Chin-Hsiang Cheng

Flow Reversal and Heat Transfer of Fully Developed Mixed Convection in Vertical Channels

The present analysis is concerned with flow reversal phenomena and heat transfer characteristics of the fully developed laminar combined free and forced convection in the heated vertical channels. Three fundamental combinations of thermal boundary conditions on the respective wall surface (namely isoflux-isoflux, isofluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern. Results of the velocity distribution and temperature distribution as well as the Nusselt number in terms of bulk mean temperature are carried out. Based on the analytical solutions obtained, flow reversal adjacent to the relatively colder wall is found to exist within the channel as Re/Gr is below than a threshold value, which is related to the thermal boundary conditions. Parameter zones for the occurrence of reversed flow are presented. Comparisons and verification are made using the existing numerical solutions at locations far downstream of developing flow.

AN APPROACH COMBINING BODY-FITTED GRID GENERATION AND CONJUGATE GRADIENT METHODS FOR SHAPE DESIGN IN HEAT CONDUCTION PROBLEMS

The present study is focused on the development of a computational method for shape design of heat conduction problems by using a combination of the body-fitted grid-generation scheme and the conjugate gradient optimization method. The body-fitted coordinate transformation technique is used to generate a curvilinear grid for each iteration automatically, by sensing the change of the shape of the solution domain during the optimization process. The conjugate gradient method is incorporated with direct sensitivity analysis for seeking the optimal shape which minimizes the objective function. The temperature distribution in the solution domain is solved by means of the finite volume method. A practical problem is used for demonstration, and the results show that the proposed method provides a simple and efficient approach for determining the shape profile.

A SIMPLIFIED CONJUGATE-GRADIENT METHOD FOR SHAPE IDENTIFICATION BASED ON THERMAL DATA

The present study is focused on simplification of the conjugate-gradient method so as to extend the flexibility of the inverse heat transfer method for applications in the shape identification problems associated with various forms of objective functions. The capability of the simplified conjugate-gradient method (SCGM) in seeking the shapes of inner structures is tested for several cases. These test cases use three kinds of thermal data measured on the outer surface of a solid body, including temperature distribution, local heat flux distribution, and the overall heat transfer rate. The aim of these test cases is to identify the boundary of the inner voids in the solid bodies based on the thermal data. Results show that for all test cases, the optimization process leads to acceptable accuracy for the objective functions of different forms.

Numerical prediction of lock-on effect on convective heat transfer from a transversely oscillating circular cylinder

Abstract Heat transfer characteristics and the flow behavior of cross flow over a transversely oscillating cylinder are investigated. The lock-on phenomenon has been predicted numerically and its influence on the heat transfer performance of the cylinder is evaluated. The SOLA method is employed to solve the unsteady velocity field in a non-inertial reference frame, and the energy equation is solved by a finite-volume method. Transient variations of the Nusselt number and the drag and lift coefficients are calculated for various oscillation conditions. The ranges of the dominant parameters considered in this study are 0 ⩽ Re ⩽ 300, 0⩽ S c ⩽ 0.3 and 0 ⩽ A / D ⩽ 0.7.. The Prandtl number is considered to be 0.71 or 7.0. In the lock-on regime, an appreciable heat transfer increase caused by the oscillation is observed; however, outside this regime, the heat transfer is almost unaffected by the oscillation. A correlation formula expressing the dependence of heat transfer on these dominant parameters in this lock-on regime is presented. The numerical predictions have been compared with the existing information, and good agreement has been found.

Numerical predictions of entropy generations for mixed convective flows in a vertical channel with transverse fin array

Abstract This study is concerned with local entropy generation of the laminar mixed-convective flow in a vertical channel with a series of transverse fins. These fins, placed on the hotter wall, provide more areas for heat-transfer but meanwhile cause a significant increase in local irreversibilities. Numerical solutions of the elliptic momentum and energy equations are carried out with the stream functoin-vorticity method. Distribution of local entropy generation is further predicted by solving the entropy generation equation based on the obtained velocity and temperature data. Results for various physical and geometric parameters are presented. Consequently, the geometric configuration of the finned channel with higher second-law efficiency is proposed.

PREDICTIONS OF FROST GROWTH ON A COLD PLATE IN ATMOSPHERIC AIR

Abstract A theoretical model for frost formation on a cold plate placed in atmospheric air has been developed in this study. Effects of plate surface temperature (Tw) and air conditions, such as air velocity (V), temperature (Ta), and humidity ratio (ωa), on the frost growth rate can be evaluated by using this model. Results show that the predictions of frost growth rate by the developed model agree closely with the existing experimental data during the forst layer growth period for most of the cases considered. Predictions by this model have also been compared with those obtained by the existing theoretical models.

Shape design for a cylinder with uniform temperature distribution on the outer surface by inverse heat transfer method

Abstract Performance of the inverse heat transfer method in application to the shape design for the heat convection problems has been evaluated. The approach is constructed by combining curvilinear grid generation scheme, direct problem solver, conjugate gradient optimization method, and redistribution method. Shape design for the outer surface profile of a solid medium in a crossflow that contains a heating element and features an isothermal outer surface has been carried out. Practical cases under different combinations of the dominant physical parameters, including Reynolds number (Re), thermal conductivity ratio (kf/ks), desired outer surface temperature (θd), and Prandtl number (Pr), are studied to evaluate the effects of the physical parameters on the shape design.

Observations of Early-Stage Frost Formation on a Cold Plate in Atmospheric Air Flow

The present study is conducted to investigate the frost formation on a cold plate in atmospheric air flow by means of experimental and theoretical methods. In order to provide observations for the early stage of the frost growth process, a microscopic image system is used to record the pattern and the thickness of the frost layer per five seconds after the onset of frost formation. In this study, a multiple-step ascending frost growth pattern caused by melting of frost crystals at the frost surface has been observed. Effects of velocity, temperature and relative humidity of air (V, T a , and Φ) are studied, and the surface temperature of the cold plate (T w ) is also varied. The considered ranges of these dominant variables are: 2≤V≤13 m/s, 20≤T a ≤35°C, 40 percent≤Φ≤80 percent, and -13≤T w ≤-2°C. The theoretical model presented by Cheng and Cheng [22] for predicting the frost growth rate during the frost layer growth period is verified. Results show that the predictions of frost growth rate by the model agree with the experiment data, especially for the frost layer growth period.

Buoyancy-assisted flow reversal and convective heat transfer in entrance region of a vertical rectangular duct

Abstract In this study, predictions of buoyancy-assisted flow reversal and convective heat transfer in the entrance region of a vertical rectangular duct are reported for the first time. In line with the current trend toward the use of computationally efficient numerical methods, the present study is based on the use of a three-dimensional parabolic, boundary-layer model and the FLARE approximation. Physical situations investigated include cases with various asymmetric heating conditions over wide ranges of parameters. Analytical solutions for the fully developed flows are also presented, and the criteria for the flow reversal to occur are predicted. Solutions for the developing flow obtained in this study agree closely with the elliptic-model solutions, and precisely approach the fully developed solutions downstream.

Frost formation and frost crystal growth on a cold plate in atmospheric air flow

Abstract The present study is concerned with the spatial variation of the frost thickness as well as the pattern of the frost crystals formed on a cold plate in atmospheric air. Experimental results regarding the two-dimensional variation of the frost thickness at the leading edge and observation on the growth of the frost crystals on the frost formation are provided. A microscopic image system is used to observe the structure of the frost layer. The environmental variables considered in this study include the velocity, temperature, and relative humidity of the air (V, Ta, and φ), as well as the surface temperature of the cold plate (Tw), which is varied by adjusting the cooling refrigerant temperature (Tref). The ranges of the physical variables considered in this study are 2⩽V⩽8 m/s, 18⩽Ta⩽30 °C, 40%⩽φ⩽70%, − 18⩽T ref ( and T w )⩽0 °C.