Uniform Internal Heat Generation Research Articles

Microstructural, Electrochemical, and Hot Corrosion Analysis of CoCrFeCuTi High Entropy Alloy Reinforced Titanium Matrix Composites synthesized by Microwave Sintering

CoCrFeCuTi High Entropy Alloy (HEA) is reinforced in Ti6Al6V2Sn alloy through microwave sintering-assisted powder metallurgy and its corrosion behaviour is investigated under different conditions. The ball-milled CoCrFeCuTi HEA powder exhibits 17 μm average particle size of irregular fragments with a single-phase BCC structure and is added as reinforcement in Ti alloy at 3, 6, 9, and 12 wt%. As more reinforcement is added, the α-Ti decreases and β-Ti increases which enhances the interfacial bonding. The pinning effects from reinforcements inhibit grain growth contributing to improved properties including higher relative density with less porosity. The 12 wt% composite showed remarkable microhardness of 734 HV which is increased by 43.8% over Ti alloy. The 12 wt% composite also achieved finer grains (0.345 μm) due to uniform internal heat generation from the process. Corrosion behaviour is assessed through electrochemical corrosion and hot corrosion analysis, with 12 wt% composite demonstrating 59.5% better corrosion resistance compared to Ti alloy. The induced corrosion products, formation of passivation films, and their mechanism are examined by morphological analysis.

Assessment of thermal damage for plasmonic photothermal therapy of subsurface tumors.

Plasmonic photothermal therapy (PPTT) involves the use of nanoparticles and near-infrared radiation to attain a temperature above 50°C within the tumor for its thermal damage. PPTT is largely explored for superficial tumors, and its potential to treat deeper subsurface tumors is dealt feebly, requiring the assessment of thermal damage for such tumors. In this paper, the extent of thermal damage is numerically analyzed for PPTT of invasive ductal carcinoma (IDC) situated at 3-9mm depths. The developed numerical model is validated with suitable tissue-tumor mimicking phantoms. Tumor (IDC) embedded with gold nanorods (GNRs) is subjected to broadband near-infrared radiation. The effect of various GNRs concentrations and their spatial distributions [viz. uniform distribution, intravenous delivery (peripheral distribution) and intratumoral delivery (localized distribution)] are investigated for thermal damage for subsurface tumors situated at various depths. Results show that lower GNRs concentrations lead to more uniform internal heat generation, eventually resulting in uniform temperature rise. Also, the peripheral distribution of nanoparticles provides a more uniform spatial temperature rise within the tumor. Overall, it is concluded that PPTT has potential to induce thermal damage for subsurface tumors, at depths of upto 9mm, by proper choice of nanoparticle distribution, dose/concentration and irradiation parameters based on the tumor location. Moreover, intravenous administration of nanoparticles seems a good choice for shallower tumors, while for deeper tumors, uniform distribution is required to attain the necessary thermal damage. In the future, the algorithm may be extended further, involving 3D patient-specific tumors and through mice model-based experiments.

Role of periodic irradiation and incident beam radius for plasmonic photothermal therapy of subsurface tumors

Plasmonic photothermal therapy (PPTT) is a potential technique to treat tumors selectively. However, during PPTT, issue of high temperature region and damage to the surrounding healthy is still need to be resolved. Also, treatment of deeper tumors non-invasively is a challenge for PPTT. In this paper, the effect of periodic irradiation and incident beam radius (relative to tumor size) for various gold nanorods (GNRs) concentrations is investigated to avoid much higher temperatures region with limiting thermal damage to the surrounding healthy tissue during PPTT of subsurface breast tumors located at various depths. Lattice Boltzmann method is used to solve Pennes’ bioheat model to compute the resulting photothermal temperatures for the subsurface tumor embedded with GNRs subjected to broadband near infrared radiation of intensity 1 W/cm2. Computation revealed that low GNRs concentration leads to uniform internal heat generation than higher GNRs concentrations. The results show that deeper tumors, due to attenuation of incident radiation, show low temperature rise than shallower tumors. For shallower tumors situated 3 mm deep, 70% irradiation period resulted in around 20 °C reduction (110 °C–90 °C) of maximum temperature than that with the continuous irradiation. Moreover, 70% beam radius (i.e., beam radius as 70% of the tumor radius) causes less thermal damage to the nearby healthy tissue than 100% beam radius (i.e., beam radius equal to the tumor radius). The thermal damage within the healthy tissue is minimized to the 1 mm in radial direction and 3 mm in axial direction for 70% beam radius with 70% irradiation period. Overall, periodic heating and changing beam radius of the incident irradiation lead to reduce high temperature and limit healthy tissue damage. Hence, discussed results are useful for selection of the irradiation parameters for PPTT of sub-surface tumors.

HEAT TRANSFER ANALYSIS ON BASE OF HEAT SINK WITH UNIFORM HEAT GENERATION

The present work describes the important results of problem of combined conduction, convection and radiation from a rectangular heat sink base subjected to uniform internal heat generation in its base. The governing equations for temperature distribution within the base are obtained by a relevant energy balance between rate of heat generation, heat conducted, convected and radiated. The derived non-linear partial differential equations are converted into algebraic form using finite difference method with 2nd order accuracy. The obtained algebraic equations have been solved simultaneously by Gauss-siedel iterative method with stringent convergence criteria and a C code has been written for above purpose. The computational domain has been discretized uniformly in all directions. A grid convergence test has been carried out to optimize the size of element. A complete parametric study has been carried out to study the effect of material of heat sink, regime of convection and role of radiation on local temperature distribution and maximum heat sink base temperature. It has been observed that material with high conductivity decreases the local temperature gradient and thus the maximum temperature. The regime of convection has a great influence on maximum temperature of heat sink with 15K of drop in Tmax. for a change in flow regime from free convection to forced convection. A special study on exclusive role of convection on maximum temperature reveals that one should not ignore the role forced convection in heat dissipation. Key Words: Heat generation, Multimode heat transfer, Radiation

Thermal Analysis of Magneto-Natural Convection Flows within a Partially Thermally Active Rectangular Enclosure

In this study, we numerically investigate heat transfer enhancement in a partially thermally active rectangular enclosure. The enclosure is filled with a ternary hybrid nanofluid (water, Carbon Nanotube, Al2O3, and Graphene). It is subjected to a magnetic field and uniform internal heat generation. The study also investigates the effect of magnetic field strength and direction on the natural convection flow, which arises from density fluctuations caused by partial heating of the left vertical wall. To solve the dimensionless governing equations, the finite element approach is employed. The parameters studied in detail include Rayleigh number (Ra), Hartmann number (Ha), nanoparticle volume fraction (ϕ), and heat generation coefficient (λ). The findings are presented graphically for the range of the parameters as follows: 103≤Ra ≤106, 0≤Ha≤20, 0.01≤ϕ≤0.05, and 0≤λ≤15. It is noted that these parameters have an impact on heat transfer enhancement, flow patterns, and temperature fields. The results show that the average Nusselt number (Nu¯) increases with an increasing value of ϕ. Moreover, it has been noted that Nu¯ decreases as the value of Ha increases, and the impact becomes more obvious at higher Ra values. Finally, the influence of the heat generation coefficient on the heat transfer rate inside an enclosure is examined.

Convection heat transfer under the effect of uniform and periodic magnetic fields with uniform internal heat generation: a new comprehensive work to develop the ability of the multi relaxation time lattice Boltzmann method

Convection heat transfer under the effect of uniform and periodic magnetic fields with uniform internal heat generation: a new comprehensive work to develop the ability of the multi relaxation time lattice Boltzmann method

Inverse Analysis of Steady Heat Conduction with Heat Generation for a Hollow Cylinder.(Dept.M)

This work is concerned with the inverse analysis of estimating two dimensional steady state temperature distribution in a hollow cylinder wall involving uniform internal heat generation by utilizing the axial distribution of temperature and that of heat flux at the outside surface of the cylinder; both are functions of the axial coordinate. Different version of the solution has also been found by utilizing the corresponding two boundary conditions specified at the inner surface or the hollow cylinder. Exactness and validity of the present solution have been checked up by comparison with exact solutions. The general solution is capable to accommodate boundary conditions data of sharp axial variation. The method may also be of a considerable practical interest, however, for some steady heat transfer investigations using a circular test tube.

Analysis of transient thermoelastic temperature distribution of a thin circular plate and its thermal deflection under uniform heat generation

Analysis of transient thermoelastic temperature distribution of a thin circular plate and its thermal deflection under uniform internal heat generation is investigated. The upper and lower surfaces are thermally insulated, while the perimetric surface is subjected to convection heat transfer with convection coefficient hc and fluid temperature while the plate is also subjected to uniform internal energy generation g0 (W.m–3). The integral transform method is used to obtain the analytical solution for the temperature field and thermal deflection. As a special case, the mathematical model is prepared for copper material, and temperature distribution is analyzed for two different initial conditions. The results for temperature changes and the thermal deflection are computed numerically and illustrated graphically.

Heat Conduction within Elliptic Enclosure with Internal Heat Generation

Exact and numerical solutions for steady heat conduction in the enclosure between two long isothermal elliptic tubes with uniform internal heat generation are obtained. The heat conduction process within the enclosure is mainly influenced by internal heat generation, axis ratio of inner tube and major axes ratio of the two tubes. The solutions are obtained in terms of the temperature and local heat flux distributions. The study has shown that the numerical results are in excellent agreement with the analytical results.

The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise.

Integral transform solution of natural convection in a cylinder cavity with uniform internal heat generation

PurposeThe purpose of this study is to propose the generalised integral transform technique to investigate the natural convection behaviour in a vertical cylinder under different boundary conditions, adiabatic and isothermal walls and various aspect ratios.Design/methodology/approachGITT was used to investigate the steady-state natural convection behaviour in a vertical cylinder with internal uniformed heat generation. The governing equations of natural convection were transferred to a set of ordinary differential equations by using the GITT methodology. The coefficients of the ODEs were determined by the integration of the eigenfunction of the auxiliary eigenvalue problems in the present natural convection problem. The ordinary differential equations were solved numerically by using the DBVPFD subroutine from the IMSL numerical library. The convergence was achieved reasonably by using low truncation orders.FindingsGITT is a powerful computational tool to explain the convection phenomena in the cylindrical cavity. The convergence analysis shows that the hybrid analytical–numerical technique (GITT) has a good convergence performance in relatively low truncation orders in the stream-function and temperature fields. The effect of the Rayleigh number and aspect ratio on the natural convection behaviour under adiabatic and isothermal boundary conditions has been discussed in detail.Originality/valueThe present hybrid analytical–numerical methodology can be extended to solve various convection problems with more involved nonlinearities. It exhibits potential application to solve the convection problem in the nuclear, oil and gas industries.

Numerical analysis of the axial heat conduction with variable fluid properties in a forced laminar flow tube

In this article, a theoretical model is developed to investigate the effects of the axial heat conduction on the laminar forced convection in a circular tube with uniform internal heat generation in the solid wall. In the current work, three different fluids, i.e. water, n-decane and air, are selected on purpose since their thermophysical properties show different behavior with temperature. The effects of the axial heat conduction with varying dynamic viscosity and/or varying thermal conductivity are investigated in a systematic manner. Results indicate that the variable-property effects could alleviate the reduction in Nusselt number (Nu) due to the axial heat conduction. For the case of Peclet number (Pe) equal to 100, wall thickness to inner diameter ratio of 1 and solid wall to fluid thermal conductivity ratio of 100, the maximum Nu deviation between constant and variable properties are up to 7.33% at the entrance part for water in the temperature range of 50°C, and 4.45% at the entrance part for n-decane in the temperature range of 120°C, as well as 2.20% at the ending part for air in the temperature range of 475°C, respectively. In addition, the average Nu deviation for water, n-decane and air is 3.24%, 1.94% and 1.74%, respectively. Besides, Nu decreases drastically with decreasing Pe when Pe⩽500 and with increasing solid wall to fluid thermal conductivity ratio (ksf) when ksf⩽100. It is also found that variable properties have more obvious effects on the velocity profile at the upstream part while more obvious effects on the temperature profile at the downstream part.

A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder

ABSTRACTThis paper reports the use of Markov Chain Monte Carlo (MCMC) and Metropolis Hastings (MH) approach, to solve an inverse heat transfer problem. Three-dimensional, steady state, conjugate heat transfer from a Teflon cylinder of dimensions 100 mm diameter and 100 mm length with uniform volumetric internal heat generation is considered. The goal is to estimate volumetric heat generation and heat transfer coefficient, given the temperature data at certain fixed location on the surface of the cylinder. The internal volumetric heat generation is specified as input and the temperature and heat transfer coefficient values are obtained by a numerical solution to the governing equation. The temperature values also depend on heat transfer coefficient which is obtained by solving Navier–Stokes equation to obtain flow information. In order to reduce the computational cost, a neural network is trained from the computational fluid dynamics simulations. This is posed as an inverse problem wherein volumetric heat generation and heat transfer coefficient are unknown but the temperature data is known by conducting experiments. The novelty of the paper is the simultaneous determination of volumetric heat generation and heat transfer coefficient for the experimentally measured steady-state temperatures from a Teflon cylinder using MCMC-MH as an inverse model in a Bayesian framework and finally, the estimates are reported in terms of mean, maximum a posteriori, and the standard deviation which is the uncertainty associated with the estimated parameters.

LAMINAR FORCED CONVECTION IN HORIZONTAL CHANNEL WITH HEAT GENERATION PLATES COOLED BY WATER

This paper describes the study of the behavior of two-dimensional and parallel horizontal flat plates with uniform internal heat generation subjected to laminar forced convection of water. The governing equations are solved numerically using the finite volume technique with Power-Law interpolating scheme and the SIMPLE algorithm. After the simulations the temperature and velocity fields were obtained for various plates spacing and fluid inlet velocities, as well as the Nusselt number values.

Extending the diffusion approximation to the boundary using an integrated diffusion model

The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi 1, Biot number for convection on the outside surface Bi 2, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.

Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials

This paper studies a radial fin of uniform thickness with convective heating at the base and convective–radiative cooling at the tip. The fin is assumed to experience uniform internal heat generation. The exposed surfaces of the fin lose heat by simultaneous convection and radiation to the surroundings. Two types of fin materials are investigated: homogeneous material and functionally graded material (FGM). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM fin the thermal conductivity is modeled as a linear function of the dimensionless radial coordinate. The analysis is conducted using the differential transformation method (DTM). The accuracy of DTM is verified by comparing the results for the simplified versions of the present model with an exact analytical solution derived here. Once the accuracy of DTM is authenticated, the method is used to generate results for the general problem formulated here. These results illustrate the effects of various dimensionless parameters on the thermal performance of homogeneous material fins and FGM fins.

MHD boundary-layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary-layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth-order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM-Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

AbstractThe transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21012

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

AbstractThe paper presents an entropy generation analysis for steady conduction in a slab with temperature‐dependent volumetric internal heat generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the slab. The total entropy generation rate depends on five dimensionless parameters: reference heat generation temperature Q, the heat generation–temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi1 and Bi2. Graphs illustrating the effect of these five parameters on the local and total entropy generation rates are presented and discussed. It is found that the total entropy generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform internal heat generation confirm the results presented in a 2003 paper. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20404