Ching-Yang Cheng

Ecological optimization of an irreversible Brayton heat engine

Finite-time thermodynamics is used to determine the maximum ecological function, its corresponding thermal efficiency and power output of an irreversible Brayton heat engine. The ecological function of a heat engine is defined as the power output minus the loss power, which is equal to the product of the environmental temperature and the entropy production rate. The ecological function is optimized with respect to the thermal conductance ratio and the adiabatic temperature ratio. The optimum values of adiabatic temperature ratios and thermal conductance ratios of irreversible Brayton heat engines are presented. To obtain a higher ecological function, the thermal conductance of the cold-side heat exchanger should be larger than that of the hot-side heat exchanger. The effects of the total number of transfer units of heat exchangers, turbine and compressor isentropic efficiencies, thermal reservoir temperature ratios and heat leaks on the maximum ecological function and its corresponding parameters are studied and discussed. Results can be used as important criteria in the design of Brayton heat engines.

Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium

Abstract This paper reports a study of the phenomenon of natural convection heat and mass transfer near a vertical wavy surface embedded in a fluid-saturated porous medium. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate, and the obtained boundary layer equations is then solved by the local nonsimilarity method and the cubic spline collocation method. Effects of the Lewis number, the buoyancy ratio, and the wavy geometry on the local Sherwood number and the local Nusselt number are studied. The harmonic curves for the local Sherwood number and the local Nusselt number have a frequency twice the frequency of the wavy surface. Moreover, increasing the amplitude-wavelength ratio tends to increase the amplitude of the local Sherwood number and the local Nusselt number. Further, the average Sherwood number and the average Nusselt number for a sinusoidal wavy surface are found to be constantly smaller than that of the corresponding flat plate.

An integral approach for heat and mass transfer by natural convection from truncated cones in porous media with variable wall temperature and concentration

Abstract A study on the combined heat and mass transfer by natural convection from truncated cones embedded in fluid saturated porous media with variable wall temperature and concentration is reported. The integral method is applied to obtain the analytic solution. Results are illustrated graphically for the local Nusselt number, the local Sherwood number, and the reciprocal of the boundary layer thickness ratio. The thickness ratio of the thermal boundary layer to the concentration boundary layer is independent of the exponent of the power function used to describe the wall concentration and concentration. Moreover, the ratio of the thermal boundary layer thickness to the concentration boundary layer thickness increases as the buoyancy ratio is increased for Le ≠ 1.

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.

Non-Darcy natural convection heat and mass transfer from a vertical wavy surface in saturated porous media

Abstract This work examines the effects of spatially wavy surface and fluid inertia on the natural convection heat and mass transfer near a vertical wavy surface embedded in a non-Darcy fluid-saturated porous medium. A simple coordinate transformation is employed to transform a wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of surface amplitude–wavelength ratio, buoyancy ratio, Lewis number, and modified Grashof number. The modified Grashof number is used for evaluating the relative importance of inertial effects and viscous effects. For the free convection heat and mass transfer near a vertical wavy surface, increasing the modified Grashof number tends to decrease the heat and mass transfer rate, while higher amplitude–wavelength ratio decreases the average Nusselt and Sherwood numbers.

Nonsimilar solutions for double diffusive convection near a frustum of a wavy cone in porous media

A nonsimilar boundary layer analysis is presented for double diffusive convection flow near a vertical frustum of a sinusoidal wavy cone in a porous medium with constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy conical surface to a smooth conical surface, and the transformed nonsimilar boundary layer governing equations are then solved by the cubic spline collocation method. Effects of the Lewis number, buoyancy ratio, half cone angle and wavy geometry on the Nusselt and Sherwood numbers for a frustum of a sinusoidal wavy cone in porous media are studied. The harmonic curves for the local Nusselt number and those for local Sherwood number as functions of streamwise coordinate have a frequency twice the frequency of the wavy conical surface. Moreover, an increase in the amplitude-wavelength ratio raises the amplitude of the local Nusselt number and the local Sherwood number. Further, the average Sherwood number and the average Nusselt number for a frustum of a wavy cone are found to be smaller than those for the corresponding smooth frustum cone.

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.

Transient response of annular fins subjected to constant base temperatures

Abstract A hybrid method is used to investigate the transient response of annular fins of various shapes subjected to constant base temperatures. The time-dependent terms in the governing equations are removed by using the Laplace transformation, and the integral method is used to solve the transformed boundary value problem. The inverse Laplace transform is calculated by applying the Fourier series technique with modification. It is shown that the Biot number and geometrical parameters have pronounced effect on the transient heat transfer in annular fins.

The optimum allocation of heat transfer equipment for an irreversible combined heat engine with ecological criteria

Finite-time thermodynamics with an ecological criterion is used to optimize the performance of an irreversible combined Carnot heat-engine. The irreversiblities come from two sources: (1) finite heat conductance for the three heat exchangers; (2) irreversibility inside the heat engine. The ecological function is defined as the power output minus the loss power or the product of the environmental temperature and the entropy rate. The ecological function is optimized with respect to two dimensionless cycle temperatures and thermal efficiency. The maximum ecological function and its corresponding power output and thermal efficiency are presented. It is shown that the ecological function is an important criterion for the design of an irreversible combined Carnot heat engine, considering not only the power output but also the thermal efficiency. When the three heat exchangers have equal heat transfer coefficients, the optimum heat-transfer area ratio for the middle heat exchanger is always equal to 1/3, independent of the irreversibility parameters for the top and bottom cycles and the heat reservoir temperature ratio. Furthermore, the optimum heat-transfer area ratio for the hotend heat exchanger decreases while that for the cold-end heat exchanger increases as the irreversibility parameters of the top and bottom cycles are increased.

Transient Mixed Convection Heat and Mass Transfer with Chemical Reaction along a Vertical Wavy Plate in a Micropolar Fluid

The transient mixed convection heat and mass transfer with chemical reaction along a vertical wavy surface in micropolar fluids is studied by the coordinate transformation and the cubic spline collocation method. Effects of chemical reaction parameter, vortex viscosity parameter, thermal buoyancy number, concentration buoyancy number, Prandtl number, and Schmidt number on the transient local values of Nusselt number and Sherwood number are presented. In a mixed convection boundary layer, forced convection is the dominant mode of heat and mass transfer near the leading edge or at small time, while in regions farther downstream or at large time, natural convection becomes the dominant mode of heat and mass transfer. Increasing the generative chemical reaction parameter increases the surface heat transfer rate and decreases the surface mass transfer rate.