• Buoyancy Effects On Building Pressurization In Extreme Cold Climates

      Bargar, Harold Edward; Das, Debendra K.; Goering, Douglas J.; Johnson, Ronald A.; Lin, Chuen-Sen; Quang, Pham X. (2003)
      This research investigates building pressurization due to buoyancy effect. The American Society of Heating, Refrigeration, and Air Conditioning Engineers (ASHRAE) presents an idealized equation to calculate the buoyancy effect. This dissertation compares differential pressure measurements from an actual building exposed to extremely cold temperatures to this idealized model. It also presents new statistical models based on the collected data. These new models should provide engineers with improved tools to properly account for building pressurization for designs in extreme cold climates. Building pressurization, the differential pressure between the interior of a building and its exterior surroundings, is an important design consideration. Pressurization is the driving force in building infiltration/exfiltration. It also affects air flow within building zones. Improper calculation of pressurization can result in under-sizing the building's heating and cooling systems, improper operation of air distribution systems, improper operation of elevators, and freezing and failure of water distribution and circulation systems. Building pressurization is affected by: wind (speed and direction), exterior-to-interior temperature difference, and mechanical equipment operation. In extreme cold climates, the predominant effect is air buoyancy due to temperature differences across the building envelope. The larger the temperature difference, the larger the buoyancy effect. In extreme cold climates, the largest temperature differences often occur at times when wind speed is negligible. This dissertation also demonstrates the use of existing data sources such as building automation systems to collect data for basic research. Modern systems automation provides a tremendous amount of data that, in the past, had to be collected through separate instrumentation and data acquisition systems. Taking advantage of existing automation systems can provide the required data at greatly reduced costs when compared to previous industry practices. The statistical analysis approach taken in this research expands the tools for engineering design. Actual interactions of real world variables are analyzed and used to produce prediction models. These techniques allow the model to incorporate relationships which may not be fully understood at the underlying principle level but are evidenced in the data collected from actual installations.* *This dissertation includes a CD that is compound (contains both a paper copy and CD as part of the dissertation). The CD requires the following applications: Internet Browser; Adobe Acrobat; Microsoft Office; Image Viewer.
    • Climate, seasonal snow cover and permafrost temperatures in Alaska north of the Brooks Range

      Zhang, Tingjun; Osterkamp, T. E.; Bowling, S. A.; Goering, D.; Gosink, J.; Hopkins, D.; Wendler, G. (1993)
      Climatological data, active layer and permafrost measurements, and modeling were used to investigate the response of permafrost temperatures to changes in climate in Alaska north of the Brooks Range. Mean annual air temperature (MAAT) from 1987 to 1991 within about 110 km from the Arctic Coast was ${-12.4}\pm0.3\sp\circ C,$ while the mean annual permafrost surface temperature (MAPST) ranged from ${-9.0}\sp\circ C$ along the coast to ${-5.2}\sp\circ C$ inland. Air temperature changes alone can not explain the permafrost warming from the coast to inland. Measurements show that MAPST are about $3\sp\circ C$ to $6\sp\circ C$ warmer than MAAT in the region. The interaction of local microrelief and vegetation with snow appears to change the insulating effect of seasonal snow cover and may be the major factor which controls the permafrost temperature during the winter and thus the MAPST. Sensitivity analyses show that for the same MAAT conditions, changes in seasonal snow cover parameters can increase or decrease the MAPST about $7\sp\circ C.$ Snowfall was greater during the cold years and less during the warm years and was poorly correlated between stations. These results suggest that the effects of changes in air temperatures on permafrost temperatures historically may also have been modified by changes in snow cover. A numerical model was used to investigate the effect of changes in initial permafrost temperature conditions, MAAT, seasonal snow cover and thermal properties of soils on the permafrost temperatures. Permafrost may have started warming about the same time as the atmosphere did in the late 1800's, and the long term mean surface temperature of the permafrost may have been established prior to this time. Variations in the penetration depth of the warming signal may be related to differences in thermal properties of permafrost. Variations in the magnitude of the permafrost surface warming may be due to the effect of local factors such as soil type, vegetation, microrelief, soil moisture, and seasonal snow cover. The effect of the interaction of vegetation and snow cover may amplify the signal of temperature change in the permafrost.
    • Critical Parameters In Magmatic Degassing

      Mongrain, Joanna; Larsen, Jessica (2008)
      Decompression experiments conducted at pressures up to 200MPa and temperatures of 825�C-880�C on hydrated K-phonolite and rhyolite melts were used to explore the critical parameters controlling nucleation, exsolution and degassing behavior. Experiments on the low viscosity/surface tension K-Phonolite melt highlighted the role of melt properties. Although the sample porosities deviated below equilibrium values for pressures less than ~40MPa, the melt exsolved water in equilibrium over all the pressures and decompression rates studied. Melt shearing is proposed to have caused bubble deformation and alignment, lowering the porosity at which extensive permeability develops and significant degassing occurs compared to rhyolite. Experiments on a rhyolite melt decompressed slowly from 100 MPa and then held at 10 MPa for up to 900 s highlighted the critical parameters controlling the formation and stability of a highly vesicular magma: bubble number density, bubble size distribution and porosity. The porosity of the interconnected, highly vesicular network decreased during "Stage I" degassing and the bubble size distribution evolved from a unimodal population to include a population of much larger bubbles. During Stage II degassing, the network collapsed. Pre-collapse and collapse degassing rates were obtained and a coalescence-induced coalescence model proposed to explain the rapid destabilization. The ability of a melt to efficiently exsolve volatiles and the ease of bubble coalescence are both a function of the initial distribution of nucleated bubbles. The development of a new method for quantifying this distribution using spatial statistics will allow future researchers to explore the underlying controls on nucleation such as melt structure and the occurrence of a prior nucleation event. To investigate the critical parameters controlling shallow dike intrusion and therefore magmatic ascent rate, the fracture mechanics of intrusion into homogeneous and layered (weak sandstone/strong granite) particle models under lithostatic, compressive and extensional regimes were examined. Although the scale of the model intrusions were an order of magnitude greater than field observations, extensive microfracturing across the weaker layers, parallel dike jointing in the stronger layers and a length scale dependence to fracture toughness were observed suggesting that the use of a particle code is a promising approach to intrusion modeling.
    • Experimental Investigations Of Fluid Dynamic And Thermal Performance Of Nanofluids

      Kulkarni, Devdatta Prakash; Das, Debendra K. (2007)
      The goal of this research was to investigate the fluid dynamic and thermal performance of various nanofluids. Nanofluids are dispersions of metallic nanometer size particles (<100 nm) into the base fluids. The choice of base fluid is an ethylene or propylene glycol and water mixture in cold regions. Initially the rheological characterization of copper oxide (CuO) nanofluids in water and in propylene glycol was performed. Results revealed that higher concentrations of CuO nanoparticles (5 to 15%) in water exhibited time-independent pseudoplastic and shear-thinning behavior. Lower concentrations (1 to 6%) of CuO nanofluids in propylene glycol revealed that these nanofluids behaved as Newtonian fluids. Both nanofluids showed that viscosity decreased exponentially with increase in temperature. Subsequent correlations for viscosities as a function of volume concentration and temperature were developed. Effects of different thermophysical properties on the Prandtl number of CuO, silicon dioxide (SiO2) and aluminum oxide (A12O 3) nanofluids were investigated. Results showed that the Prandtl number increased with increasing volume concentrations, which in turn increased the heat transfer coefficients of the nanofluids. Various nanofluids were compared for their heat transfer rates based on the Mouromtseff number, which is a Figure of Merit for heat transfer fluids. From this analysis, the optimal concentrations of nanoparticles in base fluids were found for CuO-water nanofluids. Experiments were performed to investigate the convective heat transfer enhancement and pressure loss of CuO, SiO2 and A12O 3 nanofluids in the turbulent regime. The increases in heat transfer coefficient by nanofluids for various volume concentrations compared to the base fluid were determined. Pressure loss was observed to increase with nanoparticle volume concentration. It was observed that an increase in particle diameter increased the heat transfer coefficient. Calculations showed that application of nanofluids in heat exchangers in buildings could result in volumetric flow reduction, reduction in the mass flow rate and size, and pumping power savings. Experiments on a diesel electric generator with nanofluids showed a reduction of cogeneration efficiency due to the decrease in specific heat compared to the base fluids. However, it was found that the efficiency of the waste heat recovery heat exchanger increased for nanofluids.
    • Finite Element Modeling Of Photoplastic Process In The Cold Drawing Of Polycarbonate Bars

      Choi, Dong Ju; Lee, Jonah H. (2001)
      The numerical simulation of the mechanical behavior and the photoplasticity method of polycarbonate have been studied by simulating an existing photoplastic experiment of a cold drawing process. This study will allow understanding the mechanical and optical behavior of polymers and also assessing of the adequacy of existing numerical models and the photoplastic experimental method such that both can be validated and improved in the future. We proposed several optical-mechanical relationships for the photoplasticiy method and also adopted two existing viscoplastic models for polymers. Among the studied optical-mechanical relationships, the Non-Gaussian optical-mechanical relationship for photoplasticity of large deformation of polycarbonate is found to agree well with existing photoplastic calibration tests. Two types of viscoplastic numerical models adopted in this study are the physically based constitutive model and the phenomenological constitutive model with J2 flow theory. The model with the physically based constitutive model and a non-Gaussian optical-mechanical relationship for the photoplastic method could simulate the cold drawing experiment better than the phenomenological viscoplastic model. This study included a parametric study of the physically based constitutive model with the imperfection geometry and several material property variances to understand the mechanical and optical behavior of polycarbonate.
    • Fracture and shakedown of pavements under repeated traffic loads

      Zhang, Tinggang; Raad, Lutfi; Lee, Jonah H.; Hulsey, J. Leroy; Gislason, Gary A.; Covey, David (1998)
      Under repeated external loads, engineering structures or objects may fail by large plastic deformation or fatigue. Shakedown will occur when the accumulation of plastic deformation ceases under repeated loads; the response of the system is then purely elastic. Fatigue and shakedown have been individually studied for decades and no attempt has been made to couple these two mechanisms in the mechanics analysis. In this study, an attempt is made to couple shakedown and fatigue in pavement mechanics analysis using numerical simulation. The study covers three main areas: fatigue, static shakedown, and kinematic shakedown analysis. A numerical approach to fatigue analysis is proposed based on elastic-plastic fracture mechanics. The amount of the crack growth during each load cycle is determined by using the J-integral curve and $\rm R\sb{-}curve.$ Crack propagation is simulated by shifting the $\rm R\sb{-}curve$ along the crack growth direction. Fatigue life is predicted based on numerically estabiished fatigue equation. The numerical results indicate that the algorithm can be applied to fatigue analyses of different materials. A numerical algorithm based on the finite element method coupled with the nonlinear programming is proposed in static shakedown analysis. In this algorithm, both the inequality and equality constraints are included in the pseudo-objective function. These constraints are normalized by the material yield stress and the reference load, respectively. A multidirectional search algorithm is used in the optimization process. The influence of finite element mesh on shakedown loads is investigated. An algorithm that utilizes eigen-mode to construct the arbitrary admissible plastic deformation path is proposed in kinematic shakedown analysis. This algorithm converts the shakedown theorem into a convex optimization problem and can be solved by using a multidirectional search algorithm. Fatigue behavior of a two-layer full-depth pavement system of asphalt concrete is analyzed using the proposed numerical algorithm. Fatigue crack growth rate is estimated and fatigue life is predicted for the system. Shakedown analyses are also carried out for the same pavement system. The comparison between the shakedown load and the fatigue failure load with respect to the same crack length indicates that the shakedown dominates the response of the pavement system under traffic load.
    • Massive ice interactions with offshore structures

      Lu, Mingchi (1992)
      The interaction between a multiyear sea ice floe of variable thickness, and an offshore structure, has been examined using a 3-dimensional finite element method. Elastic response within the ice floe was assumed initially, and a uniform loading of the ice floe by the adjacent pack ice was used. As an example of the results for a frozen boundary condition at the ice/structure contact zone, with a central region of the ice floe having its thickness reduced to 50% as compared to the floe thickness at the structure ($\Delta$t/t = 0.5), tensile cracks first form at the top surface in the thinnest area of the floe. The total force on the structure was 108 MN, as compared with 1500 MN which would be present in the case of an ice floe of uniform thickness. Parameters varied were ice/structure contact zone (located in the centric or the eccentric region), the sliding boundary condition, two-dimensional ice thickness variation, variable ice elastic modulus as a function of depth, and viscoelastic ice behavior. Cases of rigid and of compliant structure and foundation were included. In a second part of the study, the ice island loads acting upon a cylindrical rigid structure were analyzed by this 3-dimensional finite element method. A force of 6600 MN was computed to be acting on the structure with a maximum penetration distance of 8.2 m. A different theoretical method based upon multiyear ice field data resulted in a force of 336 MN and a maximum penetration distance of 75 m. The ice forces on the structure are reduced by ice floe thickness variations, and also are affected by the geometries at the ice floe/structure and ice floe/pack ice boundaries. The reduced elastic modulus in the warmer. lower part of an ice sheet promotes ice bending failure and causes lower structure loads.
    • Modeling Of A Novel Triple Turbine Solid Oxide Fuel Cell Gas Turbine Hybrid Engine With A 5:1 Turndown Ratio

      Burbank, Winston Starr, Jr.; Witmer, Dennis E. (2009)
      Electrical production using solid oxide fuel cell gas turbine (SOFC-GT) hybrid systems has received much attention due to high-predicted efficiencies, low pollution and the availability of natural gas. Solid oxide fuel cell (SOFC) systems and hybrid variants designed to date have had narrow operating ranges due largely to the lack of control variables available to control the thermal requirements within the SOFC. Due to the higher value of peak power, a system able to meet fluctuating power demands while retaining high efficiencies is strongly preferable to only base load operation. This thesis presents results of a novel SOFC-GT hybrid configuration designed to operate over a 5:1 turndown ratio. The proposed system utilizes two control variables that allow the hybrid to maintain the SOFC stack exit temperature at a constant 1000�C throughout the turndown. The first control variable is the setting of a variable-geometry inlet nozzle turbine, which most directly influences the system airflow. The second control variable is an auxiliary combustor, which allows control of the thermal and power needs of the turbomachinery independently from that of the SOFC. At low turndown the proposed hybrid operates similarly to previous hybrids, in that roughly 80% of the power is delivered from the SOFC. However, the newly proposed hybrid uses the unique turbomachinery to drastically increase the delivered power at higher power demands. A unique aspect of the proposed hybrid is the contribution of half the rated power being supplied by the inexpensive turbomachinery with the expensive SOFC contributing the other half. This will significantly lower system capital costs compared to previous hybrid designs. The proposed hybrid has high efficiencies throughout turndown with peak efficiencies occurring at low turndown levels.
    • Nanotribological Characterization Of Dynamic Surfaces

      Ingole, Sudeep Prabhakar; Liang, Hong (2005)
      This dissertation research includes three fundamental areas: utilizing an atomic force microscope (AFM) to study the nanomechanical and tribological properties, to understand friction and wear at nanometer length, and to study wear mechanisms of boride coatings for biological applications. This was the first time that an AFM was used to study the nanomechanical and tribological properties and the performance of the materials. The AFM enables detailed investigation of the wear modes at multi-length scales as well as the surface mechanical properties. Surface analysis using an AFM included the surface texture, profile of indents, wear tracks, and wear scars. The friction force microscope (FFM) revealed the relationship between surface texture and frictional properties, thus contributing to the fundamental understanding of nanotribology. A new wear model was proposed. Also, hardening was discovered under the indents. The multi-scale wear study was focused on fundamental wear mechanisms. New wear modes, different than the traditional ones, were proposed. In this research, nanocracks and other damage (hardening and plastic flow) were found at different scales. Boride coatings on refractory metals were investigated for biological applications. Tribological performance of these coatings was studied in dry and wet (biofluid) conditions. It was found that boron plays an important role in forming amorphous and crystalline wear debris.
    • Numerical Simulation Of Single Phase And Boiling Microjet Impingement

      Ragunathan, Srivathsan (2008)
      This work presents results from the numerical simulation of single phase and boiling microjets primarily for high density electronics cooling. For the single phase microjets, numerical simulation results for the flow fields and heat transfer characteristics in a laminar, confined microjet (76 mum in diameter) impingement arrangement are presented. The parameters varied included the jet Reynolds Number, the fluid Prandtl Number and the ratio of the nozzle-to-plate distance to the jet diameter. Primary and secondary recirculation zones were observed in the stagnation region and the radial outflow region which had a significant impact on the local Nusselt Number distribution on the heated surface. The location and the displacement of the primary and secondary recirculation zones are of particular importance and are associated with secondary peaks in the Nusselt Number similar to those observed for turbulent jet impingement in larger conventional jets. Numerical simulation results are presented for boiling microjet impingement in a confined arrangement. The Rensselaer Polytechnic Institute (RPI) model was modified for laminar flow boiling for simulating these types of flows. The model primarily proposes three different heat transfer components, the single phase heat transfer, the quenching heat transfer and the evaporative heat transfer. The model was first validated with experimental results from the literature and then extended to study the effects of liquid subcooling, microjet Reynolds Number based on the nozzle inlet, and heat flux levels. The simulation results were in good agreement with results from comparable experiments in the literature. The average wall temperature increases as the applied wall heat flux is increased. The slopes of the temperature curves in the radial direction flatten out at higher heat fluxes and lower levels of subcooling indicating the effectiveness of boiling heat transfer. For the cases considered in this study, the single phase heat transfer component dominates the other two modes of heat transfer The liquid velocity profile has a considerable impact on the vapor bubble nucleation, vapor drag and the bubble departure diameter. Lower levels of subcooling are associated with boiling inception and more vigorous boiling in the vicinity of the stagnation zone rather than those with higher levels of subcooling. The degree of subcooling emerged as the single largest factor controlling the lateral temperature rise in an electronic chip cooled by a single, confined impinging microjet. Increases in the jet inlet Reynolds Number for the same heat flux and subcooling levels increased the dominance of forced convection heat transfer over the boiling heat transfer. Lower Reynolds Number flows are marked by partial nucleate boiling in contrast to higher Reynolds Number flows marked by forced convection boiling. For all the cases considered in this work, the single phase heat transfer component dominated the other two modes of heat transfer. The evaporative mode dominates the quenching heat transfer mode, an observation that is markedly different from those observed for turbulent evaporative jets found in the literature.
    • Pitorifices and small pumps in cold region water distribution systems

      Mauser, Michael William; Zarling, John; Carlson, Robert; Kane, Douglas; Goering, Douglas (1995)
      Most buried potable water distribution systems in colder regions of Alaska rely on pitorifices to provide circulation between the water main and service connections for freeze protection. Pitorifices are scoops which project into the main. When water is circulated in the main, they create a differential head which induces flow through dual service lines. Pitorifices have provided an inexpensive and simple alternative to installing a small pump at each service to provide circulation. However, very little information was available on the hydraulic performance of these devices. The objectives of this study were to: (i) develop techniques to measure pitorifice performance in the field; (ii) characterize performance of commonly used pitorifice shapes with different insertion depths and relative sizes in full-scale testing; (iii) develop an improved shape; (iv) research the competing technology of small pumps; and (v) present the information in a way that is useful to engineers. An inexpensive device for field checks of both differential head and flow rates at service lines was developed and the use of a low head loss meter was initiated. Methods and results of field studies in four different water systems are presented. Five commonly used pitorifice shapes and four new shapes were evaluated. The best shape was found to be one of the existing shapes, which is also one of the easiest to produce but not the most popular. It was also determined using a larger service line size can be cost effective. Test results are graphed and a theoretical framework is provided for designers. Smaller, energy efficient pumps may provide a cost effective alternative to pitorifices in some situations. Requirements for small pumps used for circulation in place of or to supplement pitorifices are given. Performance test results for different pumps are presented, most of which have not been used previously for service line circulation. Pumps with significantly lower operating costs than those in current use are identified. Several of these pumps were installed in services for long term testing.
    • Size Effects In Mesoscale Mechanical Testing Of Snow

      Huang, Daisy; Lee, Jonah; Newman, David; Peterson, Rorik; Truffer, Martin (2013)
      Snow is a naturally-occurring, heterogeneous material whose interactions with humans make it desirable for analysis as a geotechnical engineering material. In this study, clean, undisturbed, natural snows of two common types were collected in and around Fairbanks, Alaska and subjected to laboratory testing, and the results were compiled and analyzed. Three types of tests--flat pin indentation, unconfined compression, and cone penetration--were carried out while varying size parameters, and size effects were observed and studied. From flat-pin indentation testing, it was observed that first peak indentation strength initially fell exponentially with increasing indenter cross-sectional area, with the exponent averaging 0.84. Furthermore, the strength eventually rose to a plateau value, and the compression strength of snow could be calculated from this plateau value. This plateau, too, initially depended exponentially on the pin cross-sectional area for smaller pins. From unconfined compression testing, it was observed that as cross-sectional area of a flat pin indenter increased, plateau strength eventually reached that value found from unconfined compression testing. Furthermore, initial strength, plateau strength, and energy absorption density all increased linearly with increasing aspect ratio. From cone penetration testing, it was found that empirical values of snow strength may be obtained on both a micromechanical and macromechanical scale using cone penetration. Size effects, were also observed--smaller cone diameters and larger cone included angles yielded larger values for apparent snow strength. Some of the mechanisms behind all of these size effects are explainable from theory; others must be regarded for now as empirical in nature. In both cases, the results are quite reliable descriptors for a natural material, and may be safely interpolated from.
    • The mechanics of diamond core drilling of rocks

      Wang, Zhengwen W. (1995)
      In an attempt to study the mechanics of diamond core drilling in rocks, an investigation on rock drillability was conducted at the University of Alaska Fairbanks. A series of drilling and coring tests was conducted on six types of rock using several different diamond bits. Factors involved in a diamond coring and drilling process such as weight-on-bit, rotational speed, and rock type were identified and the effects of those parameters were experimentally evaluated based on the penetration rate, applied torque, and specific energy. Statistical techniques were used to design the drilling tests and to develop drilling models. Fundamentals of rock failure mechanics in relation to rock drilling were reviewed. Several existing rock drilling models were also examined with the data from this study. Results indicated that all of the three drilling parameters, i.e., the penetration rate, applied torque, and specific energy, were significantly affected by the weight-on-bit and rock type. The penetration rate of a bit was also affected by the rotational speed. The effects of the rotational speed on the applied torque and specific energy, however, were found to be insignificant. It was also found that the theoretical models can be used to predict the maximum effective weight-on-bit and penetration rate. Among the four theoretical models examined, the elastic model predicted the most accurate penetration rate. The maximum effective weights-on-bit predicted by the plastic model and the two fracture models, however, were close to each other and in agreement with the experimental observation. Statistical models developed in this study were used to predict the penetration rate in the Rock Drilling under the Greenland Ice Sheet project. The variation between the predicted value and the actual value was less than 10%.
    • Theoretical And Experimental Analysis Of Two-Phase Closed Thermosyphons

      Xu, Jianfeng; Goering, Douglas J. (2008)
      This work presents an analytical and numerical model of a long inclined two-phase closed thermosyphon, known as a hairpin thermosyphon, which is representative of a new configuration for thermosyphons used in arctic applications. A laboratory experiment and a full scale road experiment along with associated modeling are described in detail. The laboratory experiment studies the condensation heat transfer performance of carbon dioxide inside the thermosyphon condenser under conditions of limited heat flux. The operating condition is not far from the critical point for carbon dioxide, which has a significant impact on the condensation heat transfer. An experimental correlation is developed to predict the carbon dioxide condensation heat transfer performance under these specific conditions. The full scale road experiment studies the overall performance of hairpin thermosyphons under actual field conditions. The model is a quasi one-dimensional formulation based on two-dimensional two-phase flow simulations at each cross section. The proposed model is useful for predicting steady state system operating characteristics such as pressure, temperature, liquid film thickness, mass flow rate, heat flow rate, etc., at local positions as well as over the entire system. The comparison of the modeling predictions with both laboratory and field experiments showed a strong correlation between modeling predictions and experimental results.
    • Two-dimensional analysis of natural convection and radiation in utilidors

      Richmond, Paul W., Iii; Zarling, John; Das, Debendra; Gislason, Gary; Kinney, Thomas (1997)
      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.