An Analytical Solution for the Laminar Forced Convection in a Pipe with Temperature-Dependent Heat Generation

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An Analytical Solution for the Laminar Forced Convection in a Pipe with Temperature-Dependent Heat Generation

An analytical solution is presented for the case of laminar forced convection in a pipe with heat generation linearly dependent on the local temperature of the fluid. The flow is fully developed and the boundary conditions of the third kind. Within the general analysis presented, some particular cases are identified and discussed. A detailed analysis of the thermal entrance is given. It is shown that in the fully developed region the temperature distribution does not depend on the axial coordinate. An analytical expression of the fully developed Nusselt number is given. Finally, the practical significance of the problem is discussed

An Analytical Solution for the Laminar Forced Convection in a Pipe with Temperature-Dependent Heat Generation

An analytical solution is presented for the case of laminar forced convection in a pipe with heat generation linearly dependent on the local temperature of the fluid. The flow is fully developed and the boundary conditions of the third kind. Within the general analysis presented, some particular cases are identified and discussed. A detailed analysis of the thermal entrance is given. It is shown that in the fully developed region the temperature distribution does not depend on the axial coordinate. An analytical expression of the fully developed Nusselt number is given. Finally, the practical significance of the problem is discussed

Contributions of phonological and verbal working memory to language development in adolescents with fragile X syndrome

Fragile X syndrome (FXS) is the most common inherited cause of intellectual disability. Although language delays are frequently observed in FXS, neither the longitudinal course of language development nor its cognitive predictors are well understood. The present study investigated whether phonological and working memory skills are predictive of growth in vocabulary and syntax in individuals with FXS during adolescence. Forty-four individuals with FXS (mean age = 12.61 years) completed assessments of phonological memory (nonword repetition and forward digit recall), verbal working memory (backward digit recall), vocabulary, syntax, and nonverbal cognition. Vocabulary and syntax skills were reassessed at a 2-year follow-up. In a series of analyses that controlled for nonverbal cognitive ability and severity of autism symptoms, the relative contributions of phonological and working memory to language change over time were investigated. These relationships were examined separately for boys and girls. In boys with FXS, phonological memory significantly predicted gains in vocabulary and syntax skills. Further, verbal working memory was uniquely associated with vocabulary gains among boys. In girls with FXS, phonological and working memory skills showed no relationship with language change across the 2-year time period. Our findings indicate that, for adolescent boys with FXS, acquisition of vocabulary and syntax may be constrained by the ability to maintain and manipulate phonological representations online. Implications for the identification and treatment of language disorders in this population are discussed. The present study is the first to identify specific cognitive mechanisms contributing to language growth over time in individuals with FXS

Laminar natural convection in a square cavity: Low Prandtl numbers and large density differences

Steady natural convection at low Prandtl numbers caused by large density differences in a square cavity heated through the side walls is investigated numerically and theoretically. An appropriate dimensionless parameter characterizing the density differences of the working fluid is identified by the Gay-Lussac number. The Boussinesq assumption is achieved when the Gay- Lussac number tends to zero. The Nusselt number is derived for the ranges in Rayleigh number 10 6 Ra 6 108, in Prandtl number 0.0071 6 Pr 6 7.1 and in Gay-Lussac number 0 6 Ga < 2. The effects of the Rayleigh, Prandtl and Gay-Lussac numbers on the Nusselt number are discussed on physical grounds by means of a scale analysis. Finally, based on physical arguments, a heat transfer correlation is proposed, valid for all Prandtl and Gay-Lussac number ranges addressed

THERMO-FLUID ANALYSIS OF A CYLINDRICAL COLLINEAR OHMIC STERILIZER IN LAMINAR FLOW

The present work deals with a thermo-fluid analysis of a collinear cylindrical ohmic heater in laminar flow. The geometry of interest is a circular electrical insulated glass pipe with two electrodes at the pipe ends. For this application, since the electrical conductivity of a liquid food strongly depends on the temperature, the thermal analysis of an ohmic heater requires the simultaneous solution of the electric and thermal fields In the present work the analysis of the above fields has been decoupled by means of an iterative procedure. The thermal field has been calculated by means of an analytical solution, which leads to fast calculations for the temperature distribution in the heater. Some considerations of practical interest for the design are finally given

CFD wall functions strategies for natural convective: turbulent flows: some literature remarks

The reliability for turbulent natural convection flows of some wall functions treatments proposed in the literature is discussed. Velocity and temperature wall functions are compared and discussed against experimental data provided in the literature for natural convection. The often used assumption of local equilibrium in the near wall region is examined on the basis of DNS data provided in the literature. Finally some considerations of practical interest on the choice of appropriate wall functions for natural convection are given