R.K. Sahoo

Hyperbolic axial dispersion model for heat exchangers

Flow maldistribution in heat exchangers for steady-state and transient processes can be described by dispersion models. The traditional parabolic model and the proposed hyperbolic model which includes the parabolic model as a special case can be used for dispersive flux formulation. Instead of using the heuristic approach of parabolic or hyperbolic formulation, these models can be quantitatively derived from the axial temperature profiles of heat exchangers. In this paper both the models are derived for a shell-and-tube heat exchanger with pure maldistribution (without back mixing) in tube side flow and the plug flow on the shell side. The Mach number and the boundary condition which plays a key role in the hyperbolic dispersion have been derived and compared with previous investigation. It is observed that the hyperbolic model is the best suited one as it compares well with the actual calculations. This establishes the hyperbolic model and its boundary conditions.

Effect of Darcy, fluid rayleigh and heat generation parameters on natural convection in a porous square enclosure: A Brinkman-extended Darcy model

Abstract A Pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analysed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Raf, Darcy number, Da, and heat generating number, Qd. The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical walls of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators[4,6], can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate.

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

Rewetting of an Infinite Slab With Uniform Heating Under Quasi-Steady Conditions

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite slab, with one side flooded and the other side subjected to a constant heat flux, has been solved by Wiener-Hopf technique. The solution yields the quench front temperature as a function of various model parameters such as Peclet number, Riot number and dimensionless heat flux. Also, the critical (dryout) heat flux is obtained by setting the Peclet number equal to zero, which gives the minimum heat flux required to prevent the hot surface being rewetted.

Thermodynamic optimization of regenerators

This paper presents a second law of thermodynamics analysis technique for regenerators in single blow operation. Unlike earlier analyses, this technique accounts for the gas and matrix temperature variation along the temporal and spatial coordinates. The results of this study indicate that: 1, well defined optima exist with regard to charging time and number of heat transfer units for maximizing the useful work stored; and 2, whereas in earlier analyses a finite optimum charging time results as Ntu approaches infinity, in the present analysis a square wave of specific irreversibility propagates in the medium. To obtain an appropriate analytical expression, this analysis is approximated to suit a low Ntu regenerator. Nomenclature A Cs E f

Propagation of thermal waves with lateral heat transfer

Abstract The wave nature of heat propagation in a one-dimensional semi-infinite medium with lateral convective heat transfer is investigated by solving the hyperbolic heat conduction equation in the longitudinal direction. The situation involves a large relaxation time which is relevant at low temperatures or for materials with a non-homogeneous inner structure, and the heat conduction in the lateral direction is assumed to be parabolic due to the number of lateral heat wave reflections compared to those in the longitudinal direction. The results for a unit heat flux condition at the boundary are compared with those obtained from parabolic heat conduction. This reveals that the classical heat diffusion theory predicted by parabolic heat conduction significantly underestimates the magnitude of the temperature and heat flux in thermal wave propagation. The results also reveal that when the dimensionless lateral heat transfer, known as the wave shape factor, is equal to unity, the thermal wavefront which travels through the medium at a finite speed decays exponentially along its path of travel while retaining the shape of the input wave. This theoretical prediction can be implemented experimentally for estimation of thermal relaxation times.

Analysis of rewetting of an infinite tube by numerical fourier inversion

Abstract A semi—analytical model for the two—dimensional quasi—steady conduction equation, governing conduction controlled rewetting of an infinite tube, has been suggested. The solution yields the temperature field as a function of various input model parameters such as Peclet number, Biot number and radius ratio of the tube. Unlike earlier investigations, the present semi-analytical model predicts the temperature field for the entire domain of a tube, employing the Wiener—Hopf technique and by inverse discrete Fourier transform (IDFT) algorithm.

Exergy maximization in cryogenic regenerators

This paper presents an improved irreversibility analysis of regenerators with singleblow operation. Unlike earlier analyses, this investigation deals with the gas and matrix temperature variation along spatial and temporal co-ordinates. The results of this study show that the earlier analyses involving a lumped model and an averaged model applied to high Ntu regenerators may run the risk of operating in the zone of high irreversibility, while the models are well suited for Ntu < 1.0 and Ntu < 2.0, respectively. The present analysis is more relevant for exergetic analysis applied to cryogenic regenerators with high Ntu.

Effect of temperature-dependent specific heat of the working fluid on the performance of cryogenic regenerators

Abstract The governing differential equations of a regenerator operating with a fluid with temperature-dependent specific heat have been formulated in terms of characteristic reduced parameters. A numerical solution of these equations is presented for several combinations of fluid-flow parameters using normal and parahydrogen as working fluid. It is observed that a constant specific heat model with the harmonic mean reduced length is adequate except at large values of reduced length or period and when the specific heat variation exceeds a factor of two over the temperature range. The matrix and gas exit temperature profiles, however, show a significant difference between the two models, which may be critical in some applications.

Exergy maximization in refrigeration storage units with heat leak

Abstract This Paper presents Second Law of Thermodynamics analysis techniques for sensible refrigeration energy storage units with non-adiabatic boundaries. The investigation is based on the minimization of entropy production due to a finite temperature difference. The results of this study indicate three basic points: 1, in the presence of heat leaks, the irreversibility rate is more than in its absence; 2, the increase in irreversibility due to heat leaks reduces the effective N tu exponentially; 3, there exists a dimensionless optimum time parameter which relates two other fundamental dimensionless parameters for the maximization of useful work stored. These fundamental parameters are N tu associated with heat flow across the non-adiabatic wall and N tu of the storage unit. These points suggest that the leakage heat affects the entropy production adversely and hence it should be kept at a minimum.