Improved Hybrid Lumped-Differential Formulation for Double-Pipe Heat Exchanger Analysis

1993 ◽  
Vol 115 (4) ◽  
pp. 921-927 ◽  
Author(s):  
F. Scofano Neto ◽  
R. M. Cotta
Keyword(s):  
System Analysis ◽  
Integral Transform ◽  
Annular Channel ◽  
Differential Formulation ◽  
Recent Developments ◽  
Integral Equation Approach ◽  
Double Pipe ◽  
Integral Transform Technique ◽  
Pipe Heat ◽  
Diffusion Problems

Based on recent developments in the so-called Coupled Integral Equation Approach for the approximate solution of heat and mass diffusion problems, the classical lumped-differential formulation for double-pipe heat exchangers is extended and significantly improved in terms of overall accuracy. The energy equation for the outer annular channel is formally integrated and temperature gradients approximately taken into account, in contrast to the conventional lumped system analysis. The resulting partial differential equation for the inner stream, involving a more general type of boundary condition, is analytically handled through the generalized integral transform technique. A critical accuracy analysis is then performed in order to demonstrate the improvement over the plain lumped-differential formulation.

An Integral Equation Approach to the Semi-Infinite Strip Problem

1973 ◽  
Vol 40 (4) ◽  
pp. 948-954 ◽  
Author(s):  
G. D. Gupta
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Laminate Composite ◽  
Integral Transform ◽  
Stress Singularity ◽  
Infinite Strip ◽  
Integral Equation Approach ◽  
Fixed End ◽  
Integral Transform Technique

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

scholarly journals SOLUTION OF MULTIPHASE HEAT CONDUCTION PROBLEMS VIA THE GENERALIZED INTEGRAL TRANSFORM TECHNIQUE WITH DOMAIN CHARACTERIZATION THROUGH THE INDICATOR FUNCTION

2016 ◽  
Vol 15 (2) ◽  
pp. 53
Author(s):  
H. A. Machado ◽  
N. G. C. Leite ◽  
E. Nogueira ◽  
H. Korzenowisk
Keyword(s):  
Heat Conduction ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Transport Equations ◽  
Indicator Function ◽  
Vast Number ◽  
Convection Diffusion ◽  
The Common ◽  
Integral Transform Technique ◽  
Diffusion Problems

The Generalized Integral Transform Technique (GITT) has appeared in the literature as an alternative to conventional discrete numerical methods for partial differential equations in heat transfer and fluid flow. This method permits the automatic control of the error and is easy to program, since there is no need for a discretization. The method has being constantly improved, but there still a vast number of practical problems that has not being solved satisfactory. In several brands of engineering, the transport equations have to be solved for a combination of different phases or materials or inside irregular domains. In this case, the mathematical resource of the Indicator Function can be employed. This function is a representation of the phases or parts of the domain with the numbers 0 and 1 for each phase. According to the method, the Indicator Function is defined by Poisson’s equation, which is added to the system of the transport equations. An integral is done along the curve that defines the interface that will generate the source term in Poisson’ equation used to calculate the Indicator Function distribution. The solution of the system of equations is done using the common GITT approach. Then, an analytical expression for each transformed potential of the indicator function and the other variables are available. Once the transformed potentials are known, the Indicator Function can be analytically operated, and the interface can be represented by an analytical continuous function. In this work, the use of the GITT in conjunction with the Indicator Function is proposed. The methodology is described and some previous results are presented. GITT is applied to a two-dimensional heat conduction problem in a multiphase domain with an irregular geometry, inside a square domain. The methodology presented here can be extended to all brands of convection-diffusion problems already solved via GITT.

Derive The NTU-Effectiveness Formula For The Double Pipe Heat Exchanger In Parallel Flow Arrangement

2017 ◽  
pp. 1
Author(s):  
Elmuataz Moftah ◽  
Ahmad Abdelaly ◽  
Ali Gebriel ◽  
Wahbe Pohwess
Keyword(s):  
Heat Exchanger ◽  
Parallel Flow ◽  
Double Pipe ◽  
Pipe Heat
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