An experimental and numerical study of laminar natural convection in a water-filled enclosure with an aspect ratio of 2:1 was conducted. Two opposing vertical walls were held at different uniform temperatures. The remaining four walls of the enclosure were insulated. The Rayleigh number based upon the height of the enclosure was 6.4×108 while that based upon the distance between the two isothermal plates was 8×107. The mean vertical velocities were measured using a two-beam laser Doppler anemometer system with forward scatter. The mean temperature profiles were obtained using a small, 0.07 mm diameter, chromelalumel thermocouple probe. A multilevel-multigrid algorithm was used to predict the flow for the experimental conditions studied. The predicted and experimental results for the mean vertical velocity profiles were compared and found to be in excellent agreement.

The use of a laser-Doppler anemometer to measure velocities in a fluid with a larger variation in its refractive index perpendicular to the laser beams may introduce appreciable errors. This situation is commonly encountered in convective heat transfer studies. The beams are refracted as they pass through the fluid and the distance of the intersection of the beams, control volume, from the surface may be significantly different than the distance of the beams from the surface when they entered the fluid. If the flow is unsteady or turbulent, the relative movement of the beams may be such that the size and location of the control volume is constantly changing causing appreciable errors.

Technical Briefs Transient Response of a Hollow Cylindrical-Cross-Section Solid Sensible Heat: Storage Unit—Single Fluid F. W. Schmidt, F. W. Schmidt Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, 16802 Search for other works by this author on: This Site PubMed Google Scholar J. Szego J. Szego Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, 16802 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information F. W. Schmidt Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, 16802 J. Szego Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, 16802 J. Heat Transfer. Nov 1978, 100(4): 737-739 (3 pages) https://doi.org/10.1115/1.3450891 Published Online: November 1, 1978 Article history Received: April 27, 1978 Online: August 11, 2010

The optimization of the design of a solid sensible heat storage unit initially at a uniform-temperature is presented. The storage unit is composed of a number of rectangular cross-sectional channels for the flowing fluid, connected in parallel and separated by the heat storage material. The complex method for constrained nonlinear optimization as presented by M. J. Box is utilized, with some modifications. The design optimization is based upon achieving maximum utilization of the heat storage or removal capabilities of the material for a given set of operating conditions. This is achieved by varying the storage unit’s geometry while placing constraints on the maximum and minimum length of the unit, fluid channel size, storage material thickness, maximum and minimum outlet fluid temperature, and the minimum amount of heat to be stored.

The transient response characteristics of a solid sensible heat storage exchanger which interacts with two energy transporting fluids are presented. The storage unit is composed of a series of large aspect ratio rectangular channels for the fluids, separated by slabs of the heat storage material. The hot and cold fluids flow in counter current fashion, in alternate channels so that each slab of storage material is in contact with both fluids. The entire system is considered to be initially in equilibrium at a uniform temperature, a step change in the inlet temperature of one of the fluids is imposed, and the thermal response of the unit is predicted until steady state conditions are reached. The response of the storage exchanger to an arbitrary time variation of one of the fluids’ inlet temperature may be obtained using superposition.

The transient response of a solid sensible heat storage unit which receives or supplies heat to a single flowing fluid is presented. The storage unit is composed of a number of rectangular cross-sectional channels for the flowing fluid, connected in parallel and separated by the heat storage material. The energy equation for the fluid and the transient conduction equation for the storage material are solved using finite difference techniques. The parameters which characterize the transient behavior of these units are identified. Results suitable for the prediction of the rate of heat storage and the outlet temperature of the fluid leaving the storage unit are presented as functions of the identified nondimensional parameters.

The influence of gravity on developing forced, laminar flow in a vertical isothermal tube was investigated by means of a numerical analysis and an associated experiment. Numerically predicted velocity profiles and Nusselt numbers for combined forced–free convection with Gr/Re = −30 are compared with their counterparts for pure forced convection, Gr/Re = 0, for air with Re = 500. The analysis was performed for both the uniform irrotational and the fully developed velocity entrance models. Velocity profiles were measured in a vertical-tube apparatus designed to provide an approximately uniform entrance velocity using air as the test fluid. These are compared with numerical predictions based on test conditions.

A finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The velocity profile is fully developed and flow in a tube and between parallel plates is studied. Local and average Nusselt numbers and mixing temperatures are presented as a function of the Péclet number. A criterion is also established which proves useful for predicting the conditions under which axial conduction may be ignored.

An evaluation of light refraction errors in interferometric heat transfer studies is reported. The differential equation describing the path of a light ray passing through an arbitrary thermal boundary layer surrounding a heated surface has been solved using numerical techniques. Results for cubic and parabolic temperature profiles have been presented. The method of analysis reported is of particular value in the estimation of the refraction errors in an experimental unit if an approximation of the temperature distribution in the boundary can be made. It is noted that these errors may be minimized by careful design of the test section. In many cases it is also possible to use these techniques to correct actual interferometric data for refraction errors.