Now showing items 3283-3302 of 3496

• #### Trophic Dynamics In Marine Nearshore Systems Of The Alaskan High Arctic (Kelp, Laminaria, Carbon Isotope, Productivity)

This dissertation describes two ecological studies in the arctic Alaskan nearshore zone: the productivity and growth strategies of arctic kelp and the use of natural carbon isotope abundances to examine food web structure and energy flow in the marine ecosystem. Linear growth of the kelp, Laminaria solidungula is greatest in winter and early spring when nutrients are available for new tissue growth. Since over 90% of this growth occurs in complete darkness beneath a turbid ice canopy, the plant draws on stored food reserves and is in a carbon deficit during the ice covered period. Annual productivity of L. solidungula under these conditions is about 6 g C m('-2) compared to about 10 g C m('-2) if light penetrates the ice canopy. Carbon isotope abundances were used to assess food web structure and energy flow in the Boulder Patch, an isolated kelp bed community, and in the Alaskan Beaufort Sea fauna. Isotopic analyses of the resident fauna of the Boulder Patch revealed that kelp carbon contributes significantly to the diet of many benthic animals, including suspension feeders. Some crustaceans, such as mysids and euphausiids (which are key prey species for fishes, birds and marine mammals), also incorporate large amounts of kelp carbon into their tissues when resident in the Boulder Patch. Across the shelf of the Alaskan Beaufort Sea, a distinct gradient in the isotopic composition of marine zooplankton and benthic fauna was related to the intrusion of the Bering Sea water and upwelling in the eastern Beaufort Sea near Barter Island. The ('13)C depletion in fauna of the eastern Beaufort Sea is presumed due to the cycling of ('13)C depleted inorganic carbon into the euphotic zone.
• #### Trophic dynamics of boreal lakes in a changing northern landscape: impacts of lake drying and forest fires

The abundant lakes of northern latitudes are the primary breeding grounds for many waterbird species. In recent decades, temperatures in the north have increased by twice the global average. This substantial warming has caused lake drying and increased wildfires, both of which may impact waterbird habitats. Fires release nutrients locked in terrestrial resources, making them available for transport to lakes, while lake drying concentrates nutrients and other solutes into smaller water volumes. Increased nutrients may fundamentally alter ecosystem processes of lakes by changing the timing and abundance of phytoplankton blooms, which in turn affects the abundance of aquatic invertebrates - the primary food source for breeding waterbirds and their broods. I examined effects of forest fires and lake drying on ecosystems of Subarctic boreal lakes in the Yukon Flats, Alaska, documenting changes to (1) aquatic nutrient and chlorophyll concentrations, (2) aquatic invertebrate densities, and (3) abundance and occupancy of waterbirds. Nutrient, chlorophyll, and invertebrate levels were largely unaffected by a recent forest fire. This ecosystem stability transferred upward to waterbirds, as brood abundance was also unaffected by the fire. On drying lakes, nitrogen and phosphorus concentrations increased >200% and >100%, respectively, from the 1980s to present. At the same time, concentrations of 4 major ions increased, including increases of >500% for chloride and >100% for sodium. Nonetheless, chlorophyll levels, aquatic invertebrate abundance, and occupancy of waterbird broods were largely unaffected by these chemical changes on drying lakes. Overall, ecosystems of Yukon Flats were largely resilient to short-term effects of forest fires and rising chemical concentrations associated with lake drying. Moreover, this resilience spanned multiple trophic levels, from phytoplankton to aquatic invertebrates to waterbirds.
• #### Trophic dynamics of pinniped populations in Alaska using stable carbon and nitrogen isotope ratios

Trophic changes in populations of Stellar sea lions (Eumetorias jubatus), northern fur seals (Callorhinus ursinus) and harbor seals (Phoca vitulina) in the eastern Bering Sea and Gulf of Alaska were studied using stable isotope analysis. Declining populations of all three species of pinnipeds prompted this study to determine if changes in diet, likely resulting from food limitation, contributed to the declines. Stable carbon and nitrogen isotope ratios were analyzed in the vibrissae (whiskers) and body tissues of pinnipeds from 1993-1998 and compared with muscle tissue from prey species during the same time period to determine pinniped trophic dynamics. Vibrissae growth rate studies revealed harbor seal vibrissae are only retained for one year and then replaced, while Steller sea lions maintain their vibrissae for several years. Isotopic data from all three species are consistent with diets composed of walleye pollock (Theragra chalcogramma) at various times and locations throughout the year. Steller sea lion and northern fur seal vibrissae revealed regular oscillations along their lengths in both carbon and nitrogen isotope ratios that likely corresponded to regional isotopic differences. As these animals moved or migrated from one region to another during the year, they metabolically incorporated the different regional isotope ratios through their prey. Because these animals return to their rookery to pup, breed and molt each year, the isotope ratios in the vibrissae showed a regular pattern of enrichment and deplection. Harbor seals, which tend to stay in one geographic location, have relatively static isotope ratios in their vibrissae, while seals that moved into offshore waters had fluctuating isotope ratios that corresponded to regional difference. No trophic shifts, as evidenced by major changes in nitrogen isotope ratios, were present in any tissues from the three species over the period 1975-1998. Stable isotope ratios of bone collagen for all three species from 1950-1997 indicated no change in trophic level but did reveal that the seasonal primary production in the North Pacific Ocean has declined and may have contributed to a decreased carrying capacity impacting these top trophic organisms
• #### Trophic ecology of nearshore fishes in glacially-influenced estuaries of Southeast Alaska

Estuaries in Southeast Alaska (SEAK) are linked to terrestrial ecosystems by the flow of freshwater from plentiful precipitation and glacial runoff. This thesis examined the trophic ecology of nearshore fishes in SEAK estuaries to advance our understanding of how deglaciation and resulting shifts in the timing and magnitude of freshwater runoff will affect estuarine food webs. The goals of this work were to characterize seasonal variation in the feeding ecology of an abundant estuarine predator across three glacially-influenced sites and to examine the relative contribution of organic matter (OM) from terrestrial-riverine sources to the diets of estuarine consumers. In chapter one, stomach contents of Pacific staghorn sculpin (Leptocottus armatus) were analyzed to test the hypothesis that diets would differ across sampling sites and months, reflecting variation in freshwater runoff and the phenology of estuarine organisms. Stomach contents of staghorn sculpins were collected monthly between April and September 2014, from intertidal sites at mouths of rivers that differ in their headwater hydrology. Staghorn sculpins consumed a variety of prey, including gammarids, mysids, isopods, polychaetes, and other freshwater-tolerant prey, as well as juvenile fish. Weak to moderate differences observed in diet composition across sites and months likely reflected spatial and seasonal shifts in the occurrence of freshwater-tolerant invertebrates and young-of-the-year fishes. Overall, the ability of staghorn sculpins to take advantage of a variety of prey across variable conditions may make them resilient to environmental change. In chapter two, I examined trophic linkages between terrestrial and marine food webs by using stable isotope analysis to evaluate the relative contribution of terrestrial-riverine OM to the diets of estuarine consumers. Analyses showed limited use of terrestrial-riverine OM by marine fishes (Leptocottus armatus and Platichthys stellatus) and more variable use by anadromous fishes (Salvelinus malma and Oncorhynchus kisutch). Intertidal invertebrates used more terrestrial-riverine OM than fish, with greater use of allochthonous OM earlier in the summer. Despite the documented availability of terrestrial-riverine OM, estuarine consumers showed limited use of this resource. These findings inform our baseline understanding of trophic linkages in glacially-influenced estuaries, a critical first step in evaluating future climate driven changes to coastal ecosystems.
• #### Trophic pathways supporting Arctic Grayling in a small stream on the Arctic Coastal Plain, Alaska

Arctic Grayling (Thymallus arcticus) are widely distributed on the Arctic Coastal Plain (ACP) of Alaska, and are one of the few upper level consumers in streams, but the trophic pathways and food resources supporting these fish are unknown. Grayling migrate each summer into small beaded streams, which are common across the landscape on the ACP, and appear to be crucial foraging grounds for these and other fishes. I investigated prey resources supporting different size classes of grayling in a beaded stream, Crea Creek, where petroleum development is being planned. The specific objectives were to measure terrestrial prey subsidies entering the stream, quantify prey ingested by Arctic Grayling and Ninespine Stickleback (Pungitius pungitius), determine if riparian plant species affect the quantity of terrestrial invertebrates ingested by grayling, and determine if prey size and type ingested were a function of predator size. Results indicated that small grayling (< 15 cm fork length (FL)) consumed mostly aquatic invertebrates (caddisflies, midges, and blackflies) early in the summer, and increasing quantities of terrestrial invertebrates (wasps, beetles, and spiders) later in summer, while larger fish (> 15 cm FL) foraged most heavily on stickleback. Riparian plant species influenced the quantity of terrestrial invertebrates entering the stream, however these differences were not reflected in fish diets. This study showed that grayling can be both highly insectivorous and piscivorous, depending upon fish size class, and that both aquatic and terrestrial invertebrates, and especially stickleback, are the main prey of grayling. These results highlight the importance of beaded streams as summer foraging habitats for grayling. Understanding prey flow dynamics in these poorly studied aquatic habitats, prior to further petroleum development and simultaneous climate change, establishes essential baseline information to interpret if and how these freshwater ecosystems may respond to a changing Arctic environment.
• #### Trophic pathways supporting juvenile chinook and coho salmon in the glacial Susitna River, Alaska: patterns of freshwater, terrestrial, and marine resource use across a seasonally dynamic habitat mosaic

In large, seasonally dynamic and spatially complex watersheds, the availability and relative importance of various food resources for stream fishes can be expected to vary substantially. While numerous studies have attempted to uncover the trophic linkages that support stream salmonids, much of these efforts have occurred at small scales that disregard variability of food resources inherent in lotic systems. This study aimed to determine large-scale patterns in the contributions of freshwater, terrestrial, and marine-derived food resources to juvenile Chinook and Coho salmon (Oncorhynchus tshawytscha and O. kisutch) in the large, glacially influenced Susitna River, Alaska. I quantified diet patterns both spatially, across different macrohabitat types positioned along a 169-km segment of the river corridor, and temporally, from June to October, using stable isotope and stomach content analyses. To further resolve energy pathways from basal carbon sources to juvenile salmon, I determined the relative roles of terrestrial organic matter and freshwater periphyton food sources to aquatic benthic invertebrate diets. The latter analysis showed that invertebrate consumers were more reliant on freshwater periphyton than on terrestrial organic matter. Bayesian stable isotope mixing models indicated that juvenile salmon in the middle Susitna River were, in turn, largely supported by freshwater invertebrate prey regardless of spatial and temporal context. The relative contribution of marine-derived prey (salmon eggs) to juvenile salmon diets was greatest in the fall within tributary mouth and off-channel macrohabitats during both years of the study. Terrestrial invertebrate prey contributions were generally greatest during mid-summer within all macrohabitat types sampled, however this pattern varied across years. No upstream to downstream diet pattern was apparent from the data. These results underscore the importance of freshwater energy pathways for sustaining juvenile Chinook and Coho salmon in the Susitna River and provide further spatial and temporal context for the importance of pulsed marine and terrestrial prey subsidies. As Pacific salmon stocks continue to decline, management and mitigation efforts should operate on knowledge gained from studies that encompass the largescale spatial and temporal variability inherent in riverine landscapes.
• #### Trophic relationships in an Arctic marine foodweb and implications for trace element dynamics

Tissues of subsistence-harvested Arctic marine and terrestrial mammals and potential prey species were analyzed for isotopes of carbon and nitrogen and selected trace elements describing contaminant pathways in the food web. Feeding habits of ice seals were characterized using stable isotopes and gastric contents analysis. Bearded seals (Erignathus barbatus) relied on the benthic food chain. Zooplankton and fishes were significant prey for ringed seals (Phoca hispida), while fishes were the principal prey in spotted seals (Phoca largha). Gastric prey composition and isotope ratios varied with age and sex. Effects of age, trophic level, and prey prevalence on trace element concentrations in seal tissues were investigated. Most trace elements differed significantly in phocid tissues. Bearded seals had the highest cadmium (Cd) concentrations and spotted seals the lowest. This indicates a connection of Cd with invertebrate prey, while mercury (Hg), in particular the proportion of organic to total Hg (THg), accumulated in the piscivorous food web. Silver (Ag) showed possible association to benthic feeding habits. Altered trace element accumulation patterns were observed in compromised seals. Stable isotopes illustrated belugas (Delphinapterus leucas) occupied a higher trophic level than bowheads (Balaena mysticetus) and gray whales (Eschrichtius robustus). Trace element concentrations also differed significantly among these cetaceans. Observed relationships with age or length in species analyzed were complex and nonlinear rather than previously reported continuous bioaccumulation with age. Cd was similar in belugas and bowheads but lowest in gray whales. THg was highest in belugas and near detection limit in mysticetes, supporting the connection of Hg with fish and Cd with invertebrates. The hepatic selenium (Se ):THg ratio exceeded the frequently described equimolarity in all species. Se:THg molar ratios and tissue concentrations of zinc (Zn) may show promise as indicators of immune status and animal health. Polar bears (Ursus maritimus) feed on the highest trophic level, though Cd concentrations were either similar to, or significantly lower than those in belugas or ice seals. Conversely, THg increased significantly from seal to bear. Generally, trace elements in Alaska-harvested animals were lower than for other Arctic regions, and trace metal magnification in the Arctic food web was not significant.
• #### Tsunami runup in U and V shaped bays

Tsunami runup can be effectively modeled using the shallow water wave equations. In 1958 Carrier and Greenspan in their work "Water waves of finite amplitude on a sloping beach" used this system to model tsunami runup on a uniformly sloping plane beach. They linearized this problem using a hodograph type transformation and obtained the Klein-Gordon equation which could be explicitly solved by using the Fourier-Bessel transform. In 2011, Efim Pelinovsky and Ira Didenkulova in their work "Runup of Tsunami Waves in U-Shaped Bays" used a similar hodograph type transformation and linearized the tsunami problem for a sloping bay with parabolic cross-section. They solved the linear system by using the D'Alembert formula. This method was generalized to sloping bays with cross-sections parameterized by power functions. However, an explicit solution was obtained only for the case of a bay with a quadratic cross-section. In this paper we will show that the Klein-Gordon equation can be solved by a spectral method for any inclined bathymetry with power function for any positive power. The result can be used to estimate tsunami runup in such bays with minimal numerical computations. This fact is very important because in many cases our numerical model can be substituted for fullscale numerical models which are computationally expensive, and time consuming, and not feasible to investigate tsunami behavior in the Alaskan coastal zone, due to the low population density in this area
• #### Tua'll (and then) I used math to tell a story: Using think alouds to enhance agency and problem solving in an indigenous high school mathematics class

This paper examines action research in a high school math classroom with a focus on student discourse and agency. Students' use of language to explain their problem-solving processes was documented and analyzed. Specifically, the focus was on variations in student language and how the teacher responded to students during the problem-solving process. The following questions guided the analysis of what happened in the classroom: 1) How do my students talk about their math process? 2) How do I mediate their problem solving? One of the teacher researcher's earliest realizations was that she interfered in students' opportunities to problem solve on their own. Additionally, the students' explanations of their "problem-solving process" included more narration than justification or explanation of the process. On reflection, the teacher researcher decided to return to the research process to look further into these interactions while students were problem-solving. The second phase of research focused on student agency and how teachers can mediate for their students. Over a four-week period, the teacher researcher looked at the influences of multiple levels of assistance while each student was talking through his or her problem-solving process. Data sources include field notes, student artifacts, videos of student think aloud videos, and transcriptions of group work from the teacher researcher's classroom. The findings provide detailed insights into how these high school students approach math problems and how they describe and explain their problem-solving processes. The teacher researcher explores implications for teacher actions, insights into how students work together, and observations of students discussing their problem solving. Specifically, the teacher researcher noticed a need for language focus in mathematics instruction. In addition, teachers should problem solve with their students, rather than for their students; and allow students to mediate with each other to develop student agency.
• #### Tumitchiat: Iñuqqaat aullarrisiatun iḷisaġviit = A new pathway: indigenous leadership in higher education

After centuries of colonization and assimilation policies in education, Indigenous people across our world are making commitments to nurture the next generation of Indigenous leaders. One area of focus is on Indigenous leadership through various forms of Higher Education. This dissertation supports the need for Indigenous leadership programs that have a foundation in Indigenous ways of knowing and learning and suggests a definition of what Indigenous leadership embodies. Specific Indigenous leadership programs are described. Within the United States, tribal colleges are unique entities, but they share the same goals. These institutions create opportunities for hope and sustained Indigenous self-determination through their students, who are the next generation of Indigenous leaders. A broad review of tribal colleges is presented here. Then a particular tribal college, Iḷisaġvik College, located in Barrow, Alaska, is discussed in more detail. The research also illuminates circumstances at University of Hawai‘i (UH), a settler-colonial institution, that has recently decided to become a Native Hawaiian (NH) serving institution. How is this new responsibility viewed by UH’s Indigenous leaders? I conclude with an overview and syllabus for an Arctic Indigenous leadership program to be implemented at Iḷisaġvik College. The intent is to provide a path that others may use to create their own programs to meet their Indigenous communities’ needs.
• #### Tutor strategies in face-to-face and distance tutorial sessions: tutor and student perceptions

As university populations become increasingly dependent on distance learning and support services for distance learning, writing centers progressively offer services by telephone, email, or virtual worlds in addition to the traditional face-to-face tutorials. The University of Alaska Fairbanks (UAF) Writing Center offers a "telephone tutorial" service for students from remote locations who fax their papers to a tutor who then conducts a tutorial session over the telephone. This study investigates tutor strategies in face-to-face and telephone tutorial sessions and tutor and student perceptions of effectiveness. I audio recorded 30 tutorial sessions with five tutors in six sessions each, half in a face-to-face setting and half via telephone. After each tutorial session I conducted semi-structured interviews with the student and the tutor. Following data collection, I conducted a member check with each of the tutors and an in-depth interview with the UAF Writing Center Director. I then transcribed, coded and analyzed the data from the audiorecording. Results indicate that the use of affective strategies positively influenced both student and tutor evaluations of a session's effectiveness.

• #### Twin citizen: a memoir

Twin Citizen: A Memoir is a book-length work recounting the writer's life in the Minneapolis/St. Paul metropolitan area from 2004 to 2012. The primary plot motivator is the writer's inability to obtain and maintain stable housing; the work is divided chronologically into eight sections, one for each address he lived at, to reinforce the plot. Two secondary plots further guide the writing. First is a disability narrative depicting the writer's struggle for the accurate diagnosis and appropriate treatment of multiple psychological disorders, originating from an abusive childhood and the conflict between his evangelical Christian faith and gay sexual orientation. The second plot line involves the writer's job in customer service at a museum and the interrelationship between how his disabilities interfere with his job performance and how the high-stress work further exacerbates his symptoms. The memoir tackles the subject of intersectionality by illustrating how the writer both enjoys privilege as a white male American citizen and suffers lack of privilege as a gay lower-class disabled individual. This paradox serves as the basis for the work's fundamental themes of duality, deception, and misrepresentation. Furthermore, these themes help to challenge the cultural norms of Minnesota that allow for a liberal and progressive environment but hold at arm's length the marginalized communities that most benefit from progressive policies. Stylistically, the prose relies on fragmentation and experimentation, making much use of stream-of-consciousness and adopting poetic devices such as caesura and concrete poetry. This approach attempts to simulate for the reader the psychological state of the narrator.
• #### Two centuries of primary succession at Glacier Bay, Alaska: A test of a classic glacial retreat chronosequence

The classic account of primary succession inferred from a 220-year glacial retreat chronosequence at Glacier Bay, Alaska was tested against site-specific dendroecological reconstructions of successional development and against measured 37-year changes in soil nitrogen pools. Differences between young and old portions of the chronosequence in the invasion and radial trunk growth of Sitka spruce (Picea sitchensis) indicate that the nitrogen-fixing shrub Sitka alder (Alnus sinuata) has been an important and long-lived species only at sites deglaciated since 1840. Confirming this result, the soil nitrogen pool at sites deglaciated since 1840 has accumulated rapidly (2.3 to 3.6 g N m$\sp{-2}$ yr$\sp{-1}$) and is currently larger at some sites than at older sites where alder has not been important. A late-successional decrease in soil nitrogen inferred from the chronosequence did not occur at sites where soil nitrogen was measured in 1952 and again in 1989. Consequently, uncritical use of the entire Glacier Bay chronosequence to infer successional trends in community composition, nutrient dynamics, or soil development is unwarranted. Although the nitrogen and organic matter added by alder thickets have an apparent facilitative effect on the growth of individual spruce trees, alder thickets are associated with substantially reduced stand density of spruce. Thus, at the level of the population, a long-term, net facilitation of spruce by alder has not been demonstrated at Glacier Bay. Differences in texture and lithology of soil parent material cannot explain the differences in successional development between young and old portions of the Glacier Bay chronosequence. However, distance from each study site to the closest seed source of Sitka spruce at the time of deglaciation explains up to 58% of the among-site variance in early spruce recruitment. Multiple successional pathways have apparently resulted from changes in seed rain to newly deglaciated surfaces caused by (1) linear ice retreat exposing land surfaces more distant from refugial old growth forests, and (2) shifts in the species composition of the advancing front of successional vegetation and in its seed output.
• #### Two dimensional computational fluid dynamics model of pollutant transport in an open pit mine under Arctic inversion

A better understanding of the microscale meteorology of deep, open pit mines is important for mineral exploitation in arctic and subarctic regions. During strong temperature inversions in the atmospheric boundary layer--which are common in arctic regions during the winter--the concentrations of gaseous pollutants in open pit mines can reach dangerous levels. In this research, a two dimensional computational fluid dynamics (CFD) model was used to study the atmosphere of an open pit mine. The natural airflow patterns in an open pit mine are strongly dependent on the geometry of the mine. Generally, mechanical turbulence created by the mine topography results in a recirculatory region at the bottom of the mine that is detached from the freestream. The presence of a temperature inversion further inhibits natural ventilation in open pit mines, and the air can quickly become contaminated if a source of pollution is present. Several different exhaust fan configurations were modeled to see if the pollution problem could be mitigated. The two dimensional model suggests that mitigation is possible, but the large quantity of ventilating air required would most likely beimpractical in an industrial setting.
• #### Two old women: culturally relevant literature discussions in the 4th grade

Magnetic reconnection and the Kelvin-Helmholtz (KH) instability regulate the transport of magnetic flux, plasma, momentum and energy from the solar wind into the magnetosphere. In this thesis, I use two-dimensional and three-dimensional MHD simulations to investigate the KH instability, magnetic reconnection, and their relationship. Two basic flow and magnetic field configurations are distinguished at the Earth's magnetopause: (1) configurations where the difference in plasma velocity between the two sides of the boundary $\Delta$v (velocity shear) is parallel to the difference of the magnetic field $\Delta$b (magnetic shear), and (2) configurations where the velocity shear is perpendicular to the magnetic shear. For configuration (1), either magnetic reconnection is modified by the shear flow, or the KH instability is modified by the magnetic shear and resistivity. The evolution of the basic configuration (2) requires three dimensions. In this case, both processes can operate simultaneously in different planes. If the KH instability grows faster initially, it can wrap up the current layer and thereby initiate a very fast and turbulent reconnection process. The resulting magnetic turbulence can provide the first explanation of often very turbulent structures of the magnetopause current layer. For the first time, it is quantitatively confirmed that the KH instability operates at the magnetospheric boundary at low latitudes.
Central heating plants are often used on large building complexes such as university campuses or military bases. Utilidors can be used to contain heat distribution lines and other utilities between a utility station and serviced buildings. Traditional thermal analysis of utilidors is one-dimensional, with heat transfer correlations used to estimate the effects of convection, radiation, and two-dimensional geometric effects. The expanding capabilities of computers and numerical methods suggest that more detailed analysis and possibly more energy-efficient designs could be obtained. This work examines current methods of estimating the convection and radiation that occur across an air space in square and rectangular enclosures and compares them with numerical and experimental data. A numerical model was developed that solves the energy, momentum, and continuity equations for the primitive variables in two dimensions; radiation between free surfaces was also included. Physical experiments were conducted with two 10-ft-long apparatuses; one had a 1-ft $\times$ 1-ft cross section, the other was 2 ft $\times$ 4 ft. Several pipe sizes and configurations were studied with the 1-ft $\times$ 1-ft apparatus. The 2-ft $\times$ 4-ft apparatus was limited to containing 4- and 8-inch insulated pipes. Corresponding numerical studies were conducted. Difficulties in modeling large enclosures or those with large temperature differences (Rayleigh numbers above 10$\sp7$) were encountered. Results showed good agreement between numerical and experimental average heat transfer rates, and for insulated pipe cases these results also compared well with rates obtained from one-dimensional analysis. A new effective conductivity correlation for air in a square enclosure was developed, and its use was demonstrated in numerical conduction solutions and compared with full numerical convection and radiation solutions and with experimental data. Reasonably good results were achieved when there was a small temperature difference across the air gap.