Jane Y. Chang

Natural Convection Patterns in Right-Angled Triangular Cavities with Heated Vertical Sides and Cooled Hypotenuses

The present investigation deals with the numerical computation of laminar natural convection in a gamma of right-angled triangular cavities filled with air. The vertical walls are heated and the inclined walls are cooled while the upper connecting walls are insulated from the ambient air. The defining apex angle α is located at the lower vertex formed between the vertical and inclined walls. This unique kind of cavity may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method is used to perform the computational analysis encompassing a collection of apex angles α compressed in the interval that extends from 5° to 63°. The height-based Rayleigh number, being unaffected by the apex angle α, ranges from a low 103 to a high 106. Numerical results are reported for the velocity field, the temperature field and the mean convective coefficient along the heated vertical wall. Overall, the matching between the numerically predicted temperatures and the experimental measurements of air at different elevations inside a slim cavity is of ordinary quality. For purposes of engineering design, a Nu¯H correlation equation was constructed and also a figure-of-merit ratio between the Nu¯H and the cross sectional area A of the cavity was proposed.

Streamlining the teaching of unsteady heat conduction in regular solid bodies with heat convection to neighboring fluids

In the analysis of unidirectional, unsteady heat conduction for simple solid bodies (large slab, long cylinder and sphere), the modern tendency adopted by authors of heat transfer textbooks is to calculate the temperatures and total heat transfer with “one-term” series accounting for the proper eigenquantities, which are expressed in terms of the Biot number. The supporting information is available in tables for a large slab, a long cylinder and a sphere. To avoid linear and quadratic interpolation for the Biot numbers listed in the tables, the goal of the present study is to use regression analysis in order to develop compact correlation equations for the first eigenvalues, the first eigencontants and the first constants (for the total heat transfer) varying with the Biot number for large slabs, long cylinders and spheres, all in the ample range 0 < Bi ≤ 100. This direct approach will speed up the step-by-step calculations of a multitude of unsteady heat conduction problems for engineering students.

Screening for Differential Gene Expressions from Microarray Data

Living organisms need proteins to provide structure, such as skin and bone, and to provide function to the organism through, for example, hormones and enzymes. Genes are translated to proteins after first being transcribed to messenger RNA. Even though every cell of an organism contains the full set of genes for that organism, only a small set of the genes is functional in each cell. The levels at which the different genes are functional in various cell types (their expression levels) can all be screened simultaneously using microarrays. The design of two-channel microarray experiments is discussed and ideas are illustrated through the analysis of data from a designed microarray experiment on gene expression using liver and muscle tissue. The number of genes screened in a microarray experiment can be in the thousands or tens of thousands. So it is important to adjust for the multiplicity of comparisons of gene expression levels because, otherwise, the more genes that are screened, the more likely incorrect statistical inferences are to occur. Different purposes of gene expression experiments may call for different control of multiple comparison error rates. We illustrate how control of the statistical error rate translates into control of the rate of incorrect biological decisions. We discuss the pros and cons of two forms of multiple comparisons inference: testing for significant difference and providing confidence bounds. Two multiple testing principles are described: closed testing and partitioning. Stepdown testing, a popular form of gene expression analysis, is shown to be a shortcut to closed and partitioning testing. We give a set of conditions for such a shortcut to be valid.

Teaching Flow and Thermal Characteristics of Laminar Forced Convection in Tubes with Variable Internal Straight Fins

The primary goal of this educational paper is to construct, for the first time, compact and reliable correlation equations for the asymptotic friction factor and the asymptotic Nusselt numbers for internal, longitudinal finned tubes as a function of the number of fins, the relative fin height and the laminar Reynolds number. Neither textbooks nor the thermofluid dynamics literature provides this information which is extremely useful to instructors of courses on heat transfer to elucidate passive augmentation techniques using fins. The resulting correlation equations for f and NuD have been tested in classroom environments with a great amount of success.