Analytical and Hybrid Solutions for Heat Transfer in Combined Electroosmotic and Pressure-Driven Flows

2012 ◽  
Author(s):  
L. A. Sphaier
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Integral Transform ◽  
Temperature Fields ◽  
Double Layers ◽  
Driving Mechanisms ◽  
Micro Channels ◽  
Hybrid Solutions ◽  
Axial Heat ◽  
Transfer Problems

This paper presents solutions to heat transfer problems that occur in flow micro-channels driven by the combined effect of electroosmosis and a pressure gradient. Fully developed velocity profiles are considered, and the thermal developing region is analyzed. The solution methodology is based on the Generalized Integral Transform Technique, which leads to fully analytical solution for all presented cases. With the solution of the temperature fields, the behavior of the Nusselt number is investigated for different test-cases. The effects of the flow driving mechanisms, viscous dissipation and Joule heating, as well as axial diffusion are analyzed. The approximated solution with thin Electric Double Layers (EDL) is considered, but cases without this restriction are also analyzed. The cases including axial heat conduction are analyzed for a simplified case of purely electroosmotic-driven flow with a thin-EDL, which leads to a simple analytical solution.

scholarly journals Analytical solution for the 1-D heat transfer equations with radiative loss

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 47-53
Author(s):  
You-Chang Lv ◽  
Man Wang ◽  
Ying-Wei Wang
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Transfer Equation ◽  
Integral Transform ◽  
Radiative Loss ◽  
Heat Transfer Equation ◽  
Transfer Equations ◽  
Type Integral ◽  
Transfer Problems

In this paper, we consider the 1-D heat transfer equation with radiative loss. The variational iterative Sumudu type integral transform is used to obtain the analytical solution for the heat transfer problems. The presented method is efficient and accurate.

Conjugated Heat Transfer in Micro-Channels With a Single Domain Formulation and Integral Transforms

2012 ◽  
Author(s):  
Diego C. Knupp ◽  
Carolina P. Naveira Cotta ◽  
Renato M. Cotta
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Eigenvalue Problem ◽  
Space Variable ◽  
Variable Coefficients ◽  
Single Domain ◽  
Axial Conduction ◽  
Micro Channels ◽  
Conjugated Heat Transfer ◽  
Transfer Problems

The present work is an extension of a novel methodology recently proposed by the authors for the analytical solution of conjugated heat transfer problems in channel flow, here taking into account the axial diffusion effects which are often of relevance in micro-channels. This methodology is based on a single domain formulation, which is proposed for modeling the heat transfer phenomena at both the fluid stream and the channel walls regions. By making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface, the mathematical model is fed with the information concerning the transition of the two domains, unifying the model into a single domain formulation with space variable coefficients. The Generalized Integral Transform Technique (GITT) is then employed in the hybrid numerical-analytical solution of the resulting convection-diffusion problem with variable coefficients. When the axial conduction term is included into the formulation, a non-classical eigenvalue problem must be employed in the solution procedure, which is itself handled with the GITT. In order to covalidate the results obtained by means of this solution path, we have also proposed an alternative solution, including a pseudo-transient term, with the aid of a classical Sturm-Liouville eigenvalue problem. The remarkable results demonstrate the feasibility of this single domain approach in handling conjugated heat transfer problems in micro-channels, as well as when fluid axial conduction cannot be neglected.

Conjugated Heat Transfer in 2-Dimensional Mini and Micro Channels: Influence of Axial Conduction in the Walls

2004 ◽  
Author(s):  
G. Maranzana ◽  
I. Perry ◽  
D. Maillet
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer Coefficient ◽  
Reynolds Numbers ◽  
Analytical Models ◽  
Conductive Heat ◽  
Axial Conduction ◽  
Micro Channels ◽  
Small Reynolds Numbers ◽  
Conjugated Heat Transfer ◽  
Axial Heat

For small Reynolds numbers, conductive heat transfer in the wall of mini-micro channels can become quite multidimensional: the wall heat flux density does not stay uniform and heat transfer mainly occurs at the entrance of the channels. The use of a ID model to invert measurements designed for estimating the convective heat transfer coefficient can lead to misinterpretations such as a variation of the Nusselt number with the Reynolds number. Three analytical models of conjugated heat transfer in channels are proposed, and the potential inversion of measurements is considered. A non-dimensional number M quantifying the relative part of conductive axial heat transfer in walls is introduced.

scholarly journals A variational iteration method integral transform technique for handling heat transfer problems

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 55-61 ◽  
Author(s):  
Yuejin Zhou ◽  
Shun Pang ◽  
Guo Chong ◽  
Xiaojun Yang ◽  
Xiaoding Xu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Integral Transform ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Excess Temperature ◽  
Variational Iteration ◽  
Transfer Equations ◽  
Transfer Problems ◽  
Integral Transform Technique

In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.

scholarly journals SOLVING TRANSIENT INVERSE HEAT TRANSFER PROBLEMS IN COMPLEX GEOMETRIES USING PHYSICS-GUIDED NEURAL NETWORKS (PGNN)

2021 ◽  
Vol 2021 (3) ◽  
pp. 4540-4547
Author(s):  
D. Emonts ◽  
◽  
J. Yang ◽  
R. H. Schmitt ◽  
◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flow ◽  
Input Parameter ◽  
Temperature Fields ◽  
Elastic Behavior ◽  
Transient Temperature ◽  
Complex Geometries ◽  
Inverse Heat Transfer ◽  
Geometric Inspection ◽  
Transfer Problems

Temporally and spatially unstable thermal conditions lead to transient or inhomogeneous thermo-elastic behavior of workpieces during manufacturing or geometric inspection. Temperature monitoring by means of sensors consign transient temperature fields, but do not yield information about the heat flow acting as thermal boundary condition, which is a relevant input parameter for nearly any thermal simulation. Addressing the need for efficient methods, the authors propose an approach to solve inverse heat transfer problems in complex geometries. In the presented study, locally acting heat loads are experimentally investigated based on virtual demonstrators running in FEM. The conducted method shows high potential for transient heat flow modelling in terms of accuracy and computational efficiency.

scholarly journals An integral transform applied to solve the steady heat transfer problem in the half-plane

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 105-111
Author(s):  
Tongqiang Xia ◽  
Shengping Yan ◽  
Xin Liang ◽  
Pengjun Zhang ◽  
Chun Liu
Keyword(s):  
Heat Transfer ◽  
Half Plane ◽  
Laplace Equation ◽  
Integral Transform ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Linear Heat ◽  
Transfer Problems ◽  
Steady Heat

An integral transform operator U[?(t)= 1/? ???? ?(t)?-i?t dt is considered to solve the steady heat transfer problem in this paper. The analytic technique is illustrated to be applicable in the solution of a 1-D Laplace equation in the half-plane. The results are interesting as well as potentially useful in the linear heat transfer problems.

Hybrid Eigenfunction-Discretization Methodology for Solving Convective Heat Transfer Problems

2012 ◽  
Author(s):  
D. J. M. N. Chalhub ◽  
L. A. Sphaier ◽  
L. S. de B. Alves
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Integral Transform ◽  
Integral Transformation ◽  
Temperature Dependent ◽  
Discretization Schemes ◽  
Upwind Discretization ◽  
Transfer Problems ◽  
Approximation Parameter

This paper presents a novel methodology for the solution of problems that include diffusion and advection effects, as naturally occur in convective heat transfer problems. The methodology is based on writing the unknown temperature field in terms of eigenfunction expansions, as traditionally carried-out with the Generalized Integral Transform Technique (GITT). However, a different approach is used for handling advective derivatives. Rather than transforming the advection terms as done in traditional GITT solutions, upwind discretization schemes (UDS) are used prior to the integral transformation. With the introduction of upwind approximations, numerical diffusion is introduced, which can be used to reduce unwanted oscillations that arise at higher Péclet values. This combined methodology is termed the GITT-UDS for convective problems. The procedure is illustrated for a simple case of one-dimensional Burgers’ equation with temperature-dependent velocities. Numerical results are calculated, showing that augmenting the upwind approximation parameter can effectively reduce solution oscillations for higher Péclet values.

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