Search results for: macroscopic heat conduction models in microchannel

Authors: A. F. Khadrawi

Abstract:

The transient hydrodynamics and thermal behaviors of fluid flow in open-ended vertical parallel-plate porous microchannel are investigated semi-analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number , Darcy number , and thermal relaxation time  on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic heat conduction models. It is found that as  increases the slip in the hydrodynamic and thermal boundary condition increases. This slip in the hydrodynamic boundary condition increases as  increases. Also, the slip in the thermal boundary condition increases as  decreases especially the early stage of time.

Keywords: free convection, hyperbolic heat conduction, macroscopic heat conduction models in microchannel, porous media, vertical microchannel, microchannel thermal, hydrodynamic behavior.

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Authors: Yew Mun Hung, Ching Sze Lim, Tiew Wei Ting, Ningqun Guo

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The effect of streamwise conduction on the thermal characteristics of forced convection for nanofluidic flow in rectangular microchannel heat sinks under isothermal wall has been investigated. By applying the fin approach, models with and without streamwise conduction term in the energy equation were developed for hydrodynamically and thermally fully-developed flow. These two models were solved to obtain closed form analytical solutions for the nanofluid and solid wall temperature distributions and the analysis emphasized details of the variations induced by the streamwise conduction on the nanofluid heat transport characteristics. The effects of the Peclet number, nanoparticle volume fraction, thermal conductivity ratio on the thermal characteristics of forced convection in microchannel heat sinks are analyzed. Due to the anomalous increase in the effective thermal conductivity of nanofluid compared to its base fluid, the effect of streamwise conduction is expected to be more significant. This study reveals the significance of the effect of streamwise conduction under certain conditions of which the streamwise conduction should not be neglected in the forced convective heat transfer analysis of microchannel heat sinks.

Keywords: fin approach, microchannel heat sink, nanofluid, streamwise conduction

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Authors: Yue-Tzu Yang, Shu-Ching Liao

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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/cm² ≦q"≦ 40W/cm². 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.

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

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

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

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Authors: Mansour A. Al Qubeissi

Abstract:

The current paper presents a numerical approach in solving the conjugate heat transfer problems. A heat conduction code is coupled internally with a computational fluid dynamics solver for developing a couple conjugate heat transfer solver. Methodology of treating non-matching meshes at interface has also been proposed. The validation results of 1D and 2D cases for the developed conjugate heat transfer code have shown close agreement with the solutions given by analysis.

Keywords: Computational Fluid Dynamics, Conjugate Heat transfer, Heat Conduction, Heat Transfer

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Authors: Manay E., Sahin B., Yilmaz M., Gelis K.

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In the present study, the pressure drop and laminar convection heat transfer characteristics of nanofluids in microchannel heat sink with square duct are numerically investigated. The water based nanofluids created with Al2O3 and CuO particles in four different volume fractions of 0%, 0.5%, 1%, 1.5% and 2% are used to analyze their effects on heat transfer and the pressure drop. Under the laminar, steady-state flow conditions, the finite volume method is used to solve the governing equations of heat transfer. Mixture Model is considered to simulate the nanofluid flow. For verification of used numerical method, the results obtained from numerical calculations were compared with the results in literature for both pure water and the nanofluids in different volume fractions. The distributions of the particles in base fluid are assumed to be uniform. The results are evaluated in terms of Nusselt number, the pressure drop and heat transfer enhancement. Analysis shows that the nanofluids enhance heat transfer while the Reynolds number and the volume fractions are increasing. The best overall enhancement was obtained at φ=%2 and Re=100 for CuO-water nanofluid.

Keywords: Microchannel Heat Sink, Nanofluid, Heat transfer enhancement, pressure drop

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Authors: A. Amiri Delouei

Abstract:

In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: Functionally graded materials, unsteady heat conduction, cylinder, Temperature distribution.

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Authors: Rahim Jafari, Tuba Okutucu-Özyurt

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The hydrodynamics and heat transfer characteristics of a vaporized elongated bubble in a rectangular microchannel have been simulated based on Cahn-Hilliard phase-field method. In the simulations, the initially nucleated bubble starts growing as it comes in contact with superheated water. The growing shape of the bubble compared well with the available experimental data in the literature.

Keywords: Microchannel, boiling, Cahn-Hilliard method, Two-phase flow, Simulation.

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

Abstract:

Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter N_rc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.

Keywords: Convective boundary, radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate.

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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.

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: Analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction.

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

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: A. M. Tahsini, S. A. Hosseini

Abstract:

In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux and the one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.

Keywords: Aerodynamic heating, Heat conduction, Numerical simulation, Supersonic flight, Launch vehicle.

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: D. Zabala, N. Sánchez, J. Pinto

Abstract:

A transient heat transfer mathematical model for the prediction of temperature distribution in the car body during primer baking has been developed by considering the thermal radiation and convection in the furnace chamber and transient heat conduction governing equations in the car framework. The car cockpit is considered like a structure with six flat plates, four vertical plates representing the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transient heat conduction in each flat plate is modeled by the lumped capacitance method. Comparison with the experimental data shows that the heat transfer model works well for the prediction of thermal behavior of the car body in the curing furnace, with deviations below 5%.

Keywords: Transient heat transfer, car body, lumpedcapacitance, primer baking.

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Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

Abstract:

Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The control volume finite element method (CVFEM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the CVFEM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 2-D cylindrical geometries were considered. In order to establish the suitability of the LBM, the energy equation of the present problem was also solved using the the finite difference method (FDM) of the computational fluid dynamics. The CVFEM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FDM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the CVFEM for the radiative information, results were analyzed for the effects of various parameters such as the boundary emissivity. The results of the LBMCVFEM combination were found to be in excellent agreement with the FDM-CVFEM combination. The number of iterations and the steady state temperature in both of the combinations were found comparable. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature distribution.

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

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Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: Analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition.

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Authors: Ruxandra Barbulescu, Daniel Ioan, Gabriela Ciuprina

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The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and it is regenerated in the Ranvier nodes due to the ion channels allowing the flow across the membrane. For an efficient simulation of populations of neurons, it is important to use reduced order models both for myelinated compartments and for Ranvier nodes and to have control over their accuracy and inner parameters. The paper presents a reduced order model of this neural system which allows an efficient simulation method for the saltatory conduction in myelinated axons. This model is obtained by concatenating reduced order linear models of 1D myelinated compartments and nonlinear 0D models of Ranvier nodes. The models for the myelinated compartments are selected from a series of spatially distributed models developed and hierarchized according to their modeling errors. The extracted model described by a nonlinear PDE of hyperbolic type is able to reproduce the saltatory conduction with acceptable accuracy and takes into account the finite propagation speed of potential. Finally, this model is again reduced in order to make it suitable for the inclusion in large-scale neural circuits.

Keywords: Saltatory conduction, action potential, myelinated compartments, nonlinear, Ranvier nodes, reduced order models, POD.

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Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

Abstract:

In this paper, the 1-D conduction-radiation problem is solved by the lattice Boltzmann method. The effects of various parameters such as the scattering albedo, the conduction–radiation parameter and the wall emissivity are studied. In order to check on the accuracy of the numerical technique employed for the solution of the considered problem, the present numerical code was validated with the published study. The found results are in good agreement with those published

Keywords: Conduction, lattice Boltzmann method, planar medium, radiation.

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Authors: Salah Aljbour, Hiroshi Yamada, Tomohiko Tagawa

Abstract:

A microchannel with two inlets and two outlets was tested as a potential reactor to carry out two-phase catalytic phase transfer reaction with phase separation at the exit of the microchannel. The catalytic phase transfer reaction between benzyl chloride and sodium sulfide was chosen as a model reaction. The effect of operational time on the conversion was studied. By utilizing a multiphase parallel flow inside the microchannel reactor with the aid of a guideline structure, the catalytic phase reaction followed by phase separation could be ensured. The organic phase could be separated completely from one exit and part of the aqueous phase was separated purely and could be reused with slightly affecting the catalytic phase transfer reaction.

Keywords: Green engineering, microchannel reactor, multiphase reaction, process intensification.

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Authors: Saeed Sarabadan, Kamal Rashedi

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This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Dalvir Singh, Somnath Chattopadhyaya

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During welding or flame cutting of metals, the prediction of heat affected zone (HAZ) is critical. There is need to develop a simple mathematical model to calculate the temperature variation in HAZ and derivative analysis can be used for this purpose. This study presents analytical solution for heat transfer through conduction in mild steel plate. The homogeneous and nonhomogeneous boundary conditions are single variables. The full field analytical solutions of temperature measurement, subjected to local heating source, are derived first by method of separation of variables followed with the experimental visualization using infrared imaging. Based on the present work, it is suggested that appropriate heat input characteristics controls the temperature distribution in and around HAZ.

Keywords: Conduction Heat Transfer, Heat Affected Zone (HAZ), Infra-Red Imaging, Numerical Method, Orthogonal Function, Plasma Arc Cutting, Separation of Variables, Temperature Measurement.

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Authors: Po-Jen Su, Huann-Ming Chou

Abstract:

In this article, we used the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: Maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response.

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Authors: U. Prasopchingchana

Abstract:

The temperature distribution and the heat transfer rates through a multi-layer door of a furnace were investigated. The inside of the door was in contact with hot air and the other side of the door was in contact with room air. Radiation heat transfer from the walls of the furnace to the door and the door to the surrounding area was included in the problem. This work is a two dimensional steady state problem. The Churchill and Chu correlation was used to find local convection heat transfer coefficients at the surfaces of the furnace door. The thermophysical properties of air were the functions of the temperatures. Polynomial curve fitting for the fluid properties were carried out. Finite difference method was used to discretize for conduction heat transfer within the furnace door. The Gauss-Seidel Iteration was employed to compute the temperature distribution in the door. The temperature distribution in the horizontal mid plane of the furnace door in a two dimensional problem agrees with the one dimensional problem. The local convection heat transfer coefficients at the inside and outside surfaces of the furnace door are exhibited.

Keywords: Conduction, heat transfer, multi-layer door, natural convection

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

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In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: O. Afshar

Abstract:

A solar receiver is designed for operation under extremely uneven heat flux distribution, cyclic weather, and cloud transient cycle conditions, which can include large thermal stress and even receiver failure. In this study, the effect of different oil velocity on convection coefficient factor and impact of wind velocity on local Nusselt number by Finite Volume Method will be analyzed. This study is organized to give an overview of the numerical modeling using a MATLAB software, as an accurate, time efficient and economical way of analyzing the heat transfer trends over stationary receiver tube for different Reynolds number. The results reveal when oil velocity is below 0.33m/s, the value of convection coefficient is negligible at low temperature. The numerical graphs indicate that when oil velocity increases up to 1.2 m/s, heat convection coefficient increases significantly. In fact, a reduction in oil velocity causes a reduction in heat conduction through the glass envelope. In addition, the different local Nusselt number is reduced when the wind blows toward the concave side of the collector and it has a significant effect on heat losses reduction through the glass envelope.

Keywords: Receiver tube, heat convection, heat conduction, Nusselt number.

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Authors: Huei Chu Weng

Abstract:

This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: Microfluidics, forced convection, thermal creep, second-order boundary conditions.

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Authors: Jianhua Zhou, Yuwen Zhang

Abstract:

A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: Conduction, inverse problems, conjugated gradient method, laser.

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Authors: D Bhargavi, J. Sharath Kumar Reddy

Abstract:

The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γ_p on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: Porous material, channel partially filled with a porous material, axial conduction, viscous dissipation.

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Authors: A. Ashok, K.Satapathy, B. Prerana Nashine

Abstract:

The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.

Keywords: Radiative transfer equation, finite volume method, conduction, transient radiation.

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