L. Malinowski

Parametric study of exergetic efficiency of a small-scale cogeneration plant incorporating a heat pump

A comparative parametric analysis is carried out of a small-scale combined heat and power plant incorporating a heat pump and the conventional system in which heat is produced in a hot water boiler and electrical energy is drawn from the power grid. Relative exergetic efficiency is defined as the quotient of exergetic (rational) efficiencies of the cogeneration plant and the related conventional system. Dependence of this efficiency on the power-to-heat ratio for chosen values of parameters characterizing the compared systems is calculated and shown pictorially.

A relaxation model for heat conduction and generation

A relaxation model for heat conduction and generation is presented which takes into account the finite velocity of heat propagation and the inertia of the internal heat source. Special attention is given to the effect of the source terms in the newly formulated heat conduction equation on the temperature field. The novel heat conduction equation is transformed into a dimensionless form and its special cases are considered. Several initial value problems are solved analytically for a zero-dimensional case of heat conduction and generation. It is observed that, unlike the classical hyperbolic model, the relaxation solutions generally do not tend to approach the corresponding parabolic solutions.

Critical energy of thermally insulated composite superconductors

Abstract An analytical method for calculation of the critical energy of thermally insulated composite superconductors is presented. It takes into account temperature dependent conductor properties and the finite duration and finite length of heat disturbances. The method, which includes no adjustable parameters, yields critical energies which are in fair agreement with experimental results and numerical analysis.

AN ANALYTICAL METHOD FOR CALCULATION OF TRANSIENT TEMPERATURE FIELD IN THE COUNTER-FLOW HEAT EXCHANGERS

We present an analytical solution to the system of partial differential equations with homogeneous initial conditions, describing transient temperature field in countercurrent heat exchangers. The system of partial differential equations is Laplace-transformed and the resultant set of ordinary differential equations is solved analytically. Analytical solution in the original domain is obtained for a special case of the heat exchanger where the thermal capacities and velocities of fluids are equal in both channels. Exemplary calculations are carried out to determine the unsteady response of the heat exchanger to a step change in the inlet temperature of one fluid

A semi-analytical method for determining unsteady temperature field in a parallel-flow three-fluid heat exchanger

This paper presents a semi-analytical solution of a set of partial differential equations describing the transient temperature field in a parallel-flow three-fluid heat exchanger. The set of partial differential equations is Laplace-transformed and the resultant set of ordinary differential equations is solved analytically. The inverse of the solution is obtained numerically. Exemplary calculations are performed for the case of a step change in the inlet temperature of one fluid and steady state initial conditions.

Novel model for evolution of normal zones in composite superconductors

Abstract This paper presents a numerical analysis of the evolution of normal zones in a composite superconductor based on a novel heat conduction equation which takes into account the finite speed of thermal wave propagation and the inertia of the internal heat source. The results are compared with those obtained from the classical parabolic heat conduction equation. It is shown that appreciable differences can occur between the two models, in qualitative as well as quantitative terms. For large times these differences do not disappear because of the effect of internal heat generation.

Explicit expression for critical energy of uncooled superconductors considering transient heat conduction

An analytical method for calculation of critical energies of uncooled composite superconductors is presented based on the transient model for heat conduction. In the model, the dependence of the ohmic heat generation on temperature as well as the finite duration and the finite length of thermal disturbances are taken into account while the thermophysical parameters of the conductor are assumed to be constant. Critical energies, determined on the basis of analysis of the time-dependent maximum temperature in the normal zone, are used to formulate a simple explicit expression for the critical energy by the method of non-linear regression.

Analytical Method for Determining Critical Energies of Uncooled Superconductors Based on the Hyperbolic Model of Heat Conduction

The paper presents an analytical method for calculation of critical energies of uncooled composite superconductors based on the hyperbolic equation of heat conduction. The mathematical model developed takes into account: the finite speed of heat transport, the temperature dependence of the ohmic heat generation, the finite duration and the finite length of thermal disturbances. The thermophysical parameters of the conductor are assumed constant. Critical energies are determined by the analysis of variation of the maximum temperature in the normal zone with time. The results obtained are compared with those predicted by the related model based on the classical parabolic equation of heat conduction. The differences are not large but they can be substantial especially in the case of high current density devices.

Analytical method for calculation of critical energy of technical superconductors taking into account transient heat transfer

Abstract This paper presents an analytical method for calculation of the minimum quench energy (MQE) of stabilized superconductors, with regard to transient heat transfer in the conductor and coolant, and the finite duration and finite length of heat disturbances. Critical energies calculated from the derived analytical expressions are in fair agreement with available experimental data and the results of a numerical analysis.

Effect of relaxation of internal heat source capacity on the temperature field in the semi-infinite body

Abstract The novel heat conduction equation [1,2] which takes into account both the heat flux relaxation (the finite speed of thermal wave propagation) and the relaxation of internal heat source capacity is solved numerically by the MacCormack predictor-corrector method [3]. The temperature field in the body due to a step change in heat flux at the surface is analysed for various ratios of relaxation times. It is shown that the relaxation of internal heat source capacity can have an appreciable influence on the temperature distribution in the body.