes

1964 ◽  
Vol 60 (3) ◽  
pp. 653-656 ◽  
Author(s):  
Krishna Lal
Keyword(s):  
Temperature Distribution ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Point Of View ◽  
Circular Pipe ◽  
Oscillatory Function ◽  
Heat Addition ◽  
Temperature Distributions ◽  
Circular Pipes ◽  
Theoretical Considerations

Solutions for the temperature distribution in a circular pipe have been given by various authors, notably Gretz, Nusselt, Goldstein; all these are cited in (1), section 266. I have already considered in one paper the temperature distribution in a circular pipe when viscous incompressible fluid is flowing through the pipe and rate of heat addition is an oscillatory function of time. In this paper expressions for the temperature distributions are derived when viscous incompressible fluid is flowing through the channel, the dissipation due to friction is neglected and the rate of heat addition is an exponential function of time. From the engineering point of view this situation has some importance.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

THE TEMPERATURE DISTRIBUTION PRODUCED BY ACOUSTIC ABSORPTION: I. MACROSCOPIC TREATMENT

1966 ◽  
Vol 44 (12) ◽  
pp. 3001-3011 ◽  
Author(s):  
S. Simons
Keyword(s):  
Temperature Distribution ◽  
Acoustic Wave ◽  
Numerical Results ◽  
Time Dependent ◽  
Acoustic Absorption ◽  
Space And Time

A calculation is given of the temperature distribution in space and time produced by the absorption of an acoustic wave propagated inside a medium, under conditions in which the situation may be described macroscopically. The problem is considered for various geometries, and for both constant and time-dependent energies of the incident acoustic wave. Numerical results are obtained, and a discussion is given of their relevance to various experiments.

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