Analysis of heat conduction in bridge slab

Summary An analytical procedure is presented for the heat transfer in a bridge slab of finite dimensions and arbitrary initial temperature distribution. The thermal conductivity and surface conductance may be different on the top and bottom surfaces of the slab. The ambient temperature and heat input into the slab may vary both spacewise and timewise.Two solutions, one more rapidly convergent for long times and the other for short times, are given.

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Analyse der Wärmeleitung in einer Brückendecke

Zusammenfassung Es wird ein analytisches Verfahren zur Bestimmung des Wärmeflusses in einer Brückendecke endlicher Abmessungen und bei beliebiger Verteilung der Anfangstemperatur angegeben. Die Wärmeleitfähigkeit und die Wärmeübergangszahlen können auf beiden Seiten der Decke verschiedene Werte haben. Die Umgebungstemperatur und die in die Decke einströmende Wärme können räumlich und zeitlich veränderlich sein.Es werden zwei Lösungen angegeben; die eine zeigt bessere Konvergenz für lange, die andere für kurze Zeiten.

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Nomenclature a,b length and width of slab - B defined by Equation (57) - D defined by Equation (19) - c specific heat - erfc complementary error function - F ₁,F ₂ defined by Equations (34) and (35) - f ₁,f ₂...f ₈ defined by Equation (38) - f,g defined by Equation (45) - H,H ₀,H ₁ surface conductance - h thickness of slab - ,i _p roots of Equation (17) - K,K ₀,K ₁ thermal conductivity - m,n,p,q integers - Q defined by Equation 1 (a) - R defined after Equation (29) - S defined after Equation (22) - S ₁,S ₂ defined by Equation (33) - s Laplace transform parameter - T,T ₀,T ₁,T ₁ ^*,T ₂ temperature - t time - U(h),V(h) defined by Equation (57) - x,y,z rectangular cartesian coordinates - Z ₁ defined by Equation (20) - Z ₂ defined by Equation (22) - Z ₃ defined by Equation (56) - defined by Equation (14) - , =K/c thermal diffusivity - defined by Equation (21) - mass density With 1 FigureThis work was carried out under Contract HR-12-4 between the National Academy of Sciences and Southwest Research Institute as part of the National Cooperative Highway Research Program. Publication of this article does not necessarily indicate acceptance by the Academy or by the Bureau of Public Roads or by any State Highway Department of the findings or conclusions either implied or specifically expressed herein.The author is indebted to Dr.Wen-Hwa Chu for valuable suggestions.     

Toughening and phase separation behavior of nylon 6–PEG block copolymers and in situ nylon 6–PEG blend via in situ anionic polymerization

We have prepared in situ molded products of morphologically different nylon 6/polyethylene glycol (PEG) copolymers and their blends via anionic polymerization of ε-caprolactam in the presence of several kinds of PEG derivatives using sodium caprolactamate as a catalyst and carbamoyl caprolactam derivative as an initiator. Three carbamoyl caprolactams, such as tolylene dicarbamoyl dicaprolactam (TDC), hexamethylene dicarbamoyl dicaprolactam (HDC), and cyclohexyl carbamoyl caprolactam (CCC), with different functionalities and activities were used. Phase separation behavior was investigated by dynamic mechanical thermal analysis (DMTA) and DSC during in situ polymerization and melt crystallization. The mechanical properties of these molded products were evaluated. PEG segments in the block copolymers showed amorphous characteristics, whereas a large fraction of unreacted PEG segments was crystallized in as-polymerized samples, except for the products obtained using the CCC activator. The presence of PEG derivatives retarded the crystallization of nylon 6 part during in situ polymerization as well as melt crystallization. However, PEG segments did not alter the crystalline structure of nylon 6, showing α-crystalline modification. The nylon 6–PEG–nylon 6 triblock copolymers showed the highest impact strength, whereas the nylon 6–PEG diblock copolymers and in situ nylon 6–PEG blends showed no improved toughness. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1285–1303, 1999     

Cocrystallization and miscibility studies of blends of ultrahigh molecular weight polyethylene with conventional polyethylenes

Ultrahigh molecular weight polyethylene (UHMWPE) was mechanically mixed with conventional polyethylenes (LLDPE, HDPE, and LLDPE) using an internal mixer. Rheological studies of these blends suggest that UHMWPE seems to be miscible with LLDPE, HDPE, and LDPE in the melt state. Yield characteristics are observed in all blend systems, particularly in high UHMWPE blend compositions. Differential scanning calorimetry and small-angle light scattering studies show that cocrystallization takes place in the blends of UHMWPE/LLDPE and UHMWPE/HDPE blends. However, separate crystals are formed in UHMWPE/LDPE. The formation of separate crystals may be attributed to long chain branching of conventional low-density polyethylene. Tensile properties of the former two blends vary almost linearly with blend compositions, while deviations are seen in the latter UHMWPE/LDPE blends.     

Nonoperative treatment for patellofemoral pain

Patellofemoral pain, often called patellofemoral stress syndrome or patellofemoral joint dysfunction, is a commonly seen knee pain syndrome in patients of all ages. It is often a frustrating problem for both the patient and the clinician, as the source of pain can be elusive, making treatment choices difficult. Strategies have been proposed based upon potential sources of pain, including both operative techniques as well as conservative management. Current nonoperative treatment strategies and techniques in the treatment of patellofemoral pain are reviewed. Recommendations and criteria for progression of rehabilitation and suggestions for future research regarding patellofemoral pain are suggested.     

Vibration of quadrilateral plates

A novel method for the solution of vibration problems of quadrilateral plates is proposed. With this method, the boundary conditions at the four edges and the differential equation are exactly satisfied. The frequency of vibration is found by satisfying the continuity conditions along a diagonal. The method also yields the mode shape of vibration of the plate under any of the classical boundary conditions and has been implemented on a digital computer.     

Modeling particle inflation from poly(amic acid) powdered precursors. I. Preliminary stages leading to bubble growth

Morphological characteristics of polyimide microstructures obtained by solid‐state powder foaming determine the geometric properties of the unit cell, in polyimide foams prepared by this process. Morphological analysis of precursor particles has shown that particle size and shape, as well as the presence of embedded microvoids, exert a strong influence on the final microstructure morphology. Of equal importance in the morphological development are processing conditions such as heating rate and primary blowing agent content in the particles, prior to thermal treatment. In the present paper, the first of two numerical schemes is presented. A numerical model has been developed to study the preliminary stages that lead to particle inflation. Based on this model, a parametric analysis is performed for pertinent governing parameters, with the purpose of determining their effect on the onset of particle inflation and the potential morphological characteristics of polyimide microstructures. It has been found that precursor particle morphology and nuclei density are the key parameters in determining the potential morphology of the microstructures, by limiting the number of bubbles that grow within each particle. POLYM. ENG. SCI., 47:560–571, 2007. © 2007 Society of Plastics Engineers.     

Modeling particle inflation from poly(amic acid) powdered precursors. II. Morphological development during bubble growth

The morphological development of cellular polyimide microstructures from poly(amic acid) powders has been shown to depend on the processing conditions throughout the inflation process and the morphological characteristics of the precursor particles. In an earlier publication the authors presented a numerical study of the preliminary stages prior to particle inflation when the processing temperature is below the glass transition temperature, T_g. In the present article, a second numerical scheme is presented for behavior above T_g in which bubble growth is modeled to account for the effect of multiple phenomena in the final stages of morphological development. The bubble growth kinematics and subsequent cessation of growth are predicted as a function of process parameters and material properties. Morphological characteristics of the precursor particles have also been shown to influence the kinematics of inflation. These results provide a clearer understanding of the solid‐state foaming processes for polyimide cellular materials. POLYM. ENG. SCI., 47:572–581, 2007. © 2007 Society of Plastics Engineers.