Non-dimensional Analysis of Heat Exchangers P M V Subbarao Professor Mechanical Engineering Department I I T Delhi The culmination of Innovation …..

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Presentation transcript:

Non-dimensional Analysis of Heat Exchangers P M V Subbarao Professor Mechanical Engineering Department I I T Delhi The culmination of Innovation …..

The Concept of Space in Mathematics Global Mathematical Space: The infinite extension of the three-dimensional region in which all concepts (matter) exists. Particular Mathematical Space: A set of elements or points satisfying specified geometric postulates. Euclidian Space: The basic vector space of real numbers. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. A Sobolev space is a space of functions with sufficiently many derivatives for some application domain. Development of a geometrical model for Hx in A compact Sobolev space helps in creating new and valid ideas.

The Compact Sobolev Space for HXs A model for hx is developed in terms of positive real parameters. High population of these parameters lie in 0  p . The most compact space is the one where all the parameters defining the model lie in 0  p .

History of Gas Turbines 1791: A patent was given to John Barber, an Englishman, for the first true gas turbine. His invention had most of the elements present in the modern day gas turbines. The turbine was designed to power a horseless carriage. 1872: The first true gas turbine engine was designed by Dr Franz Stikze, but the engine never ran under its own power. 1903: A Norwegian, Ægidius Elling, was able to build the first gas turbine that was able to produce more power than needed to run its own components, which was considered an achievement in a time when knowledge about aerodynamics was limited.

1872, Dr Franz Stikze’s Paradox

First turbojet-powered aircraft – Ohain’s engine on He 178 The world’s first aircraft to fly purely on turbojet power, the Heinkel He 178. Its first true flight was on 27 August, 1939.

Capacity of An infinitesimal Size HX

Define a Non Dimensional number N Maximum Possible Heat Transfer ?!?!?!? Let Then Cold fluid would experience a large temperature change.

For an infinitely long counter flow HX. Counter Flow HX Maximum Number of Transfer Units

Number of transfer units for hot fluid: Number of transfer units for cold fluid:

For an infinitely long Co flow HX. Let Then Co Flow HX

For A given combination of fluids, there exist two ideal extreme designs of heat exchangers. High Performance HX: Infinitely long counter flow HX. Low Performance HX: Infinitely long co flow HX. If First law for Heat Exchangers !!!!

For A given combination of fluids, there exist two ideal extreme designs of heat exchangers. High Performance HX: Infinitely long counter flow HX. Low Performance HX: Infinitely long co flow HX. If First law for Heat Exchangers !!!!

Second Law for HXs It is impossible to construct an infinitely long counter flow HX. What is the maximum possible?

Effectiveness of A HX Ratio of the actual heat transfer rate to maximum available heat transfer rate. Maximum available temperature difference of minimum thermal capacity fluid. Actual heat transfer rate:

Counter Flow Heat Ex T ci T ce T hi T he