Simulation Studies on Multimode Heat Transfer from a Square-Shaped Electronic Device with Multiple Discrete Heat Sources

ABSTRACT

The results of a numerical study of the problem of multimode heat transfer from a square-shaped electronic device provided with three identical flush-mounted discrete heat sources are presented here. Air, a radiatively nonparticipating fluid, is taken to be the cooling medium. The heat generated in the discrete heat sources is first conducted through the device, before ultimately being dissipated by convection and surface radiation. The governing partial differential equations for temperature distribution are converted into algebraic form using a finite-volume based finite difference method, and the resulting algebraic equations are subsequently solved using Gauss-Seidel iterative procedure. A grid size of 151 × 91 is used for discretizing the computational domain. The effects of all relevant parameters, including volumetric heat generation, thermal conductivity, convection heat transfer coefficient, and surface emissivity, on various important results, such as the local temperature distribution, the peak temperature of the device, and the relative contributions of convection and surface radiation to heat dissipation from the device, are studied in sufficient detail. The exclusive effect of surface radiation on pertinent results of the present problem is also brought out.     

Combined Mode Conduction and Radiation Heat Transfer in a Porous Medium and Estimation of the Optical Properties of the Porous Matrix

This article deals with the analysis of combined mode conduction and radiation heat transfer in a porous medium, and simultaneous estimation of the optical properties of the porous matrix. Simultaneous solution of the gas- and solid-phase energy equations encompasses local thermal nonequilibrium, while the convective heat exchange term couples the gas- and the solid-phase energy equations. A localized uniform volumetric heat generation zone is the source of heat transfer in the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the solid- and gas-phase energy equations are simultaneously solved using the finite difference method. For a given set of boundary conditions and operating parameters, the computed temperature distribution serves as the exact temperature profile necessary in the estimation of parameters. In the estimation of parameters using inverse analysis, the objective function is minimized using the genetic algorithm. Effects of measurement error, number of generations, population size, crossover probability, and mutation probability are studied in regard to the accuracy of results and the computational time required. Reasonably accurate estimations of extinction coefficient, scattering albedo, and emissivity of the porous matrix are obtained.     

A new ANN driven MCMC method for multi-parameter estimation in two-dimensional conduction with heat generation

This paper proposes a hybrid approach, wherein Markov Chain Monte Carlo (MCMC) simulations are used in a Bayesian framework, in conjunction with artificial neural networks (ANN) for solving an inverse heat conduction problem. The proposed algorithm was tested for the problem of steady state two-dimensional heat conduction from a square slab with uniform volumetric internal heat generation. Two variants of this problem namely: (a) estimation of the convection heat transfer coefficient, h and the thermal conductivity of the material, k given the rate of heat generation q_v and (b) estimation of k and q_v given the heat transfer coefficient h, are considered. For both the problems, temperature data at certain fixed locations in the slab serves as the input. For the purposes of establishing the soundness and efficacy of the algorithm, temperatures obtained by a numerical solution to the governing equation for known values of the parameters to be retrieved are treated as “measured” data. However, white noise was added to these data not only to make the analysis realistic but also to ascertain the robustness of the retrieval methodology. In order to significantly reduce the computational time associated with the MCMC simulations, first, a neural network was trained with limited number of solutions to the forward model. This network was used to replace the forward model (conduction equation) during the process of retrievals with Markov Chain Monte Carlo simulations in a Bayesian framework, thereby making the retrievals hybrid. The performance of the proposed hybrid technique was evaluated for different priors and various levels of noise. Comparisons with retrievals done directly by ANN revealed that the performance of the hybrid method is demonstrably superior, particularly with noisy data.     

The BFGS method for estimating the interface temperature and convection coefficient in ultrasonic welding

An inverse heat transfer problem is investigated in the present study by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to predict the unknown time-dependent heat generation at the weld interface and convection heat transfer coefficient during an ultrasonic metal welding process based on the knowledge of temperature measurements taken on the horn. With known temperature data at some locations on the horn, the inverse solution was rapidly obtained by solving nonlinear direct problem, Central Finite Difference and Simple Step Method. The proposed method which did not need solving adjoint and sensitivity problem revealed the characteristics of high efficiency, lower iterations for a computational algorithm and high accuracy for estimating values even when measurement error was considered. Besides, a comparison of the BFGS method with some previous methods (i.e. CGM, SCGM) was established. These results show that an excellent estimation on interfacial heat generation (or temperature), as well as a convection heat transfer coefficient, can be simultaneously obtained in this study. The current methodology will provide a useful tool to optimize welding conditions in ultrasonic welding.     

Estimation of Internal Heat Generation in a Fin Involving All Modes of Heat Transfer Using Golden Section Search Method

The present work deals with the application of the golden section search method (GSSM) for predicting the internal rate of heat generation to reconstruct a given temperature distribution within a rectangular fin involving all modes of heat transfer. The thermal conductivity has been assumed to be temperature-dependent. The forward problem is numerically solved using an implicit fourth-order Runge–Kutta method, whereas, an inverse problem has been solved using GSSM. In conjunction with GSSM, for the inverse analysis, the effect of inverse crime has been addressed using a different solver operating on fifth-order accurate Runge–Kutta method than that used for synthesizing the input data. A case study of Hastelloy generally used in gas turbine applications is also presented and the effect of measurement error in the temperature distribution has been reported. For pure temperature data, an exact estimation of the internal heat generation rate is done, whereas, even with noisy data, a satisfactory estimation of the heat generation rate is also achieved which is verified from the reconstructed temperature distributions.     

Heat Transfer in a Horizontal Cylinder With Eccentric Surfaces

Heat transfer in horizontal cylinders exposed to free convection and radiation is of importance in many industries. Usually this problem is treated by adopting a concentric geometry, disregarding that the external surface temperature is not uniform. If an eccentric geometry is used, the external surface temperature should have a larger variation, changing the flow around the cylinder and the heat transfer coefficient, either improving or reducing the heat transfer. A numerical analysis is presented of the heat transfer in a horizontal cylinder with an internal isothermal surface eccentric to the external surface that is exposed to air free convection and radiation. The conduction problem was solved analytically and integrated numerically, while the free convection was solved by the PHOENICS software. The parameters analyzed were the ratio of radius, the ratio between the material and air thermal conductivities, the Rayleigh number, the emissivity of the outer surface, and the eccentricity between the external and inner surfaces. The parameters of a proposed equation to estimate the total heat of an eccentric arrangement in terms of the total heat of the corresponding concentric arrangement and the ratio between the convective and conductive thermal resistances were determined for given ratios of radius and eccentricities.     

Heat transfer and entropy analysis for a transparent gas flowing in a tube

Heat transfer by forced convection and radiation in tubes is very important for high‐temperature heat exchangers, which find wide applications in power plants. In addition, the entropy analysis gives insight into the qualitative measure of the heat transfer processes. Consequently, in the present study, forced convection and radiation heat transfer in flow through a tube is considered. The wall and fluid sides temperature rise are predicted for different tube lengths. The entropy analysis is carried out and the influence of tube length and heat transfer coefficient on the volumetric entropy generation are examined. It is found that the wall temperature and the volumetric entropy generation increases as the tube length increases. The point of maximum volumetric entropy generation moves close to the tube inlet as the tube length increases. In addition, the maximum volumetric entropy generation becomes independent of tube length for high heat transfer coefficients. Copyright © 1999 John Wiley & Sons, Ltd.     

Determination of Heat Transfer During Gear Blank Quenching

This article presents experimental and numerical results for the quench of a gear blank in agitated and stagnant oil. The time history of temperature is determined with a whole-domain optimizer technique inverse solution method. This article offers a procedure to calculate the surface heat transfer on the quenched part by utilizing a straightforward minimization of an appropriate norm. The article presents 10 variations in setting up this inverse problem. The results indicate that dividing the boundary of the gear blank into four zones and assigning a fixed heat transfer coefficient or heat flux to each zone yields an average error of 40 K. This error can be reduced by either increasing the number of zones or by allowing the heat transfer coefficient or heat flux to vary within the zones. Of these possibilities, variation of heat transfer within the zones results in a greater reduction of the average error for the required level of computational effort.     

重力热管单线内螺纹分布强化换热实验研究

采用实验方法,研究了不同的内螺纹分布和油浴温度等因素对热管换热特性的影响。实验选用的热管材料为紫铜,外径16 mm,壁厚3 mm,长度为200 mm,传热工质为水,充液率为20%。实验结果表明:在同一油浴温度下,内螺纹重力管的启动特性要优于光滑重力热管。对比不同油浴温度下,布置内螺纹能够有效地降低热管的工作温度。实验选型的内螺纹仅布置在蒸发段不会提高热管的换热系数,而在绝热段和冷凝段布置内螺纹则能够使换热系数显著提升,且随油浴温度的增加,换热系数线性增加。     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Inverse prediction of wall temperature distribution on a cylinder exposed to radiatively active flow

In this study, the unknown wall temperature profile of a cylinder was predicted by applying the inverse method. The temperature profile of the cylinder wall was predicted from the given temperature data at measurement points near the cylinder wall. The cylinder was assumed to represent a typical pipe in a bundle of heat exchange tubes operating in a high temperature system. Radiative heat transfer was incorporated as one of major heat transfer modes to consider a hot gas flow passing over the cylinder. The corresponding inverse problem was solved by minimizing an objective function by applying the iterative conjugate gradient method. A multi-block grid composed of three different blocks was used for better computational accuracy and convenience in locating the measurement points. A new method, which could be applicable to non-symmetric geometry, was adopted to solve the adjoint equation. In this study, the effects of number and location of the measurement points were numerically investigated. When the measurement points were too close to the cylinder, the predicted temperature profile exhibited larger fluctuations. The results have also shown that an appropriate number of measurement points were required to improve the prediction of the boundary temperature profile.     

考虑沸腾和缸内局部传热的缸盖流固耦合传热分析

以某商用车直列6缸柴油机作为研究对象,基于缸内传热模型获得内燃机缸盖和缸套的燃气侧局部传热边界条件;基于均相流沸腾传热模型获得水侧传热边界;实现水侧、燃气侧边界与结构温度场计算的耦合,并判断水腔内沸腾传热的状态。结果表明:缸盖温度计算值与实测值吻合,缸盖最高温度位于缸盖底面两个排气门之间;排气门之间的燃气传热系数和燃气温度均处于较高值,缸内局部传热显著;在缸盖底面中心和排气门附近水腔内的冷却水处于部分发展泡核沸腾状态。     

Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder

Inverse transient heat conduction problems of a multilayered functionally graded (FG) cylinder are presented. The approach is based on measurement of temperature on the outer surface of the cylinder to estimate the heat flux and convection heat transfer coefficient on its inner surface. The non-Fourier heat transfer equation is employed to accurately formulate the problem. The conjugate gradient method (CGM) is used for the optimization procedure and the incremental differential quadrature method (DQM) is applied to solve the direct, sensitivity, and adjoint problems. The accuracy of the presented approach is examined by simulating the exact and noisy data through different examples. Good accuracy of the obtained results validates the presented approach.     

Asymmetrical Non-Uniform Heat Flux Distributions For Laminar Flow Heat Transfer With Mixed Convection In a Horizontal Circular Tube

Non-symmetric heat flux distributions in terms of gravity in solar collector tubes influence buoyancy-driven secondary flow which has an impact on the associated heat transfer and pressure drop performance. In this study the influence of the asymmetry angle (0°, 20°, 30° and 40°) with regard to gravity for non-uniform heat flux boundaries in a horizontal circular tube was investigated numerically. A stainless steel tube with an inner diameter of 62.68 mm, a wall thickness of 5.16 mm, and a length of 10 m was considered for water inlet temperatures ranging from 290 K to 360 K and inlet Reynolds numbers ranging from 130 to 2000. Conjugate heat transfer was modelled for different sinusoidal type outer surface heat flux distributions with a base-level incident heat flux intensity of 7.1 kW/m². It was found that average internal heat transfer coefficients increased with the circumferential span of the heat flux distribution. Average internal and axial local heat transfer coefficients and overall friction factors were at their highest for symmetrical heat flux cases (gravity at 0º) and lower for asymmetric cases. The internal heat transfer coefficients also increased with the inlet fluid temperature and decreased with an increase in the external heat loss transfer coefficient. Friction factors decreased with an increase in fluid inlet temperature or an increase in the external heat loss transfer coefficients of the tube model.     

耦合法在柴油机传热研究中的应用

利用流固耦合的分析方法,将柴油机气缸盖、气缸垫、气缸体、气缸套等柴油机主要零部件以及缸内气体、冷却介质作为一个耦合体,进行燃烧室部件的传热数值模拟实验。其中,冷却水侧的对流换热系数和温度由CFD软件Star-CD对整个水路进行模拟计算获得;底板火力面侧燃气的对流换热系数和温度由GT-POWER软件对缸内工作过程进行模拟获得;缸套燃气侧温度由活塞组——气缸套耦合传热模拟获得。最终的计算结果与实验数据较吻合,可以为柴油机热负荷分析和柴油机设计提供理论依据。     

Heat transfer and temperature jump in a polyatomic gas

A variational principle based on the integro-differential form of the linearised Wang Chang-Uhlenbeck equation, with general boundary conditions, is used to evaluate the heat conducted through a polyatomic gas between parallel plates. The result is an accurate, closed form expression for the heat transfer, valid for all degrees of rarefaction, rational in the inverse Knudsen number, and parametrised by the thermal accommodation coefficients, the heat capacity of the internal modes, full range moments of the Chapman-Enskog solution and half range bracket integrals of the free molecular solution. The temperature jump coefficient is obtained from the high density expansion of the heat flux and is dependent on the thermal accommodation coefficients, the internal heat capacity, and moments of the Chapman-Enskog solution. In the limit of vanishing internal specific heat, both the heat transfer and the temperature jump reduce to results previously given for the monatomic gas.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

缸盖温度场反求方法研究

以柴油机缸盖为研究对象,在流固耦合计算缸盖温度场的基础上,探讨了应用导热反问题理论求解缸盖燃气侧传热边界的方法。开发了基于LM算法的反求程序,有效解决了算法的准确性和收敛性等问题。建立了缸盖温度场与其燃气侧传热边界的BP神经网络,利用遗传算法对该神经网络进行了优化。结果表明:优化后的网络测试样本的输出值相对误差较小,且计算得到的缸盖温度值相对误差也较小。     

Unsteady Forced Convection Heat Transfer Over a Semicircular Cylinder at Low Reynolds Numbers

An unsteady two-dimensional numerical simulation is performed to investigate the laminar forced convection heat transfer for flow past a semicircular cylinder in an unconfined medium. The Reynolds number considered in this study ranges from 50 to 150 with a fixed Prandtl number (Pr = 0.71). Two different configurations of the semicircular cylinder are considered; one when the curved surface facing the flow and the other when the flat surface facing the flow. Fictitious confining boundaries are chosen on the lateral sides of the computational domain that makes the blockage ratio B = 5% in order to make the problem computationally feasible. A finite volume-based technique is used for the numerical computation. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag coefficient, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. It is observed that the heat transfer rate is enhanced substantially when the curved surface is facing the flow in comparison to the case when the flat surface is facing the flow.     

Transient natural convection heat transfer of liquid D-mannitol on a horizontal cylinder

Transient and steady state natural convection heat transfer for D-mannitol on a horizontal cylinder was investigated experimentally at various liquid temperatures and heat input conditions. To clarify the natural convection phenomena of D-mannitol, transient and steady heat transfer coefficients were measured under various liquid temperatures of D-mannitol and periods of heat generation rates from a horizontal platinum cylinder. The platinum cylinder with a diameter of 1 mm and a length of 43.5 mm was used as the test heater in this experiment. Experimental results indicated that the steady heat transfer coefficient of D-mannitol was affected by the liquid temperature. As the liquid temperature increased, it was understood that the effect of liquid temperature weakened. When the period of the heat generation rate was changed, the heat transfer process was divided into natural convection heat transfer and conductive heat transfer. It was considered that the conductive heat transfer was more dominant as the period of the heat generation rate decreased. The empirical correlations of steady and transient heat transfer coefficients for D-mannitol were obtained.