Examination of the Thermal Equilibrium Assumption in the Microscopic Parabolic Heat Conduction Model Under the Effect of Two Types of Heating Sources

Abstract

The validity of using the microscopic parabolic heat conduction model under the effect of two types of volumetric heating sources is investigated analytically. The considered volumetric heating sources are a fluctuating periodic source and a unit step source of short duration. Also, the role of the electron gas thermal capacity term is investigated. Criteria are derived to show the necessity of using the microscopic parabolic heat conduction model. Other criteria are derived to show a justification for neglecting the electron gas thermal capacity term from the microscopic parabolic heat conduction model.     

THERMOELASTIC BEHAVIOR OF A COMPOSITE SLAB UNDER A RAPID DUAL-PHASE-LAG HEATING

This work is concerned with the investigation of the thermoelastic response of a composite slab (a two-, thin-, metallic-layered plate) under the effect of an intense rapid heating applied to one side. The dual-phase-lag heat conduction model is used to derive the heat equation in each layer. The heat equations are solved using the Laplace transform technique and the Riemann-sum method. As a result, the thermal behavior, in the form of the temperature distribution along the thickness direction of the slab, is determined. The governing equation of plate deflection is formulated and solved for simply supported edge conditions. As a result, the plate deflections and the thermal stresses are calculated numerically using the finite difference method. Thermal stress distribution is found to depend on the temperature distribution in addition to the difference in the thermal and mechanical properties of the materials that compose the two layers.     

Performance enhancement of a solar dynamic LHTS module having both fins and multiple PCMs

Latent heat thermal storage units span a wide and varied range of applications in the domestic, industrial and space based activities. Numerical investigations on the performance enhancement of a solar dynamic latent heat thermal storage (LHTS) unit employing multiple phase change materials (PCM) and fins are made. The LHTS unit has been studied for the charging mode alone. Enthalpy based formulation of the energy equations governing the behaviour of the LHTS system has been made and compared with the response of a single PCM unit. The governing conjugate equations have been solved employing finite difference techniques. The results show an appreciable enhancement in the rate of melting of PCM and nearly uniform exit temperature of heat transfer fluid (HTF) in the multiple PCM LHTS unit.     

Optimization of a thermal storage unit combined with a biomass boiler for heating buildings

The performance of a boiler with a built-in thermal storage unit is presented. The thermal storage unit is an insulated water tank that absorbs surplus heat from the boiler. The stored heat in the thermal storage unit makes it possible to heat even when the boiler is not operating, thus increasing the heating efficiency. A system with three components is described. The model of the system and the mathematical model were made using the TRNSYS program package and a test reference year (TRY). The degree of efficiency, which optimizes the thermal storage volume and the heating power of the boiler, was determined. The thermal storage must also ensure that the heat is stored at the highest possible exergy level, and complete mixing of the water is a condition for optimizing the thermal storage. The matching of the boiler’s heating capacity with the thermal storage unit ensures a supply of heat even when the boiler is not operating.     

Thermal behavior of a porous electric heater

The performance of a proposed porous electric heater is investigated. The porous heater exchanges heat with the working fluid through its large volumetric surface area. As a result, it produces lower surface temperature as compared with the conventional heater for the same imposed heating power. Two mathematical models are presented to describe the thermal behavior of both heaters. Axial diffusion is included in the governing equation of the solid conventional heater. The predictions of both models are compared at different operating conditions where it is found that porous heaters have much better thermal performance than the conventional heaters.     

高温电加热下电阻率与导热系数随温度变化的传热过程模拟

高温、电加热条件下电阻率与导热系数随温度变化明显,因此研究在此条件下的热传导具有十分重要的意义.运用MATLAB中的PDE工具箱,对高温条件下,几种不同材料的发热导体电加热过程中导热系数、电导率变化所引起的导热等问题进行了数值求解.结果表明:当发热导体半径R＞5 cm时,温度的变化对发热导体的导热系数和电导率影响显著.     

Viscous Joule heating MHD–conjugate heat transfer for a vertical flat plate in the presence of heat generation

The problem of steady conjugate heat transfer through an electrically-conducting fluid for a vertical flat plate in the presence of transverse uniform magnetic field taking into account the effects of viscous dissipation, Joule heating, and heat generation is formulated. The general governing equations which include such effects are made dimensionless by means of an apposite transformation. The ultimate resulting equations obtained by introducing the stream function with the similarity variable are solved numerically using the implicit finite difference method for the boundary conditions based on conjugate heat transfer process. A representative set of numerical results for the velocity and temperature profiles, the skin friction coefficients as well as the rate of heat transfer coefficient and the surface temperature distribution are presented graphically and discussed. A comprehensive parametric study is carried out to show the effects of the magnetic parameter, viscous dissipation parameter, Joule heating parameter, conjugate conduction parameter, heat generation parameter and the Prandtl number on the obtained solutions.     

Reconstruction of local heat fluxes in pool boiling experiments along the entire boiling curve from high resolution transient temperature measurements

In this paper, we consider a transient inverse heat conduction problem (IHCP) defined on an irregular three-dimensional (3D) domain in pool boiling experiments. Heat input to a circular copper heater of 35 mm diameter and 7 mm thickness is provided by a resistance heating foil pressed to the bottom of the heater. The heat flux at the inaccessible boiling side is estimated from a number of temperature readings in the heater volume. These temperatures are measured by some high-resolution microthermocouples, which are mounted 3.6 μm below the surface in the test heater. The IHCP is formulated as a mathematical optimization problem and solved by the conjugate gradient (CG) method. The arising partial differential equations (PDEs) are solved using the software package DROPS. A simulation case study is used to validate the performance of the solution approach. Finally, we apply the solution approach to the IHCP in pool boiling experiments. The procedure enables the reconstruction of local instantaneous heat flux distribution on the heater surface at different locations along the boiling curve.     

Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow

This work deals with the study of the steady-state analysis of conjugated heat transfer process for the thermal entrance region of a developed laminar-forced convection flow of a power-law fluid in a circular tube. A known uniform heat flux is applied at the external surface of the tube. The energy equation in the fluid is solved analytically using the integral boundary layer approximation by neglecting the heat generation by viscous dissipation and the axial heat conduction in the fluid. This solution is coupled to the Laplace equation for the solid, where the axial heat conduction effects are taken into account. The governing equations are reduced to an integro-differential equation which is solved by analytical and numerical methods. The results are shown for different parameters such as conduction parameter, α, the aspect ratio of the tube, ε and the index of power-law fluid, n.     

供热机组特性系数及其在折算效率研究中的应用

由于供热机组联合供应电能和热能两种不同质量的能量，对于供热机组的经济性评价尚无完善的评价体系，现行的评价方法虽然从不同的侧面表现了供热机组的经济性，但使用不便，计算复杂，特别是可比性不强。以循环函数为基础，利用供热汽流的综合特性系数，将供热抽汽的能量折算为凝汽机组进汽量、作功量和排汽量，进而在折算特性的基础上以凝汽机组的性能指标分析供热机组的运行经济性。计算实例表明：这种折算特性具有物理意义明确、计算简便等优点，可以用于评价供热机组的运行经济性。     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.     

Heat transfer analysis in a hydromagnetic Walters' B fluid with elastic deformation and Newtonian heating

In this study, a computational investigation is carried out to examine the interaction of heat generation/absorption with elastic deformation in a viscous hydromagnetic Walters’ B model past a stretching surface under the intensity of Newtonian heating. The model equations which are responsible for the motion of the fluid and heat interactions are reworked to ordinary differential equations by the appropriate similarity variables and solved via the homotopy analysis method. The parameters encountered were discussed through graphs and tables. The result reveals among others that the heat generation and Newtionian heating magnifies the temperature across the layer and makes quiescent fluid experience a thermal effect.     

Thermophoretic hydromagnetic dissipative heat and mass transfer with lateral mass flux,heat source,Ohmic heating and thermal conductivity effects: Network simulation numerical study

A two-dimensional mathematical model is presented for the laminar heat and mass transfer of an electrically-conducting, heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule (Ohmic) heating. The Talbot–Cheng–Scheffer–Willis formulation (1980) is used to introduce a thermophoretic coefficient into the concentration boundary layer equation. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable, η. The resulting coupled, nonlinear equations are solved under appropriate transformed boundary conditions using the Network Simulation Method. Computations are performed for a wide range of the governing flow parameters, viz Prandtl number, thermophoretic coefficient (a function of Knudsen number), Eckert number (viscous heating effect), thermal conductivity parameter, heat absorption/generation parameter, wall transpiration parameter, Hartmann number and Schmidt number. The numerical details are discussed with relevant applications. Excellent correlation is achieved with earlier studies due to White (1974) and Chamkha and Issa (2000). The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and nuclear hazards.     

Transient analysis of a solar air heater of the second kind

This paper presents a theoretical analysis along with the experimental validation study of a solar air heater of the second kind. The heater consists of a flat passage between two metallic plates through which the heat transfer fluid air is made to pass by some auxiliary means. Study of the periodic response of different parameters of this solar air heater is attempted. The heat balance equations governing the behaviour of the system are solved explicitly. The results obtained from the analytical expressions for the transient variation of outlet air temperature compare well with experimental data. Predictions are also made regarding effects of different performance parameters of the air heater with variations of air mass flow rate and plate emissivity with the hope of optimizing the collector configuration.     

Natural convection in a triangle enclosure with flush mounted heater on the wall

Natural convection heat transfer has been analyzed numerically in a triangle enclosure with flush mounted heater on vertical wall. Finite difference method is used in solution of governing equations in streamfunction-vorticity form and linear algebraic equations were solved via Successive Under Relaxation (SUR). Governing parameters on heat transfer and flow fields are aspect ratio of triangle, location of heater, length of heater and Rayleigh number. It is observed that the most important parameter on heat transfer and flow field is the position of heater which can be a control parameter for the present system.     

An analytical model to predict the thermal performance of a novel parallel flow packed bed solar air heater

A design of a parallel flow solar air heater with packed material in its upper channel and capable of providing a higher heat flux compared to the conventional non-porous bed double flow systems is presented. An analytical model describing the various temperatures and heat transfer characteristics of such a parallel flow packed bed solar air heater (PFPBSAH) has been developed and employed to study the effects of the mass flow rate and varying porosities of the packed material on its thermal performance. The model employs an iterative solution procedure to solve the governing energy balance equations describing the complex heat and mass exchanges involved. To validate the proposed analytical model, comparisons between theoretical and experimental results showed that good agreement is achieved with reasonable accuracy. Also, PFPBSAH is found to perform more efficiently than the conventional non-porous double flow solar air heaters with 10–20% increase in its thermal efficiency. Furthermore, the effect of the fraction of mass flow rate in the upper or lower flow channel of PFPBSAH device on its performance, has also investigated theoretically. The fraction of the mass flow rate in the respective channels of the PFPBSAH is shown to be dominant parameter in determining the effective thermal efficiency of the heater.     

The coupling of conduction with mixed convection of micropolar fluids past a vertical flat plate

In this paper, the thermo-fluid-dynamic field resulting from the coupling of wall conduction with laminar mixed convection heat transfer of micropolar fluids along a vertical flat plate is studied. A conjugate heat transfer is proposed to serve as a controlling index that indicates the effect of wall conduction. After a suitable coordinate transformation to reduce the complex of the governing boundary layer equations, the resulting nonlinear differential equations were solved with an implicit finite difference method. The effects of the micropolar material parameters, the buoyancy parameter, the Prandtl number and the conjugate heat transfer parameter on the flow and the thermal fields are discussed in detail.     

Thermo-Elastic Analysis of a Cracked Half-Plane Under a Thermal Shock Impact Using the Hyperbolic Heat Conduction Theory

The transient thermal stresses around a crack in a thermo-elastic half-plane are obtained under a thermal shock using the hyperbolic heat conduction theory. Fourier, Laplace transforms and singular integral equations are applied to solve the temperature and thermal stress fields consecutively. The integral equations are solved numerically and the asymptotic fields around the crack tip are obtained. Numerical results show that the hyperbolic heat conduction have significant influence on the dynamic temperature and stress field. It is suggested that to design materials and structures against fracture under thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

Numerical prediction of critical heat flux in pool boiling with the two-fluid model

Three-dimensional numerical simulations of the atmospheric saturated pool boiling are performed with the aim of predicting the critical heat flux. The two-phase mixture in pool boiling is described with the transient two-fluid model. The transient heat conduction in the horizontal heated wall is also solved. Dynamics of vapor generation on the heated wall is modeled through the density of nucleation sites and the bubble residence time on the wall. The heater’s surface is divided into zones, which number per unit area equals the density of nucleation sites, while the location of nucleation site within each zone is determined by a random function. The results show a replenishment of the heater’s surface with water and surface wetting for lower heat fluxes, while heater’s surface dry-out is predicted at critical heat flux values. Also, it is shown that the decrease of nucleation site density leads to the reduction of critical heat flux values. Obtained results of critical heat flux are in good agreement with available measured data. The presented approach is original regarding both the application of the two-fluid two-phase model for the prediction of boiling crisis in pool boiling and the defined boundary conditions at the heated wall surface.