An enthalpy-based lattice Boltzmann formulation for unsteady convection-diffusion heat transfer problems in heterogeneous media

In this paper, we propose a direct extension of a previous work presented by Hamila et al. [1 R. Hamila, M. Nouri, S. Ben Nasrallah, and P. Perré, Int. J. Heat Mass Transfer, vol. 100, pp. 728–736, 2016.[Crossref], [Web of Science ®] , [Google Scholar]] dealing with the simulation of conjugate heat transfer by conduction in heterogeneous media. In [1 R. Hamila, M. Nouri, S. Ben Nasrallah, and P. Perré, Int. J. Heat Mass Transfer, vol. 100, pp. 728–736, 2016.[Crossref], [Web of Science ®] , [Google Scholar]] a novel enthalpy-based lattice Boltzmann (LB) formulation was successfully simulated in several conjugate heat transfer problems by conduction. We propose testing this enthalpic LB formulation in solving convection-diffusion heat transfer problems in heterogeneous media. The main idea of this formulation is to introduce an extra source term, avoiding any additional treatment of the distribution functions at the interface. Continuity of temperature and normal heat flux at the interface is satisfied automatically. The performance of the present method is successfully validated by comparison to the control volume methods (CVMs) solutions of several heat convection-diffusion problems in heterogeneous media.     

Heat Transfer from a Single Tube to the Flowing Gas-Solid Suspension in a CFB Riser

The first published studies concerning heat transfer between flowing gas-solid suspensions (pneumatic conveying) and pipe walls appeared in the literature in the early 1960s. More recently, experimental investigations have been extended to circulating fluidized beds. Despite the relatively large number of studies undertaken, mostly in CFB-risers of limited dimensions, the variation of the CFB heat transfer coefficient with operating gas velocity and solids' loading could not be predicted accurately. In his review paper [1 Grace, J. R. Heat Transfer in High Velocity Fluidized Beds. Proc. 9th Int. Heat Transfer Conference Heat Transfer. 1999, Hemisphere. pp.329–339.  [Google Scholar]], Grace summarized the situation as follows: “no existing correlations give consistent agreement with the available data.” The situation in a circulating fluidized bed is indeed a complex one, with a core/annulus flow and clusters of particulates being formed, leading to a non-uniform distribution of the solids over the cross-sectional area of the riser. Existing correlations largely ignore these flow characteristics. Experimental investigations using a FCC catalyst were carried out in a 100 mm ID riser, heated from an embedded heat transfer probe. Superficial velocities up to 8 m/s and solid circulation rates between 10 and 50 kg/m²s were used. Experimental results for the operation at a constant gas flow rate reveal an initial nearly constant heat transfer coefficient for low solids' loading, followed by a subsequent significantly increasing heat transfer coefficient with increasing solids' loading. Increasing the gas flow rate at a constant solids' loading significantly reduced the heat transfer coefficient. The experimental results were correlated with predictions from the theoretical approach of Molodtsof and Muzyka [2 Molodstof, Y. and Muzyka, D. W. 1989. Int. J. Eng. Fluid Mech., vol. 2: 1–24.  [Google Scholar], 3 Molodstof, Y., Muzyka, D. W., Large, J. F. and Bergougnou, M. A. The Use of Asymptotic Similar Solutions to Probabilistic Multiphase Flow Equations to Predict Heat Transfer Rates to Dilute Gas-Solids Suspension. Poc. XVIth I.C.N.M.T. Symposium. Dubrovnik, Yugoslavia.  [Google Scholar]]. A good agreement was obtained.     

Editorial

This editorial provides an overview of a special issue dedicated to the 7th conference on Process Integration, Modeling and Optimization for Energy Saving and Pollution Reduction—PRES 2004. Eight papers have been selected and peer-reviewed covering various subjects of heat transfer engineering, focusing on the recent development of various features of heat transfer equipment design and optimization. This is the fourth special issue of Heat Transfer Engineering dedicated to selected contributions from PRES conferences [1 Kleme?, J. and Stehlík, P. Heat Transfer Engineering. PRES Conference—Challenges in Complex Process Heat Transfer. vol. 23, pp.1–2. no. 6 [Google Scholar], 2 Stehlík, P. and Kleme?, J. Heat Transfer Engineering. Selected Papers from the PRES 2002 Conference. vol. 25, pp.1–3. no. 5 [Google Scholar], 3 Kleme?, J. and Stehlík, P. Heat Transfer Engineering. Selected Papers from the PRES 2003 Conference. vol. 26, pp.1–3. no. 5 [Google Scholar]].     

Effect of Sawtooth Roughness on Pressure Drop and Turbulent Transition in Microchannels

Roughness elements affect internal flows in different ways. One effect is the transition from laminar to turbulent flow at a lower Reynolds number than the predicted Re = 2300. Initial work at RIT in the subject area was performed by Schmitt and Kandlikar [1 Schmitt, D. J. and Kandlikar, S. G. Effects of Repeating Microstructures on Pressure Drop in Rectangular Minichannels. Third International Conference on Microchannels and Minichannels (ICMM05). ASME. Paper no. ICMM2005-75111 [Google Scholar]] and Kandlikar et al. [2 Kandlikar, S. G., Schmitt, D. J., Carrano, A. L. and Taylor, J. B. 2005. Characterization of Surface Roughness Effects on Pressure Drop in Single-Phase Flow in Minichannels. Physics of Fluids, vol. 17(10) October: 100606–100606-11. Paper 100606[Crossref] , [Google Scholar]], and this study is an extension of these efforts. The channel used in this study is rectangular, with varying separation between walls that have machined roughness elements. The roughness elements are saw-tooth in structure, with element heights of 107 and 117 μ m for two pitches of 405 μ m and 815 μ m, respectively. The resulting hydraulic diameters and Reynolds numbers based on the constricted flow area range from 424 μ m to 2016 μ m and 210 to 2400, respectively. Pressure measurements are taken at sixteen locations along the flow length of 88.9 mm to determine the local pressure gradients. The results for friction factors and transition to turbulent flow are obtained and compared with the data reported by Schmitt and Kandlikar [1 Schmitt, D. J. and Kandlikar, S. G. Effects of Repeating Microstructures on Pressure Drop in Rectangular Minichannels. Third International Conference on Microchannels and Minichannels (ICMM05). ASME. Paper no. ICMM2005-75111 [Google Scholar]]. The roughness elements cause an early transition to turbulent flow, and the friction factors in the laminar region are predicted accurately using the hydraulic diameter based on the constricted flow area.     

Numerical Simulation of Resistance Spot Welding Process

Laminar forced-convective heat transfer in a two-dimensional parallel-plate channel with 16 porous baffles mounted alternately on bottom and top walls was studied numerically. The numerical study was conducted by developing and using a finite-volume code. The pressure and velocity fields were linked by the SIMPLEC algorithm. The extended Darcy-Forchheimer model was used to describe resistance to flow through the porous baffles. The grid independence was established for the developed code. The code was validated against the studies by Sung et al. [7 Sung, H. J., Kim, S. Y. and Hyun, J. M. 1995. Forced Convection from an Isolated Heat Source in a Channel with Porous Medium. Int. J. Heat Fluid Flow, vol. 16: pp. 527–535.  [Google Scholar]] and Nakayama [15 Nakayama, A. PC-Aided Numerical Heat Transfer and Convection Flow, pp. 243–247. Boca Raton, FL: CRC Press.  [Google Scholar]]. The parametric runs were made for Reynolds numbers (Re) of 100, 200, 300, and 400; for Darcy number (Da) values of 8.783 × 10^?6, 1.309 × 10^?5, and 1.791 × 10^?5; for nondimensional baffle spacing values of (D?)=11, 13, and 15; for nondimensional baffle aspect ratio (W?) of 4, 6, and 12; thermal conductivity ratios (K?) of 1, 10, and 100; and nondimensional baffle height (B?) was fixed at 1/3. Consideration was given only to flow of air (Pr=0.7). It was found that heat transfer enhancement ratios for solid-baffle cases are higher than those for corresponding porous-baffle cases. The heat transfer enhancement ratio increased with increase in Re, decrease in Da, increase in K?, increase in D?, and decrease in W?. The heat transfer enhancement per unit increase in pumping power was less than unity for the range of parameters considered in this study.     

Performance Analysis of IDEAL Algorithm Combined with Bi-CGSTAB Method

An efficient segregated algorithm for fluid flow and heat transfer problems, called IDEAL, was proposed D. L. Sun et al. [11 D. L. Sun , Z. G. Qu , Y. L. He , and W. Q. Tao , An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—IDEAL (Inner Doubly-Iterative Efficient Algorithm for Linked-Equations) Part I: Mathematical Formulation and Solution Procedure , Numer. Heat Transfer, B , vol. 53 , pp. 1 – 17 , 2008 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. In addition, the IDEAL algorithm was extended to 2-D/3-D grid systems. In these IDEAL algorithms, all of the algebraic equations are solved by the alternating-direction implicit (ADI) method, called the IDEAL + ADI method. In this article, the efficient Bi-CGSTAB method is adopted instead of the ADI method to solve the algebraic equations in the IDEAL algorithm, called the IDEAL + Bi-CGSTAB method. It is found that the IDEAL + Bi-CGSTAB method is much better than the IDEAL + ADI method to solve open systems but little worse to solve closed systems.     

Achievements in Applied Heat Transfer—PRES 2006

This editorial provides an overview of a Special Issue dedicated to the 9th Conference, Process Integration, Modeling, and Optimization for Energy Saving and Pollution Reduction—PRES 2006. Six papers have been selected and peer-reviewed covering important subjects of heat transfer engineering. These papers' focus is on the recent development of various features of heat transfer equipment design and optimization. This issue of Heat Transfer Engineering is the fifth special journal issue dedicated to selected papers from PRES conferences [1 Kleme?, J. and Stehlik, P. 2002. PRES Conference—Challenges in Complex Process Heat Transfer. Heat Transfer Engineering, vol. 23: 1–2.  [Google Scholar], 2 Stehlík, P. and Kleme?, J. 2004. Selected Papers from the PRES 2002 Conference. Heat Transfer Engineering, vol. 25: 1–3.  [Google Scholar], 3 Kleme?, J. and Stehlík, P. 2005. Selected Papers from the PRES 2003 Conference. Heat Transfer Engineering, vol. 26: 1–3.  [Google Scholar], 4 Stehlík, P. and Kleme?, J. 2006. Recent Advances on Heat Transfer Equipment Design—Selected Papers from PRES 2004 Conference. Heat Transfer Engineering, vol. 27: 1–3.  [Google Scholar]].     

Heat Transfer in Industrial Applications—PRES 2008

This editorial provides an overview of a special issue dedicated to the 11th Conference on Process Integration, Modeling, and Optimization for Energy Saving and Pollution Reduction—PRES 2008. Nine papers have been selected and peer-reviewed covering important subjects of heat transfer engineering. They focus on recent development of various features of heat transfer equipment design and optimization. This issue of Heat Transfer Engineering is the sixth special journal issue dedicated to selected papers from PRES conferences [1 Kleme?, J. and Stehlik, P. 2002. PRES Conference—Challenges in Complex Process Heat Transfer. Heat Transfer Engineering, vol. 23: 1–2.  [Google Scholar], 2 Stehlík, P. and Kleme?, J. 2004. Selected Papers from the PRES 2002 Conference. Heat Transfer Engineering, vol. 25: 1–3.  [Google Scholar], 3 Kleme?, J. and Stehlík, P. 2005. Selected Papers from the PRES 2003 Conference. Heat Transfer Engineering, vol. 26: 1–3.  [Google Scholar], 4 Stehlík, P. and Kleme?, J. 2006. Recent Advances on Heat Transfer Equipment Design and Optimization—Selected Papers from PRES 2004 Conference. Heat Transfer Engineering, vol. 27: 1–3.  [Google Scholar], 5 Stehlík, P. and Kleme?, J. 2008. Achievements in Applied Heat Transfer—PRES 2006. Heat Transfer Engineering, vol. 29: 503–505.  [Google Scholar]].     

Direct Comparison between Five Different Microchannels,Part 2: Experimental Description and Flow Friction Measurement

Abstract

Part one of this paper ^[1] Eason, C., Dalton, T., O'Mathúna, C., Slattery, O. and Davies, M. 2005. Direct Comparison between Five Different Microchannels, Part 1: Channel Manufacture and Measurement. Heat Transfer Engineering Journal, vol. 26(no. 3): pp. 00–00.  [Google Scholar] investigates the manufacture of five types of microchannels produced by wet and dry etching in silicon and precision mechanical sawing in silicon and thermoset plastic. This paper describes the experimental equipment and methods used to measure the pressure flow characteristics of the manufactured channels. A test system has been built to test each sample using the same inlet and outlet manifolds, pressure tappings, pumping system, and instrumentation. The measured pressure flow behavior was compared with theoretical values calculated from macroscale theory. Error analysis was carried out in order to determine the overall accuracy of the experimental work and determine the significance of any experimental deviation from theoretical values. An area compensation term is introduced to account for the difference in cross-section between the measured actual channels and the rectangles/trapeziums that share their overall dimensions.     

Fully Consistent SIMPLE-Like Algorithms on Collocated Grids

To increase the convergence rate of SIMPLE-like algorithms on collocated grids, a compatibility condition between mass flux interpolation methods and SIMPLE-like algorithms is presented. Results of unsteady flow computations show that the SIMPLEC algorithm, when obeying the compatibility condition, may obtain up to 35% higher convergence rate as compared to the standard SIMPLEC algorithm. Two new interpolation methods, fully compatible with the SIMPLEC algorithm, are presented and compared with some existing interpolation methods, including the standard methods of Choi [9 S. K. Choi , Note on the Use of Momentum Interpolation Method for Unsteady Flows , Numer. Heat Transfer , vol. 36 , pp. 545 – 550 , 1999 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] and Shen et al. [8 W. Z. Shen , J. A. Michelsen , N. N. Sørensen , and J. N. Sørensen , Improved Rhie-Chow Interpolation for Unsteady Flow Computations , AIAA J , vol. 39 , pp. 2406 – 2409 , 2001 .[Crossref] , [Google Scholar]]. Numerical results show that the time-step dependence of the standard methods may double the total discretization error at steady state. It is furthermore shown that the new methods are independent of time step and relaxation parameter at convergence. One of the new methods is shown to give a higher accuracy than the standard methods.     

Multiphysics Model of Metal Solidification on the Continuum Level

Separate three-dimensional (3-D) models of thermomechanical behavior of the solidifying shell, turbulent fluid flow in the liquid pool, and thermal distortion of the mold are combined to create an accurate multiphysics model of metal solidification at the continuum level. The new system is applied to simulate continuous casting of steel in a commercial beam-blank caster with complex geometry. A transient coupled elastic-viscoplastic model [1 S. Koric and B. G. Thomas , Efficient Thermo-Mechanical Model for Solidification Processes , Int. J. Numer. Meth. Eng. , vol. 66 , pp. 1955 – 1989 , 2006 .[Crossref] , [Google Scholar]] computes temperature and stress in a transverse slice through the mushy and solid regions of the solidifying metal. This Lagrangian model features an efficient numerical procedure to integrate the constitutive equations of the delta-ferrite and austenite phases of solidifying steel shell using a fixed-grid finite-element approach. The Navier-Stokes equations are solved in the liquid pool using the standard K–? turbulent flow model with standard wall laws at the mushy zone edges that define the domain boundaries. The superheat delivered to the shell is incorporated into the thermalmechanical model of the shell using the enhanced latent heat method [2 S. Koric , B. G. Thomas , and V. R. Voller , Enhanced Latent Heat Method to Incorporate Superheat Effects into Fixed-Grid Multiphysics Simulations , Numer. Heat Transfer B , vol. 57 , pp. 396 – 413 , 2010 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Temperature and thermal distortion modeling of the complete complex-shaped mold includes the tapered copper plates, water cooling slots, backing plates, and nonlinear contact between the different components. Heat transfer across the interfacial gaps between the shell and the mold is fully coupled with the stress model to include the effect of shell shrinkage and gap formation on lowering the heat flux. The model is validated by comparison with analytical solutions of benchmark problems of conduction with phase change [3 J. A. Dantzig and C. L. Tucker III , Modeling in Materials Processing , pp. 282 – 321 , Cambridge University Press , Cambridge , UK , 2001 . [Google Scholar]], and thermal stress in an unconstrained solidifying plate [4 J. H. Weiner and B. A. Boley , Elasto-Plastic Thermal Stresses in a Solidifying Body , J. Mech. Phys. Solids , vol. 11 , pp. 145 – 154 , 1963 .[Crossref], [Web of Science ®] , [Google Scholar]]. Finally, results from the complete system compare favorably with plant measurements of shell thickness.     

NATURAL CONVECTION HEAT TRANSFER AROUND HEATED CYLINDERS INSIDE A CAVITY WITH CONDUCTING WALLS

A numerical study has been conducted for natural convection heat transfer for air around two vertically separated horizontal heated cylinders placed inside a rectangular enclosure having finite wall conductances. The interaction between convection in the fluid-filled cavity and conduction in the walls surrounding the cavity is investigated. Results have been obtained for Rayleigh numbers Ra between 10 ³ I. Tokura , H. Saito , K. Kishinami , and K. Muramoto , An Experimental Study of Free Convection Heat Transfer from a Horizontal Cylinder in a Vertical Arcay Set in Free Space between Parallel Walls , J. Heat Transfer , vol. 105 , pp. 102 – 107 , 1993 . [Google Scholar] and 10 ⁶ M. Lacroix , Natural Convection Heat Transfer around Two Heated Horizontal Cylinders inside a Rectangular Cavity Cooled from Above , Numer. Heat Transfer Part A , vol. 21 , pp. 37 – 54 , 1992 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], dimensionless wall-fluid thermal conductivity ratio α between 0.2 and 1000.0, and different thermal boundary conditions. The results indicate that wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer around the cylinders. Heat removal through the vertical wall is significant even when its outer surface is insulated. The overall heat transfer coefficient for both cylinders is correlated with C Raⁿ for different α and thermal boundary conditions.     

An Analytical Model for EHD-Enhanced Microscale Thin-Film Evaporation

An analytical model has been developed to predict the heat transfer and flow characteristics of electrohydrodynamic (EHD)-enhanced microscale ultra thin-film evaporation. The model described in this paper is based on a previously published microcooling device [1 Darabi, J., Ohadi, M. M. and De Voe, D. 2001. An Electrohydrodynamic Polarization Micropump for Electronic Cooling. Journal of Microelectromechanical Systems, vol. 10(no. 1): pp. 98–106. [Crossref], [Web of Science ®] , [Google Scholar]] that incorporated an active evaporative cooling surface, an EHD micropump, and temperature sensors into a single chip. The device was fabricated using microelectromechanical systems fabrication technology, allowing the EHD electrodes and temperature sensors to be integrated directly onto the cooling surface. One end of the device was immersed in a pool of liquid. The film originated at the liquid–vapor interface and flowed upward under the influence of the electric field. The model predicts the film thickness, dryout location, local and average heat transfer coefficients, and velocity profile. The agreement between the model and the experimental data is satisfactory. Both the analytical model developed in this study and the experimental results reported previously will facilitate the design of new microcooling devices capable of operating at high power levels.     

Natural Convection in a Square Enclosure with a Square Heat Source at Different Horizontal and Diagonal Eccentricities

The present article aims to extend a previous numerical study on the natural convection process in a square enclosure with a vertical eccentric square heat source (cylinder) [1]. Here, we investigated buoyancy-induced convective flow and heat transfer for horizontal and diagonal eccentric displacement in a square cylinder. Numerical studies are performed for Rayleigh numbers in the range 10³–10⁶, using our recently developed flexible forcing IB–thermal lattice Boltzmann method scheme [1 S. M. Dash, T. S. Lee, and H. Huang Natural Convection from an Eccentric Square Cylinder Using a Novel Flexible Forcing Ib-Lbm Method, Numer. Heat Transfer, Part A: Appl., vol. 65, pp. 531–555, 2013.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Detailed analysis of isotherms, streamlines, and Nusselt number distribution as functions of Rayleigh number and eccentricity is provided in this paper.     

A fully coupled OpenFOAM® solver for transient incompressible turbulent flows in ALE formulation

In this article, the previously developed single block fully coupled algorithm [1 L. Mangani, M. Buchmayr, and M. Darwish, Development of a Novel Fully Coupled Solver in OpenFOAM: Steady-State Incompressible Turbulent Flows, Numer. Heat Transfer B Fund., vol. 66, pp. 1–20, 2014.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar],2 L. Mangani, M. Buchmayr, and M. Darwish, Development of a Novel Fully Coupled Solver in OpenFOAM: Steady-state Incompressible Turbulent Flows in Rotational Reference Frames, Numer. Heat Transfer B Fund., vol. 66, pp. 526–543, 2014.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] for solving three-dimensional incompressible turbulent flows is extended to resolve transient flows in multiple rotating reference frames using the arbitrary Lagrange–Euler (ALE) formulation. Details on the discretization of ALE terms along with a recently developed extension to the conservative and fully implicit treatment of multi-block interfaces into three-dimensional space are presented. To account for turbulence, the kω???SST turbulence model in ALE formulation is solved using Navier–Stokes equations. This multi-block transient coupled algorithm is embedded within the OpenFOAM® Computational Fluid Dynamics (CFD) library, and its performance evaluated in a real case involving a turbulent flow field in a swirl generator by comparing numerical predictions with experimental measurements.     

Development of a Novel Fully Coupled Solver in OpenFOAM: Steady-State Incompressible Turbulent Flows in Rotational Reference Frames

In this article, the fully coupled block algorithm for the solution of three-dimensional incompressible turbulent flows presented in a companion article [1 L. Mangani , M. Buchmayr , and M. Darwish , Implementation and Evaluation of a Fully Coupled Solver in OpenFOAM: Steady State Incompressible Turbulent Flows , Numer. Heat Transfer B , vol. 66 , no. 1, 2014 .[Taylor & Francis Online] , [Google Scholar]] is extended for use with multiple reference frames and multiple mesh blocks. The implicit block coupling is applied to the extra rotational terms, and to the multiblock interfaces. Furthermore, implementation details on the linearization of cyclic and other boundary conditions are detailed. These modifications allow the coupled solver to retain its improved performance and robustness in addition to mesh size scalability while solving turbomachinery-type applications. The performance and mesh size scalability of the coupled solver is compared to that of a segregated pressure based solver [2 S. Patankar and D. Spalding , A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows , Heat and Mass Transfer , vol. 15 , pp. 1787 – 1806 , 1972 .[Crossref], [Web of Science ®] , [Google Scholar]] using three industrial-size test cases.     

NUMERICAL STUDY OF NATURAL CONVECTION IN VERTICAL CHANNELS WITH ADIABATIC EXTENSIONS DOWNSTREAM

ABSTRACT

Recent trends in natural-convection research are the finding of new configurations to improve heat transfer parameters or the analysis of standard configurations to determine optimal geometric parameters in order to achieve a better heat transfer rate. In this article a numerical simulation of natural convection in air in a channel–chimney system heated symmetrically at uniform heat flux is carried out. The regime analyzed is two-dimensional, laminar, and steady-state. Wall temperature profiles, air velocity and temperature profiles, and centerline pressure profiles are presented. A comparison with experimental data given in [4 A. Auletta , O. Manca , B. Morrone , and V. Naso , Heat Transfer Enhancement by the Chimney Effect in a Vertical Isoflux Channel , Int. J. Heat Mass Transfer , vol. 44 , pp. 4345 – 4357 , 2001 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]] is accomplished and some differences are observed, but thermal and dynamic behavior for different expansion ratios are the same. Results analysis explains how and why the “chimney effect” worsens. The effect is connected to the cold inflow at the outlet section, and this effect is more marked at higher Rayleigh number, Ra. Consequently, optimal thermal configuration for assigned extension ratio presents a larger value of expansion ratio at the lower Ra. values.     

A Problem on Thermoelastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermoelasticity III

The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1 A. E. Green and P. M. Nagdhi , On Undamped Heat Waves in an Elastic Solid , J. Thermal Stresses , vol. 15 , pp. 253 – 264 , 1992 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely: the extended thermoelasticity proposed by Lord and Shulman [2 H. W. Lord and Y. Shulman , A Generalized Dynamical Theory of Thermoelasticity , J. Mech. Phys. Solids , vol. 15 , pp. 299 – 309 , 1967 .[Crossref], [Web of Science ®] , [Google Scholar]], the thermoelasticity without energy dissipation (Green and Nagdhi [3 A. E. Green and P. M. Nagdhi , Thermoelasticity Without Energy Dissipation , J. Elasticity , vol. 31 , pp. 189 – 209 , 1993 .[Crossref], [Web of Science ®] , [Google Scholar]]) and thermoelasticity with energy dissipation (thermoelasticity type III [1 A. E. Green and P. M. Nagdhi , On Undamped Heat Waves in an Elastic Solid , J. Thermal Stresses , vol. 15 , pp. 253 – 264 , 1992 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained from different models of generalized thermoelasticity.     

Thermal analysis of laser-irradiated tissue phantoms using a novel separation of the variables-based discrete transfer method

Thermal analysis of tissue phantoms subjected to short pulse laser irradiation has been presented. The transient radiative transfer equation (RTE) has been solved using a novel separation of variables-based discrete transfer method (DTM) recently developed by the present authors (Nirgudkar et al. [21 H. Nirgudkar, S. Kumar, and A. Srivastava, Solution of Radiative Transfer Equation Using Discrete Transfer Method for Two-Dimensional Participating Medium, Int. Commun. Heat Mass Transfer, vol. 61, pp. 88–95, 2015.[Crossref], [Web of Science ®] , [Google Scholar]]). As an advancement, the solution of RTE has been coupled with Pennes’ bioheat transfer equation for determining the temperature distribution. Homogenous as well as phantoms embedded with optical inhomogeneity have been considered. The numerical model has been verified against the results available in the literature. This study clearly reveals the influence of the nature of the embedded inhomogeneity and its relative contrast on the resultant temperature distribution inside the body of the tissue phantom.