Prabal Talukdar

Computational efficiency improvements of the radiative transfer problems with or without conduction--a comparison of the collapsed dimension method and the discrete transfer method

Abstract This paper deals with the performance evaluation of the collapsed dimension method (CDM) and the discrete transfer method (DTM) in terms of computational time and their abilities to provide accurate results in solving radiation and/or conduction mode problems in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. For some pure radiation cases, studies were made for two representative benchmark problems dealing with radiative equilibrium and non-radiative equilibrium. For the combined mode, the transient conduction and radiation problem was solved. The alternating direction implicit scheme was used for the solution of the finite difference part of the energy equation. For the three types of problems considered, tests were performed for a wide range of aspect ratio, extinction coefficient, scattering albedo, conduction–radiation parameter and boundary emissivity. For pure radiation problems, results from the two methods were validated against the results from the Monte Carlo method. For the combined mode, some steady-state results were compared with results available in the literature. For the transient situations, results from the two methods were validated against each other. While both the methods were found to give the same results, the CDM was found to be much more economical than the DTM.

Transient conduction and radiation heat transfer with variable thermal conductivity

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.

Analysis of Laminar Mixed Convective Heat Transfer in Horizontal Triangular Ducts

Numerical simulations for fluid flow and heat transfer in triangular ducts are carried out. Flow is considered to be laminar, hydrodynamically, and thermally developing. Heat transfer by both forced and natural convection is taken into account. Simulations are carried out for constant wall temperature cases which are at a higher temperature than the inlet temperature of the fluid. The effect of Rayleigh number on bulk mean temperature and Nusselt number is studied. Isotherm and secondary velocity profile formed because of natural convection is shown at different locations with varying Rayleigh number. The effect of the apex angle of the triangular duct on Nusselt number and bulk mean temperature is studied. Results are compared with the cases of mixed convective heat transfer in a square duct.

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH HEAT GENERATION IN A PARTICIPATING MEDIUM USING THE COLLAPSED DIMENSION METHOD

Combined conduction and radiation heat transfer with and without heat generation is investigated. Analysis is carried out for both steady and unsteady situations. One-dimensional gray Cartesian enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The Crank?Nicholson scheme is used to solve the transient energy equation. The radiative part of the energy equation is solved using the collapsed dimension method. Transient and steady state temperature and heat flux distributions are found for various radiative parameters. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature and heat flux. Results are compared with the data reported in the literature. Excellent agreement has been found.

EFFECT OF ANGULAR QUADRATURE SCHEMES ON THE COMPUTATIONAL EFFICIENCY OF THE DISCRETE TRANSFER METHOD FOR SOLVING RADIATIVE TRANSPORT PROBLEMS WITH PARTICIPATING MEDIUM

This article deals with the effects of angular quadrature schemes on the computational efficiency of the discrete transfer method (DTM) used for solving radiative transport problems with a participating medium. Four different quadrature schemes are considered. The first scheme uses the ray directions and the associated weights as per the original formulation of the DTM. In the second and third schemes, the ray arrangements are different but the quadrature schemes are the same as that used in the collapsed dimension method. The fourth scheme uses the ray directions and the corresponding weights according to the imporved quadrature scheme employed in the discrete ordinates method (DOM). The effects of the four quadrature schemes on the computational efficiency are tested for four benchmark radiative transport problems. Results are compared with the exact methods and with those available in the literature. It has been found that if the ray directions and the weights are chosen as per the DOM, the computational efficiency of the DTM is the best.

Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.

Effect of Axial Radiation on Heat Transfer in a Thermally and Hydrodynamically Developing Flow between Parallel Plates

The present work investigates coupled convection-radiation heat transfer through parallel plates with both heated and cooled walls. The flow is both hydrodynamically and thermally developing. The momentum and energy equations are solved with the computational fluid dynamics (CFD) code FASTEST3D, based on the finite-volume method (FVM). The medium is considered to be radiatively participating and the radiative heat transfer is also treated by the finite-volume method. Both axial and transverse heat transfer are considered. The effect of axial radiation is shown for different optical parameters by comparing results with and without axial radiation. The effect of hydrodynamically developing flows is also considered.

Experimental Studies for Convective Drying of Potato

An experimental facility was built at the Indian Institute of Technology Delhi in order to examine the characteristics of convective drying of a moist object. The test facility consists of an inlet section, a divergent and convergent section, a settling chamber, a test section, and an outlet section. Initial moisture content and time-dependent moisture content of a rectangular shaped moist object (4 cm × 2 cm × 2 cm) are measured by this test facility. The potato slice was selected as a sample moist object. Moisture content was measured at different air temperatures of 40, 50, 60, and 70°C with an air velocity of 2 m/sec. The density of potato slice was determined for various drying temperatures. The volume shrinkage during drying decreased almost linearly with moisture content. The percentage air pores and porosity increased gradually with decreasing moisture content and increasing drying air temperature. Volumes of water, air, and solid content of potato were determined at different drying air temperatures. The results are validated with theoretical data.

Mixed Convection and Non-Gray Radiation in a Horizontal Rectangular Duct

Numerical studies for fluid flow and heat transfer in a horizontal rectangular duct are carried out. The flow is considered to be laminar, hydrodynamically and thermally developing. Heat transfer by both forced and natural convection is taken into account. The radiation from the gas is modeled with weighted sum of gray gases (WSGG) model. While considering non-gray radiation with WSGG, the fluid is considered to be a mixture of CO2 and H2O. Simulations are carried out with lower wall temperature than the inlet temperature of the gas. The effect of buoyancy and radiation on bulk mean temperature and Nusselt number are studied. The effects of temperature dependent properties are discussed. Comparative studies are carried out among forced convection, mixed convection, gray and non-gray gas radiation. It is found from the simulations that the assumption of gray gas can produce an error of ±10% over a non-gray model with WSGG for the cases studied.

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO2 with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.