Set Of Algebraic System Research Articles

On fractional Pennes bio-heat equation using Legendre collocation method

In this paper, the distribution of heat in skin tissue during thermal treatment using the time-fractional Pennes model is studied. Temperature variations concerning several parameters such as derivative [Formula: see text] time, blood perfusion, and transmitted power are described using the Legendre collocation technique. The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. The obtained results and comparison with an exact solution are illustrated.

Experimental Validation of Optimized Solar Still Using Solar Energy

This paper presents an experimental validation of a new concept of solar distiller with a condenser and coupled with water solar heater and air collector and humidifier to ameliorate the yield of freshwater of this solar still system which is placed at Sfax in Tunisia. An experimental as well as theoretical investigation is carried out. A mathematical model based on heat and mass transfers of the optimized solar system has been presented in dynamic mode. The obtained global model of the solar unit distillation has been converted to a set of algebraic system of equations to render them ordinary equations by the functional approximation method of orthogonal collocation. To compare the numerical and experimental data of the mathematical model of the solar distiller an example of the validation process that has been presented to assess the credibility of the obtained numerical model of solar distiller system, a laptop simulation program based on the model is simulated by C++ software. In this numerical study, the fourth order Runge-Kutta method is programed to solve the model of glass cover, water and basin temperature of the optimised solar still numerically. It was shown that the developed mathematical model is able to predict accurately the trends of the thermal characteristic of the optimized solar still system temperature of the optimized solar still.

Numerical study of a water distillation system using solar energy

This paper tackles an optimization approach in order to boost the fresh water production of a new design of a solar still which is located at Sfax engineering national school in Tunisia. This optimization approach is based upon the above mentioned design’s improvement by coupling the conventional solar still into at a condenser, solar air and water collector and humidifier. This new concept of a distiller solar still using humidification- dehumidification processes (HD) is exploited for the desalination purpose. As a result of this work, the humidification- dehumidification processes have an essential effect in improving the solar still performance. Performance has been predicted theoretically in terms of water and inner glass cover temperatures, the inlet temperature of air and water of the new concept of distiller on water condensation rate and fresh water production. A general model based on heat and mass transfers in each component of the unit has been developed in steady dynamic regime. The developed model is used, simulating the HD system, to investigate the influence of the meteorological and operating parameters on the system productivity. The obtained set of ordinary differential equations has been converted to a set of algebraic system of equations by the functional approximation method of orthogonal collocation. The developed model is used to simulate the HD system in order to investigate the steady state behavior of each component of the unit and the entire system exposed to a variation of the entrance parameters and meteorological conditions. The obtained results were compared with those of other studies and the comparison gives a good validity of the present results.