Solution Manual Thermal Engineering R.k. Rajputl
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Upper and lower stationary or variational bounds are obtained for functions which satisfy parabolic linear differential equations. (The error in the bound, that is, the difference between the bound on the function and the function itself, is of second order in the error in the input function, and the error is of known sign.) The method is applicable to a range of functions associated with equalization processes, including heat conduction, mass diffusion, electric conduction, fluid friction, the slowing down of neutrons, and certain limiting forms of the random walk problem, under conditions which are not unduly restrictive: in heat conduction, for example, we do not allow the thermal coefficients or the boundary conditions to depend upon the temperature, but the thermal coefficients can be functions of space and time and the geometry is unrestricted. The variational bounds follow from a maximum principle obeyed by the solutions of these equations.
In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.
Effect of Amino acid doping on the Growth and Properties of Potassium Chloride Crystal PDFA.Gandhimathi, O.N.Balasundaram, A. Elakkina kumaranSemi-organic nonlinear optical crystal of Glycine Potassium Chloride (GPC) and L-Histidine Potassium Chloride (HPC) has been grown by slow evaporation solution growth technique. The grown crystals have been investigated through various techniques. The X-ray diffraction (XRD) studies confirm the crystalline nature and purity of the grown crystals. FTIR analyses were used to estimate qualitatively the presence of the functional groups in the grown crystal. UV-Visible spectrum shows that optical quality of the as grown crystals. The emission spectra of the crystals were recorded using spectrofluorometer. The emission peaks of GPC and HPC were absorbed at 452 nm and 530 nm respectively. The optical band gap energy was estimated as 2.7468 eV and 2.3425 eV. Thermo gravimetric and Differential Thermal Analysis (TGA-DTA) measurements indicate the thermal stability of the grown crystal. Scanning electron microscope (SEM) and energy dispersive X-ray analysis (EDAX) are presented and discussed. Nonlinear optical properties of GPC were 1.33 times that of KDP and HPC was not NLO active. 2b1af7f3a8