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a b s t r a c tNonlinear problems arise in many heat transfer applications, and several analytical and numerical methods for solving these problems are described in the literature. Here, the method of variation of parameters is shown to be a relatively simple method for obtaining solutions to four specific heat transfer problems: 1. a radiating annular fin, 2. conduction-radiation in a plane-parallel medium, 3. convective and radiative exchange between the surface of a continuously moving strip and its surroundings, and 4. convection from a fin with temperature-dependent thermal conductivity and variable cross-sectional area. The results for each of these examples are compared to those obtained using other analytical and numerical methods. The accuracy of the method is limited only by the accuracy with which the numerical integration is performed. The method of variation of parameters is less complex and relatively easy to implement compared to other analytical methods and some numerical methods. It is slightly more computationally expensive than traditional numerical approaches. The method presented may be used to verify numerical solutions to nonlinear heat transfer problems.

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This study used in-depth interviews with Black and African American couples in happy, long-term marriages to capture advice that can serve to convey the hurdles and expectations of marriage in the African American community. Background: The U.S. Census Bureau reports that only 29% of African Americans are married. However, the majority of African Americans still desire marriage themselves. Therefore, the advice and experiences of enduring African American couples could be beneficial to those younger couples hoping to one day marry. Method: Interviews and a semistructured interview protocol were used to gather data on marital experiences and counsel from 35 happily married African American couples. Data were analyzed using qualitative methods consistent with Marks (2015) Numeric Content Analysis. Results: Three emergent themes related to forming and strengthening African American marriages are discussed: (a) Communication Keeps Small Issues From Becoming Big Barriers; (b) Share Roles, Share Responsibilities; and (c) Manage Your Money to Manage Your Marriage.

This work presents in situ measurements of the effective thermal conductivity in particulate coal ash deposits under both reducing and oxidizing environments. Laboratory experiments generated deposits on an instrumented deposition probe of loosely bound particulate ash from three coals generated in a down-fired flow reactor with optical access. An approach is presented for making in situ measurements of the temperature difference across the ash deposits, the thickness of the deposits, and the total heat transfer rate through the ash deposits. Using this approach, the effective thermal conductivity was determined for coal ash deposits formed under oxidizing and reducing conditions. Three coals were tested under oxidizing conditions: two bituminous coals derived from the Illinois #6 basin and a subbituminous Powder River Basin coal. The subbituminous coal exhibited the lowest range of effective thermal conductivities (0.05–0.18 W/m K) while the Illinois #6 coals showed higher effective thermal conductivities (0.2–0.5 W/m K). One of the bituminous coals and the subbituminous coal were also tested under reducing conditions. A comparison of the ash deposits from these two coals showed no discernible difference in the effective thermal conductivity based on stoichiometry. All experiments indicated an increase in effective thermal conductivity with deposit thickness, probably associated with deposit sintering.