**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2258

# Search results for: heat equation

##### 2258 Maxwell-Cattaneo Regularization of Heat Equation

**Authors:**
F. Ekoue,
A. Fouache d'Halloy,
D. Gigon,
G Plantamp,
E. Zajdman

**Abstract:**

This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

**Keywords:**
Maxwell-Cattaneo heat transfers equations,
fourierlaw,
heat conduction,
numerical solution.

##### 2257 Average Turbulent Pipe Flow with Heat Transfer Using a Three-Equation Model

**Authors:**
Khalid Alammar

**Abstract:**

Aim of this study is to evaluate a new three-equation turbulence model applied to flow and heat transfer through a pipe. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed flow. Error in the mean axial velocity, temperature, friction, and heat transfer is found to be negligible.

**Keywords:**
Heat Transfer,
Nusselt number,
Skin friction,
Turbulence.

##### 2256 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

**Authors:**
Aziz Sezgin

**Abstract:**

**Keywords:**
Backstepping,
boundary control,
2-D,
3-D,
n-D heat
equation,
distributed parameter systems.

##### 2255 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

**Authors:**
Joan Goh,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail

**Abstract:**

**Keywords:**
Heat equation,
Collocation based,
Cubic Bspline,
Extended cubic uniform B-spline.

##### 2254 Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation

**Authors:**
Raoudha Chaabane,
Faouzi Askri,
Sassi Ben Nasrallah

**Abstract:**

**Keywords:**
heat generation,
cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

##### 2253 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption

**Authors:**
Raphael Zanella

**Abstract:**

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

**Keywords:**
Axisymmetric problem,
continuous finite elements,
heat equation,
weak formulation.

##### 2252 Effect of Gravity Modulation on Weakly Non-Linear Stability of Stationary Convection in a Dielectric Liquid

**Authors:**
P. G. Siddheshwar,
B. R. Revathi

**Abstract:**

The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.

**Keywords:**
Dielectric liquid,
Nusselt number,
amplitude equation.

##### 2251 Heat and Mass Transfer of Triple Diffusive Convection in a Rotating Couple Stress Liquid Using Ginzburg-Landau Model

**Authors:**
Sameena Tarannum,
S. Pranesh

**Abstract:**

A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.

**Keywords:**
Couple stress liquid,
Ginzburg-Landau model,
rotation,
triple diffusive convection.

##### 2250 Numerical Investigation of Non Fourier Heat Conduction in a Semi-infinite Body due to a Moving Concentrated Heat Source Composed with Radiational Boundary Condition

**Authors:**
M. Akbari,
S. Sadodin

**Abstract:**

**Keywords:**
Non-Fourier,
Enthalpy technique,
Melt pool,
Radiational boundary condition

##### 2249 Numerical Analysis of Thermal Conductivity of Non-Charring Material Ablation Carbon-Carbon and Graphite with Considering Chemical Reaction Effects, Mass Transfer and Surface Heat Transfer

**Authors:**
H. Mohammadiun,
A. Kianifar,
A. Kargar

**Abstract:**

**Keywords:**
Ablation rate,
surface recession,
interior temperaturedistribution,
non charring material ablation,
Newton Rafson method.

##### 2248 Investigation of Enhancement of Heat Transfer in Natural Convection Utilizing of Nanofluids

**Authors:**
S. Etaig,
R. Hasan,
N. Perera

**Abstract:**

**Keywords:**
Computational fluid Dynamics,
Natural convection,
Nanofluid and Thermal conductivity.

##### 2247 Convective Heat Transfer of Viscoelastic Flow in a Curved Duct

**Authors:**
M. Norouzi,
M. H. Kayhani,
M. R. H. Nobari,
M. Karimi Demneh

**Abstract:**

**Keywords:**
Viscoelastic,
fluid flow,
heat convection,
CEF
model,
curved duct,
square cross section.

##### 2246 Influence of Artificial Roughness on Heat Transfer in the Rotating Flow

**Authors:**
T. Magrakvelidze,
N. Bantsadze,
N. Lekveishvili,
Kh. Lomidze

**Abstract:**

**Keywords:**
boiling,
heat transfer,
roughness.

##### 2245 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

**Authors:**
Watcharakorn Thongchuay,
Puntip Toghaw,
Montri Maleewong

**Abstract:**

**Keywords:**
Galerkin finite element method,
Heat equation ,
Lagrange basis function,
Wavelet basis function.

##### 2244 Study of Natural Convection Heat Transfer of Plate-Fin Heat Sink in a Closed Enclosure

**Authors:**
Han-Taw Chen,
Tzu-Hsiang Lin,
Chung-Hou Lai

**Abstract:**

**Keywords:**
Inverse method,
FLUENT,
Plate-fin heat sink,
Heat
transfer characteristics.

##### 2243 A Dynamic Equation for Downscaling Surface Air Temperature

**Authors:**
Ch. Surawut,
D. Sukawat

**Abstract:**

**Keywords:**
Dynamic Equation,
Downscaling,
Inverse distance
weight interpolation.

##### 2242 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 2241 Membrane Distillation Process Modeling: Dynamical Approach

**Authors:**
Fadi Eleiwi,
Taous Meriem Laleg-Kirati

**Abstract:**

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated.

**Keywords:**
Membrane distillation,
Dynamical modeling,
Advection-diffusion equation,
Thermal equilibrium,
Heat
equation.

##### 2240 Combining Molecular Statics with Heat Transfer Finite Difference Method for Analysis of Nanoscale Orthogonal Cutting of Single-Crystal Silicon Temperature Field

**Authors:**
Zone-Ching Lin,
Meng-Hua Lin,
Ying-Chih Hsu

**Abstract:**

This paper uses quasi-steady molecular statics model and diamond tool to carry out simulation temperature rise of nanoscale orthogonal cutting single-crystal silicon. It further qualitatively analyzes temperature field of silicon workpiece without considering heat transfer and considering heat transfer. This paper supposes that the temperature rise of workpiece is mainly caused by two heat sources: plastic deformation heat and friction heat. Then, this paper develops a theoretical model about production of the plastic deformation heat and friction heat during nanoscale orthogonal cutting. After the increased temperature produced by these two heat sources are added up, the acquired total temperature rise at each atom of the workpiece is substituted in heat transfer finite difference equation to carry out heat transfer and calculates the temperature field in each step and makes related analysis.

**Keywords:**
Quasi-steady molecular statics,
Nanoscale orthogonal
cutting,
Finite difference,
Temperature.

##### 2239 Study of Heat Transfer in the Absorber Plates of a Flat-Plate Solar Collector Using Dual-Phase-Lag Model

**Authors:**
Yu-Ching Yang,
Haw-Long Lee,
Win-Jin Chang

**Abstract:**

The present work numerically analyzes the transient heat transfer in the absorber plates of a flat-plate solar collector based on the dual-phase-lag (DPL) heat conduction model. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods is used to solve the linear hyperbolic heat conduction equation. This work also examines the effect of different medium parameters on the behavior of heat transfer. Results show that, while the heat-flux phase lag induces thermal waves in the medium, the temperature-gradient phase lag smoothens the thermal waves by promoting non-Fourier diffusion-like conduction into the medium.

**Keywords:**
Absorber plates,
dual-phase-lag,
non-Fourier,
solar collector.

##### 2238 Performance Evaluation of Extruded-Type Heat Sinks Used in Inverter for Solar Power Generation

**Authors:**
Jeong Hyun Kim,
Gyo Woo Lee

**Abstract:**

In this study, heat release performances of the three extruded-type heat sinks can be used in inverter for solar power generation were evaluated. Numbers of fins in the heat sinks (namely E-38, E-47 and E-76) were 38, 47 and 76, respectively. Heat transfer areas of them were 1.8, 1.9 and 2.8m^{2}. The heat release performances of E-38, E-47 and E-76 heat sinks were measured as 79.6, 81.6 and 83.2%, respectively. The results of heat release performance show that the larger amount of heat transfer area the higher heat release rate. While on the other, in this experiment, variations of mass flow rates caused by different cross sectional areas of the three heat sinks may not be the major parameter of the heat release. Despite the 47.4% increment of heat transfer area of E-76 heat sink than that of E-47 one, its heat release rate was higher by only 2.0%; this suggests that its heat transfer area need to be optimized.

**Keywords:**
Solar Inverter,
Heat Sink,
Forced Convection,
Heat Transfer,
Performance Evaluation.

##### 2237 Analyses of Natural Convection Heat Transfer from a Heated Cylinder Mounted in Vertical Duct

**Authors:**
H. Bhowmik,
A. Faisal,
Ahmed Al Yaarubi,
Nabil Al Alawi

**Abstract:**

Experiments are conducted to analyze the steady-state and the power-on transient natural convection heat transfer from a horizontal cylinder mounted in a vertical up flow circular duct. The heat flux ranges from 177 W/m^{2} to 2426 W/m^{2} and the Rayleigh number ranges from 1×10^{4} to 4.35×10^{4}. For natural air flow and constant heat flux condition, the effects of heat transfer around the cylinder under steady-state condition are investigated. The steady-state results compare favorably with that of the available data. The effects of transient heat transfer data on different angular position of the thermocouple (0^{o}, 90^{o}, 180^{o}) are also reported. It is observed that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. In the transient region, the rate of heat transfer obtained at 90^{o} and 180^{o} are higher than that of stagnation point (0^{o}). Finally, the dependence of the average Nusselt number on Rayleigh number for steady and transient natural convection heat transfer are analyzed, and a correlation equation is presented.

**Keywords:**
Steady-state,
transient,
natural convection,
Rayleigh number,
Nusselt number,
Fourier Number.

##### 2236 Analytic and Finite Element Solutions for Temperature Profiles in Welding using Varied Heat Source Models

**Authors:**
Djarot B. Darmadi,
John Norrish,
Anh Kiet Tieu

**Abstract:**

**Keywords:**
Analytic solution,
FEM,
Temperature profile,
HeatSource Model

##### 2235 Human Intraocular Thermal Field in Action with Different Boundary Conditions Considering Aqueous Humor and Vitreous Humor Fluid Flow

**Authors:**
Dara Singh,
Keikhosrow Firouzbakhsh,
Mohammad Taghi Ahmadian

**Abstract:**

In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations.

**Keywords:**
Bio-heat,
Boussinesq,
conduction,
convection,
eye.

##### 2234 Predicting Radiative Heat Transfer in Arbitrary Two and Three-Dimensional Participating Media

**Authors:**
Mohammad Hadi Bordbar,
Timo Hyppänen

**Abstract:**

**Keywords:**
Exchange factor,
Numerical simulation,
Thermal
radiation.

##### 2233 Numerical Study of Heat Release of the Symmetrically Arranged Extruded-Type Heat Sinks

**Authors:**
Man Young Kim,
Gyo Woo Lee

**Abstract:**

In this numerical study, we want to present the design of highly efficient extruded-type heat sink. The symmetrically arranged extruded-type heat sinks are used instead of a single extruded or swaged-type heat sink. In this parametric study, the maximum temperatures, the base temperatures between heaters, and the heat release rates were investigated with respect to the arrangements of heat sources, air flow rates, and amounts of heat input. Based on the results we believe that the use of both side of heat sink is to be much better for release the heat than the use of single side. Also from the results, it is believed that the symmetric arrangement of heat sources is recommended to achieve a higher heat transfer from the heat sink.

**Keywords:**
Heat Sink,
Forced Convection,
Heat Transfer,
Performance Evaluation,
Symmetrically Arranged.

##### 2232 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 2231 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

**Authors:**
F. Rezaie Moghaddam,
J. Amani,
T. Rezaie Moghaddam

**Abstract:**

**Keywords:**
Heat conduction,
Cellular automata,
convergencerate,
discrete system.

##### 2230 Numerical Optimization of Trapezoidal Microchannel Heat Sinks

**Authors:**
Yue-Tzu Yang,
Shu-Ching Liao

**Abstract:**

This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm^{2 }≦** q"**≦ 40W/cm

^{2}. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.

**Keywords:**
Microchannel heat sinks,
Conjugate heat transfer,
Optimization,
Genetic algorithm method.

##### 2229 Effect of Flow Holes on Heat Release Performance of Extruded-type Heat Sink

**Authors:**
Jung Hyun Kim,
Gyo Woo Lee

**Abstract:**

In this study, the enhancement of the heat release performance of an extruded-type heat sink to prepare the large-capacity solar inverter thru the flow holes in the base plate near the heat sources was investigated. Optimal location and number of the holes in the baseplate were determined by using a commercial computation program. The heat release performance of the shape-modified heat sink was measured experimentally and compared with that of the simulation. The heat sink with 12 flow holes in the 18-mm-thick base plate has a 8.1% wider heat transfer area, a 2.5% more mass flow of air, and a 2.7% higher heat release rate than those of the original heat sink. Also, the surface temperature of the base plate was lowered 1.5^{o}C by the holes.

**Keywords:**
Heat Sink,
Forced Convection,
Heat Transfer,
Performance Evaluation,
Flow Holes.