3,683 research outputs found
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
Analysis of heat transfer in a hot body with non-constant internal heat generation and thermal conductivity
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science.
May 27, 2016.Heat transfer in a wall with temperature dependent thermal conductivity and internal
heat generation is considered. We rst focus on the steady state models followed by the
transient heat transfer models. It turns out that the models considered are non-linear.
We deliberately omit the group-classi cation of the arbitrary functions appearing in
the models, but rather select forms of physical importance. In one case, thermal
conductivity and internal heat generation are both given by the exponential function
and in the other case they are given by the power law. We employ the classical Lie
point symmetry analysis to determine the exact solutions, while also determining the
optimal system for each case. The exact solutions for the transient models are di cult
to construct. However, we rst use the obtained exact solution for the steady state case
as a benchmark for the 1D Di erential Transform Method (DTM). Since con dence
in DTM is established, we construct steady state approximate series solutions. We
apply the 2D DTM to the transient problem. Lastly we determine the conservation
laws using the direct method and the associated Lie point symmetries for the transient
problemMT201
Analysis of models arising from heat conduction through fins using Lie symmetries and Tanh method.
Masters Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF
Exact implicit Solution of Nonlinear Heat Transfer in Rectangular Straight Fin Using Symmetry Reduction Methods
In this paper, the exact implicit solution of the second order nonlinear ordinary differential equation which governing heat transfer in rectangular fin is obtained using symmetry reduction methods. General relationship among the temperature at the fin tip, the temperature gradient at the fin base, the mode of heat transfer, and the fin parameters and ā° is obtained. Some numerical examples are discussed and it is shown that the temperature of fin increases when approaching from the heat source. The relationship between the fin efficiency and the temperature of fin tip is obtained for any value of the mode of heat transfer . The relationship between the fin efficiency and both the parameter and Īµ the temperature gradient at the fin base is obtained. To our best knowledge, solutions obtained in this paper are new
Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces
In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness
Classical symmetry reductions of steady nonlinear one-dimensional heat transfer models
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. August 8, 2014.We study the nonlinear models arising in heat transfer in extended surfaces
(fins) and in solid slab (hot body). Here thermal conductivity, internal generation
and heat transfer coefficient are temperature dependent. As such the
models are rendered nonlinear. We employ Lie point symmetry techniques to
analyse these models. Firstly we employ Lie point symmetry methods and
determine the exact solutions for heat transfer in fins of spherical geometry.
These solutions are compared with the solutions of heat transfer in fins of rectangular
and radial geometries. Secondly, we consider models describing heat
transfer in a hot body, for example, a plane wall. We then employ the preliminary
group classification methods to determine the cases of the arbitrary
function for which the principal Lie algebra is extended by one. Furthermore
we the exact solutions
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