Approximate Analytical Solution of Magnetohydrodynamics Compressible Boundary Layer flow with Pressure Gradient and suction/injection

The aim of this work is to obtain exact analytical solution to the two dimensional laminar compressible boundary layer flow with an adverse pressure gradient in the presence of heat and mass transfer with MHD. The method applied is homotopy analysis method. It is shown that this solution agrees very well with numerical solution which is obtained by Runge-Kutta Merson method and results are shown graphically for different magnetic parameters

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

In this paper, Homotopy analysis method is applied to the nonlinear coupled differential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that more artificial degrees of freedom implies larger possibility to gain better approximations by HAM

Certain New Schläfli Type Mixed Modular Equations

Schläfli (J. Reine Angew. Math. 72, 360–369, 1870) has established modular equations involving kk′ and λλ′ for degrees 3, 5, 7, 9, 11, 13, 17, and 19. On pages 86 and 88 of his first notebook, Ramanujan recorded 11 Schläfli-type modular equations for composite degrees. In this paper, we establish several new Schläfli type mixed modular equations for composite degrees by elementary algebraic manipulations which are analogous to those recorded by Ramanujan

SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal

The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z \sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.Comment: 44 pages, 17 figures; comments and suggestions are welcom

VALIDATED SPECTROPHOTOMETRIC METHOD FOR THE DETERMINATION OF CHLORAMPHENICOL IN PURE AND IN ITS DOSAGE FORM

Objective: A simple, economic, selective, precise, and accurate UV-Visible spectrophotometric method for the analysis of Chloramphenicol in bulk drug and pharmaceutical formulations was developed and validated in the present study. Methods: Based on oxidative coupling reaction with MBTH reagent at PH-4.5 which is extractable at 620 nm. The Beer's law is obeyed in the concentration range 1-6 ml (10-60 µg ml-1). Results: The RSD was found to be 0.0194% and recovery is 99.73%. The method was completely validated and proven to be rugged. The interferences of the ingredients and recipients were not observed. The repeatability and the performance of the proved method were established by point and internal hypothesis and through recovery studies. Conclusion: The method was found to be accurate and precise, as indicated by recovery studies close to 100 and % RSD is not more than 2. The summery of validation parameters of proposed UV-Visible method is given

Direct numerical simulation of supersonic turbulent flows over rough surfaces

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers -, both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature-velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating

VALIDATED SPECTROPHOTOMETRIC METHOD FOR THE DETERMINATION OF CHLORAMPHENICOL IN PURE AND IN ITS DOSAGE FORM

A simple, précis, rapid sensitive and accurate spectrophotometric methods have been developed for the estimation of Chloramphenicol UV in pure form and its pharmaceutical formulations based on oxidative coupling reaction UV with MBTH reagent at P H-4 which is extractable at 620 nm. Beer's law is obeyed in the concentration range 1-6 ml (10-60 µgml-1). The developed method was applied directly and easily for the analysis of the pharmaceutical formulations. RSD was found to be 0.0194 % and recovery 99.73%. The method was completely validated and proven to be rugged. The interferences of the ingredients and excipients were not observed. The repeatability and the performance of the proved method were established by point and internal hypothesis and through recovery studies.Keywords: Spectrophotometry, Chloramphenicol, MBTH, Oxidative coupling