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A. Haji-Sheikh
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Proceedings Papers
Kevin D. Cole, Filippo de Monte, Robert L. McMasters, Keith A. Woodbury, A. Haji-Sheikh, James V. Beck
Proc. ASME. IMECE2016, Volume 5: Education and Globalization, V005T06A021, November 11–17, 2016
Paper No: IMECE2016-66605
Abstract
Heat transfer in solids provides an opportunity for students to learn of several boundary conditions: the first kind for specified temperature, the second kind for specified heat flux, and the third kind for specified convection. In this paper we explore the relationship among these types of boundary conditions in steady heat transfer. Specifically, the normalized third kind of boundary condition (convection) produces the first kind condition (specified temperature) for large Biot number, and it produces the second kind condition (specified flux) for small Biot number. By employing a generalized boundary condition, one expression provides the temperature for several combinations of boundary conditions. This combined expression is presented for several simple geometries (slabs, cylinders, spheres) with and without internal heat generation. The bioheat equation is also treated. Further, a number system is discussed for each combination to identify the type of boundary conditions present, which side is heated, and whether internal generation is present. Computer code for obtaining numerical values from the several expressions is available, along with plots and tables of numerical values, at a web site called the Exact Analytical Conduction Toolbox. Classroom strategies are discussed regarding student learning of these issues: the relationship among boundary conditions; a number system to identify the several components of a boundary value problem; and, the utility of a web-based resource for analytical heat-transfer solutions.
Proceedings Papers
Proc. ASME. IMECE2015, Volume 3: Biomedical and Biotechnology Engineering, V003T03A101, November 13–19, 2015
Paper No: IMECE2015-53392
Abstract
Heat conduction in skin tissue is a problem of significant technological importance. A theoretical understanding of such a problem is essential as it may lead to design potential therapeutic measures for needed cancer therapy or novel medical devices for various applications including hyperthermia. To understand the physical phenomenon of energy transport in biological systems a transient model is chosen for this study. The most common transport equation to estimate temperature distribution in humans was developed by H.H. Pennes and is popularly known as the Pennes bioheat transfer equation. A generalized Pennes bioheat transfer equation accounts for the effect of various physical phenomena such as conduction, advection, volumetric heat generation, etc. are considered. In this paper, a general transient form of the Pennes bioheat transfer equation is solved analytically for a multilayer domain. The boundary value problem considers the core of the tissue is maintained at uniform temperature of 37°C, convective cooling is applied to the external surface of the skin and the sidewalls are adiabatic. The computation of transient temperature in multidimensional and multilayer bodies offers unique features. Due to the presence of blood perfusion in the tissue, the reaction term in the Pennes governing equation is modeled similar to a fin term. The eigenvalues may become imaginary, producing eigenfunctions with imaginary arguments. In addition the spacing between the eigenvalues between zero and maximum value varies for different cases; therefore the values need to be determined with precision using second order Newton’s method. A detailed derivation of the temperature solution using the technique of separation of variables is presented in this study. In addition a proof of orthogonality theorem for eigenfunctions with imaginary eigenvalues is also presented. The analytical model is used to study the thermal response of skin tissue to different parameters with the aid of some numerical examples. Results shown in this paper are expected to facilitate a better understand of bioheat transfer in layered tissue such as skin.
Proceedings Papers
Proc. ASME. IMECE2013, Volume 8A: Heat Transfer and Thermal Engineering, V08AT09A060, November 15–21, 2013
Paper No: IMECE2013-63275
Abstract
Analytical study of bioheat transfer is of significant importance for a number of biomedical applications including cryopreservation of tissue and thermal therapy for cancer. A sound fundamental understanding of thermal behavior of tissue in response to an externally applied stimulus helps design effective therapies and protocols. This paper derives an analytical solution in a multi-layer two-dimensional structure with arbitrary, space-dependent heat generation occurring in each layer. This geometry effectively models multiple layers of skin, with heat generation due to cancerous cells in the basal layer. The Pennes bioheat transfer equation is solved for the multi-layer analytically, wherein the temperature in each layer is explicitly a function of space and the thermo-physical properties of the layer. The resulting analytical temperature profile agrees well with finite-element simulations and is also in good agreement with a previously published experimental study. Results derived in this work illustrate the effect of the presence of cancerous cells on the thermal profile of the skin. Further, the model helps to understand the effect of external cooling and heating stimuli.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research-Article
J. Heat Transfer. November 2013, 135(11): 111015.
Paper No: HT-12-1332
Published Online: September 23, 2013
Abstract
The semiconductor industry, following Moore's law, has consistently followed a trajectory of miniaturization that enables design engineers to achieve greater levels of innovation in the same or smaller die footprints. According to Samsung technologists, the next generation of semiconductor technology will cost about $10 billion to create. Alternatively, improved performance through lowering of signal delays can also be achieved using stacked or 3D packaging. With this architectural achievement come cooling challenges as it is difficult to utilize conventional cooling technology and especially when stacking logic and memory processors for high end applications. The accumulation of excessive heat within the stack is a challenge that has caused thermal engineers to focus on the issue of extracting this heat from the system. Thus, one important aspect of design is the ability to obtain an accurate analytical temperature solution of the multilayer stack packages beforehand in order to sustain the reliability of the 3D stack packages albeit for a more simplified configuration. This study addresses the analytical solution of temperature distribution in multilayer bodies by using the Mathematica code developed in this study. The numerical approach using ansys Workbench is discussed, and the results are compared with the one obtained analytically.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research Papers
J. Heat Transfer. September 2009, 131(9): 091702.
Published Online: June 26, 2009
Abstract
This study uses a methodology based on the calculus of variation to determine the heat transfer in passages with two-dimensional velocity fields such as rectangular channels and in the presence of axial conduction. The mathematical procedure is presented and the subsequent numerical computations provide the Nusselt number values. To verify the accuracy of this numerical procedure, the Nusselt number values are acquired for parallel-plate channels and circular pipes and compared with similar data from the Graetz-type exact analyses. Then, rectangular passages are selected to show the capability and a square duct is used to study the domain of accuracy for this procedure. The results for small Peclet numbers lead to a simple correlation for determination of the bulk temperature and they compare well with those obtained from an asymptotic solution.
Proceedings Papers
Proc. ASME. IMECE2007, Volume 5: Electronics and Photonics, 443-449, November 11–15, 2007
Paper No: IMECE2007-43736
Abstract
Microprocessors continue to grow in capabilities, complexity and performance. Microprocessors typically integrate functional components such as logic and level two (L2) cache memory in their architecture. This functional integration of logic and memory results in improved performance of the microprocessor. However, the integration also introduces a layer of complexity in the thermal design and management of microprocessors. As a direct result of functional integration, the power map on a microprocessor is typically highly non-uniform and the assumption of a uniform heat flux across the chip surface has been shown to be invalid post Pentium II architecture. The active side of the die is divided into several functional blocks with distinct power assigned to each functional block. Previous work has been done which includes numerical analysis and thermal Based optimization of a typical package consisting of a non-uniformly powered die, heat spreader, TIM I &II and the base of the heat sink. In this paper, an analytical approach to temperature distribution of a first level package with a non-uniformly powered die is carried out for the first time. The analytical model for two layer bodies developed by Haji-Sheikh et al. is extended to this typical package which is a multilayer body. The solution is to begin by designating each surface heat flux as a volumetric heat source. An inverse methodology will be applied to solve the equations for various surfaces to calculate maximum junction temperature for given multilayer body. Finally validation of the analytical solution will be carried out using developed numerical model.
Proceedings Papers
Proc. ASME. InterPACK2005, Advances in Electronic Packaging, Parts A, B, and C, 675-682, July 17–22, 2005
Paper No: IPACK2005-73486
Abstract
Microprocessors continue to grow in capabilities, complexity and performance. The current generation of microprocessors integrates functional components such as logic and level two (L2) cache memory into the microprocessor architecture. The functional integration of the microprocessor has resulted in better performance of the microprocessor as the clock speed has increased and the instruction execution time has decreased. However, the integration has introduced a layer of complexity to the thermal design and management of microprocessors. As a direct result of function integration, the power map on a microprocessor is highly non-uniform and the assumption of a uniform heat flux across the chip surface is not valid. The objective of this paper is to minimize the thermal resistance of the package by optimizing the distribution of the uniformly powered functional blocks. In order to model the non-uniform power dissipation on the silicon chip, the chip surface area is divided into a 4 × 4 and 6×6 matrix with a matrix space representing a distinct functional block with a constant heat flux. Finally, using a FEM code, an optimization of the positioning of the functional blocks relative to each other was carried out in order to minimize the junction temperature Tj. This analysis has no constraints placed on the redistribution of functional blocks. The best possible Tjmax reduction could thus be found. In reality (and at a later date) constraints must be placed regarding the maximum separation of any 2 (or more) functional blocks to satisfy electrical timing and compute performance requirements. Design guidelines are then suggested regarding the thermal based optimal distribution for any number of functional blocks. The commercial finite element code ANSYS® is used for this analysis.
Journal Articles
Journal:
Journal of Electronic Packaging
Article Type: Research Papers
J. Electron. Packag. March 2009, 131(1): 011005.
Published Online: February 12, 2009
Abstract
Microprocessors continue to grow in capabilities, complexity, and performance. Microprocessors typically integrate functional components such as logic and level two cache memory in their architecture. This functional integration of logic and memory results in improved performance of the microprocessor. However, the integration also introduces a layer of complexity in the thermal design and management of microprocessors. As a direct result of functional integration, the power map on a microprocessor is typically highly nonuniform, and the assumption of a uniform heat flux across the die surface has been shown to be invalid post Pentium II architecture. The active side of the die is divided into several functional blocks with distinct power assigned to each functional block. Previous work ( Kaisare et al., 2005, “Thermal Based Optimization of Functional Block Distributions in a Non-Uniformly Powered Die,” InterPACK 2005, San Francisco, CA, Jul. 17–22 ) has been done, which includes numerical analysis and thermal based optimization of a typical package consisting of a nonuniformly powered die, heat spreader, thermal interface materials I and II, and the base of the heat sink. In this paper, an analytical approach to temperature distribution of a first level package with a nonuniformly powered die is carried out for the first time. The analytical model for two-layer bodies developed by Haji-Sheikh et al. (2003, “Steady-State Heat Conduction in Multi-Layer Bodies,” Int. J. Heat Mass Transfer, 46(13), pp. 2363–2379 ) is extended to this typical package, which is a multilayer body. The solution is to begin by designating each surface heat flux as a volumetric heat source. An inverse methodology is applied to solve the equations for various surfaces to calculate the maximum junction temperature for a given multilayer body. Finally validation of the analytical solution is carried out using previously developed numerical model.
Proceedings Papers
Proc. ASME. IMECE2002, Electronic and Photonic Packaging, Electrical Systems Design and Photonics, and Nanotechnology, 395-423, November 17–22, 2002
Paper No: IMECE2002-39705
Abstract
A systematic experimental method of estimating the extent of the phase front under local thermal non-equilibrium condition in porous media saturated with phase change material has been developed. During phase change in porous medium, the solid matrix and the pore material are under thermodynamic non-equilibrium condition until the phase change process is complete. It is often hypothesized that the solid matrix and the pore material are in local thermal equilibrium (LTE) condition hence, the arrival of the phase front is predicted based on this hypothesis. An understanding of the rate of freezing and thawing in a porous medium undergoing the phase change process is important to permit proper implementation of procedures such as cryopreservation, cryosurgery, and to predict the thermal performance of passive cooling systems for electronic devices. In this paper, a systematic method of estimating the extent of the phase change front is developed. Results show that during the phase change process the porous medium is far from local thermal equilibrium condition.
Proceedings Papers
Proc. ASME. IMECE2004, Heat Transfer, Volume 3, 249-258, November 13–19, 2004
Paper No: IMECE2004-59369
Abstract
The sensitivity coefficients for analyzing the interstitial properties during phase change in porous media are presented. Computation of the sensitivity coefficients is the main objective of this study. Experimentally measured temperature data provide an estimate of the phase front locations used as the state variable for this study. The derivations are based on the assumption that the phase front, X, at a given time, t, is a function of interstitial properties τ t and τ q with all other parameters remaining constant. The properties τ t and τ q are the lag-time in temperature and heat flux, respectively. The analysis includes two types of boundary conditions: prescribed temperature of phase change materials and prescribed temperature for solid matrix. Results for the first case show that for any given ratio τ t /τ q , the sensitivity coefficient decreases asymptotically to zero at large times. Furthermore, the sum of the sensitivity coefficients S t + S q = 0 when τ t /τ q ≈ 1. This is significant information because the variables S t and S q have the same magnitude with opposite signs. This implies that these two sensitivity coefficients become linearly dependent and it will be difficult to predict the values of τ t and τ q in the neighborhood of τ t /τ q ≈ 1. A similar trend but with different sensitivity values are reported for the second case.
Topics:
Porous materials
Proceedings Papers
Proc. ASME. IMECE2006, Heat Transfer, Volume 3, 43-49, November 5–10, 2006
Paper No: IMECE2006-13436
Abstract
Microprocessors continue to grow in capabilities, complexity and performance. Microprocessors typically integrate functional components such as logic and level two (L2) cache memory in their architecture. This functional integration of logic and memory results in improved performance of the microprocessor as the clock speed increases and the instruction execution time has decreased. However, the integration also introduces a layer of complexity to the thermal design and management of microprocessors. As a direct result of function integration, the power map on a microprocessor is typically highly non-uniform and the assumption of a uniform heat flux across the chip surface is not valid. The active side of the die is divided into several functional blocks with distinct power assigned to each functional block. Previous work [1,2] has been done to minimize the thermal resistance of the package by optimizing the distribution of the non-uniform powered functional blocks with different power matrices. This study further gives design guideline and key pointers to minimized thermal resistance for any number of functional blocks for a given non-uniformly powered microprocessor. In this paper, initially (Part I) temperature distribution of a typical package consisting of a uniformly powered die, heat spreader, TIM 1 & 2 and the base of the heat sink is calculated using an approximate analytical model. The results are then compared with a detailed numerical model and the agreement is within 5%. This study follows (Part II) with a thermal investigation of non-uniform powered functional blocks with a different power matrices with focus on distribution of power over die surface with an application of maximum, minimum and average uniform junction temperature over a given die area. This will help to predict the trend of the calculated distribution of power that will lead to the least thermal gradient over a given die area. This trend will further help to come up with design correlations for minimizing thermal resistance for any number of functional blocks for a given non-uniformly powered microprocessor numerically as well as analytically. The commercial finite element code ANSYS® is used for this analysis as a numerical tool.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research Papers
J. Heat Transfer. June 2006, 128(6): 550–556.
Published Online: December 1, 2005
Abstract
This is a theoretical and numerical study of fully developed forced convection in various rectangular ducts. Each duct is filled with porous materials and the Brinkman model describes the laminar fluid flow inside this fully saturated porous passage. A Fourier series solution provides the exact solution for the velocity field. Also, a Fourier series solution can produce the temperature profile for a condition of constant energy input per unit length. This includes two different wall conditions: a uniform wall temperature at any axial location and a locally uniform heat flux over the boundary. The case of constant wall temperature over the entire passage is also accommodated using a special analytical/numerical solution.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Technical Papers
J. Heat Transfer. June 2004, 126(3): 400–409.
Published Online: June 16, 2004
Abstract
Accurate estimation of heat transfer to a fluid passing through a porous medium located between impermeable walls is of practical interest. Generally, the numerical computation of heat transfer to porous media can become time consuming and correlations are needed to enable practitioners to determine this quantity rapidly. In this paper, correlations for two cases are considered: one when porous materials are between two parallel plates and the other when they are within a circular pipe. This presentation includes correlations for both local and average heat transfer coefficients in these two passages for incompressible laminar flow. These correlations require knowledge of local and average heat transfer for unobstructed fluid flowing through these passages with sufficient accuracy. Because existing correlations lack sufficient accuracy, this presentation includes an appendix that emphasizes correlations for heat transfer to fluids passing through unobstructed parallel plate channels and also for circular pipes.
Journal Articles
Journal:
Journal of Electronic Packaging
Article Type: Technical Papers
J. Electron. Packag. September 2003, 125(3): 456–460.
Published Online: September 17, 2003
Abstract
A constant heat transfer coefficient is often assumed in the computation of the temperature distribution along an extended surface. This assumption permits the use of a well-established closed form analytical solution thus simplifying the mathematical complexity of the conservation energy equation. For certain fin geometries, this assumption will lead to poor prediction of the thermal performance of the extended surface especially for tapered and triangular fins. In this study, a generalized analytical solution was developed that permits the computation of heat loss from an extended surface based on variable heat transfer coefficient, fin geometry, and surface curvature. The influence of these parameters on fin efficiency for typical fins is reported.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Technical Papers
J. Heat Transfer. April 2003, 125(2): 257–265.
Published Online: March 21, 2003
Abstract
This study concerns the flow and heat transfer characteristics of a turbulent submerged circular air jet impinging on a horizontal flat surface when free stream turbulence exceeds 20 percent. The turbulent fluctuations of the free stream velocity are the primary aerodynamics influencing heat transfer. Two regions with distinct flow characteristics are observed: the stagnation region, and the wall-jet region. According to the linear form of the energy equation, the surface heat flux may be decomposed into laminar and turbulent components. An inverse methodology can determine the turbulent component of the heat transfer coefficient in the stagnation region and in the wall-jet region as a function of the root mean square value of the fluctuating component of velocity in the bulk flow direction.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Technical Papers
J. Heat Transfer. April 2002, 124(2): 307–319.
Published Online: August 15, 2001
Abstract
The hyperbolic diffusion equation is often used to analyze laser heating of dielectric materials and in thermal processing of nonhomogeneous materials. In this paper, anomalies in existing solutions of the hyperbolic heat equation are identified. In particular, the singularities associated with the interaction of a wave front and a boundary may cause a violation of the imposed boundary condition. This violation may give rise to physically unacceptable results such as a temperature drop due to heating or a temperature rise due to cooling. The development of appropriate remedies for these happenings is a major focus of this paper. In addition, the unique mathematical features of the hyperbolic heat equation are studied and set forth. Green’s function solutions for semi-infinite and infinite bodies are presented. For finite bodies, it is demonstrated that the relevant series solutions need special attention to accelerate their convergence and to deal with certain anomalies.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Technical Papers
J. Heat Transfer. February 2001, 123(1): 24–30.
Published Online: July 10, 2000
Abstract
This paper reports the evaluation of a spectral technique for estimating thermophysical properties. It demonstrates that one can construct a virtual quasi-steady periodic experiment from a limited but properly selected set of transient non-periodic data. In the spectral domain, the phase angles of the responses at different locations relative to a periodic input signal depend on the thermophysical properties. For the purpose of this evaluation, the transient temperature responses to a surface heat flux input are analytically obtained at pre-selected sensor locations. The transient data are converted to periodic data, phase angles are computed, and thermophysical properties are estimated. All deviations from known property values due to numerical errors are reported.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research Papers
J. Heat Transfer. August 1998, 120(3): 568–576.
Published Online: August 1, 1998
Abstract
The frequency domain provides an interesting alternative platform for measuring thermophysical properties. The resulting measurement technique produces reasonably accurate thermophysical data from imprecise surface information. Having a periodic heat flux input at one surface, the thermal diffusivity is obtainable if temperature produces a measurable periodic effect at another location. The analysis shows that only the phase shift is necessary to produce needed information while the boundary conditions can affect the experimental results. This method was tested near room temperature using two different materials: Delrin and 304 stainless steel. The experiments yield accurate thermal diffusivity data for both materials but the data for Delrin exhibit smaller errors. Before performing the experiments, a sensitivity analysis was carried out to determine the best range of frequencies for an experimental investigation.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research Papers
J. Heat Transfer. August 1998, 120(3): 592–599.
Published Online: August 1, 1998
Abstract
Calculation of temperature in high-temperature materials is of current interest to engineers, e.g., the aerospace industry encounters cooling problems in aircraft skins during the flight of high-speed air vehicles and in high-Mach-number reentry of spacecraft. In general, numerical techniques are used to deal with conduction in composite materials. This study uses the exact series solution to predict the temperature distribution in a two-layer body: one orthotropic and one isotropic. Often the exact series solution contains an inherent singularity at the surface that makes the computation of the heat flux difficult. This singularity is removed by introducing a differentiable auxiliary function that satisfies the nonhomogeneous boundary conditions, Finally, an inverse heat conduction technique is used to predict surface temperature and/or heat flux.
Journal Articles
Journal:
Journal of Heat Transfer
Article Type: Research Papers
J. Heat Transfer. May 1998, 120(2): 402–409.
Published Online: May 1, 1998
Abstract
The present research is an experimental study of pool boiling nucleation behavior using flat, smooth surfaces immersed in saturated highly wetting liquids, FC-72 and FC-87. A flush-mounted, copper surface of 10 mm × 10 mm is used as a heat transfer surface, simulating a microelectronic chip surface. At the nucleation incipient points of higher wall superheats with steady increase of heat flux, vapor film blankets the smooth surface and remains on the surface. To predict this film boiling incipience phenomenon from the smooth surface, an incipience map is developed over the boiling curve. When the incipient heat flux is higher than the minimum heat flux (MHF) and the incipient wall superheat value is higher than the transition boiling curve value at the incipient heat flux, the transition from single-phase natural convection to film boiling is observed at the incipient point. To prevent film boiling incipience, a microporous coating is applied over the smooth surface, which decreases incipient wall superheat and increases minimum heat flux. The film boiling incipience should be avoided to take advantage of highly efficient nucleate boiling heat transfer for the cooling of high-heat-flux applications.