Amit Dhiman

Effects of Reynolds and Prandtl Numbers on Heat Transfer Across a Square Cylinder in the Steady Flow Regime

ABSTRACT The effects of Reynolds and Prandtl numbers on the heat transfer characteristics of an isolated square cylinder have been investigated for the range of conditions 1 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 4,000 (the maximum value of Peclet number being 4,000) in crossflow. Heat transfer correlations are obtained for the constant cylinder temperature and constant heat flux boundary conditions on a solid square cylinder in the steady flow regime. In addition, the variation of local Nusselt number on each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the steady flow regime.

Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1-30, power-law index: 0.8-1.5, Prandtl number 0.7-100 (Pe ≤ 3000) for Richardson number 0-0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening (n > 1) and shear-thinning (n < 1) fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter (Ri ≤ 0.5) for a fixed Reynolds number in the steady cross-flow regime (Re ≤ 30).

Heat Transfer to Power-Law Fluids from a Heated Square Cylinder

Forced-convection heat transfer to power-law fluids from a heated square cylinder has been investigated numerically for the range of conditions 1 ≤ Re ≤ 45, 0.5 ≤ n ≤ 2.0 and 1 ≤ Pr ≤ 100 (the maximum Peclet number being 4,000). In this range of Reynolds number, the flow is known to be steady and two-dimensional. The variation of the local Nusselt number on the individual surfaces of the square cylinder and the representative isotherm plots, for both the constant-temperature and uniform-heat-flux boundary conditions prescribed on the surface of the square obstacle, are presented to elucidate the role of Reynolds number, Prandtl number, and power-law index on the heat transfer characteristics. Using the present numerical data, appropriate predictive correlations are obtained for estimating the value of the mean heat transfer coefficient in a new application.

Artificial intelligence based modeling and optimization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) production process by using Azohydromonas lata MTCC 2311 from cane molasses supplemented with volatile fatty acids: A genetic algorithm paradigm

The present work describes the optimization of medium variables for the production of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) [P(3HB-co-3HV)] by Azohydromonas lata MTCC 2311 using cane molasses supplemented with propionic acid. Genetic algorithm (GA) has been used for the optimization of P(3HB-co-3HV) production through the simulation of artificial neural network (ANN) and response surface methodology (RSM). The predictions by ANN are better than those of RSM and in good agreement with experimental findings. The highest P(3HB-co-3HV) concentration and 3HV content have been reported as 7.35 g/l and 16.84 mol%, respectively by hybrid ANN-GA. Upon validation, 7.20 g/l and 16.30 mol% of P(3HB-co-3HV) concentration and 3HV content have been found in the shake flask, whereas 6.70 g/l and 16.35 mol%, have been observed in a 3 l bioreactor, respectively. The specific growth rate and P(3HB-co-3HV) accumulation rate of 0.29 per h and 0.16 g/lh determined with cane molasses are comparable to those observed on pure substrates.

Wall effects on the cross-buoyancy around a square cylinder in the steady regime

The effects of blockage ratio on the combined free and forced convection from a long heated square obstacle confined in a horizontal channel are investigated in this work. The numerical computations are performed in the steady regime for Reynolds number = 1 - 30, Richardson number = 0 - 1 for blockage ratios of 0.125 and 0.25 for the fixed Prandtl number of 0.7 (air). The governing equations, along with appropriate boundary conditions, are solved by using a semi-explicit finite volume method implemented on the collocated grid arrangement. The total drag and lift coefficients, local and average Nusselt numbers and the representative streamline, vorticity and isotherm patterns are presented to elucidate the role of blockage ratio on the cross-buoyancy across a confined square cylinder. The asymmetry in the flow and temperature fields decreases with increasing value of the blockage ratio. Similar to forced convection, the total drag coefficient increases with increasing value of the blockage ratio for the fixed values of the Reynolds and Richardson numbers.

Unsteady Heat Transfer from an Equilateral Triangular Cylinder in the Unconfined Flow Regime

Effects of Reynolds number on the heat transfer characteristics of a long (heated) equilateral triangular cylinder are investigated for the range of conditions Re = 50–150 (in the steps of 10) and Prandtl number = 0.71 (air) in the unconfined unsteady cross-flow regime. In order to simulate the present situation, the computational grid is created by using commercial grid generator GAMBIT and the numerical computations are carried out by using FLUENT (6.3). The SIMPLE method is used to solve continuity, Navier-Stokes and energy equations along with the appropriate boundary conditions. The second order upwind scheme is used to discretize the convective terms, while the central difference scheme is used to discretize the diffusive terms in the governing equations. The present results are in an excellent agreement with the literature values. The temperature isotherms and temporal history of Nusselt number are presented in detail. The local as well as time-averaged Nusselt numbers are calculated. The time-averaged Nusselt number increases with increasing Reynolds number for the fixed value of the Prandtl number. Finally, the present numerical results are used to develop the simple heat transfer correlation for the range of conditions covered here.

CFD ANALYSIS OF TWO-DIMENSIONAL NON-NEWTONIAN POWER-LAW FLOW ACROSS A CIRCULAR CYLINDER CONFINED IN A CHANNEL

Flow of non-Newtonian power-law fluids across a long circular bluff body confined symmetrically between infinitely long two parallel plane walls is investigated numerically by solving the continuity and momentum equations using the finite volume method–based solver Fluent. The numerical calculations are performed in the full computational domain for the following ranges: Reynolds number = 50–150 and power-law index = 0.4–1.8 (covering shear-thinning, Newtonian, and shear-thickening behaviors) for the blockage ratio of 0.25. Global characteristics such as drag and lift coefficients, and Strouhal number and derived variables such as stream function are calculated for the above range of conditions. It is observed that the shear-thinning behavior yields a lower value of the time-averaged drag coefficient than the corresponding Newtonian value; however, an opposite trend is observed in the shear-thickening behavior. The Strouhal number increases with increasing Reynolds number for the fixed value of the power-law index.

Buoyancy-aided momentum and heat transfer in a vertical channel with a built-in square cylinder

This study focuses on the confined upward flow and heat transfer around a square cylinder under the effect of aiding buoyancy (Richardson number, Ri=0–1) in the vertical channel for Reynolds number (Re)=1–40 and blockage ratio (BR)=25–50% for the air as working fluid. Flow is found to be steady and symmetric for the range of settings. For Re≤2, no separation zone occurs for BR=25% and 30%. However, for BR=50%, no wakes are observed for Re≤3. The onset of flow separation takes place between Re=2 and 3 for BR=25% and 30%; whereas, for BR=50%, it exists between Re=3 and 4, irrespective of the value of Ri. Heat transfer correlations have also been obtained at different values of Re, BR and Ri.

Non-Newtonian power-law flow across a confined triangular bluff body in a channel

Wall effects on the flow of incompressible non-Newtonian power-law fluids across an equilateral triangular cylinder confined in a horizontal plane channel have been investigated for the range of conditions: Reynolds number, Re=1–40, power-law index, n=0.4–1.8 (covering shear-thinning, Newtonian and shear-thickening behaviors) and blockage ratio=0.125–0.5. Extensive numerical results on flow pattern, wake/recirculation length, individual and overall drag coefficients, variation of pressure coefficient on the surface of the triangular cylinder and so forth are reported to elucidate the combined effect of power-law index, blockage ratio and Reynolds number. The size of vortices decreases with an increase in the value of the blockage ratio and/or power-law index. For a fixed value of the Reynolds number, individual and overall drags decrease with decrease in power-law index and/or blockage ratio in steady confined flow regime. Simple correlations of wake length and drag are also obtained for the range of settings considered.

Flow and Heat Transfer Phenomena Across Two Confined Tandem Heated Triangular Bluff Bodies

Confined flow and heat transfer phenomena across two long triangular bars in tandem arrangement in a horizontal channel have been studied for the range of Reynolds number (Re) = 1–40, Prandtl number (Pr) = 0.71–50 and gap ratio (S/B) = 1–4 for a fixed blockage ratio of 25%. The average Nusselt number of the first triangular cylinder is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Heat transfer correlations in terms of the Colburn jh factor have been established in the steady regime.