scholarly journals Hybrid integral transform analysis of supercooled droplets solidification

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Igor S. Carvalho ◽  
Renato M. Cotta ◽  
Carolina P. Naveira-Cotta ◽  
Manish K. Tiwari
Keyword(s):  
Heat Transfer ◽  
Moving Boundary ◽  
Integral Transform ◽  
Transfer Problem ◽  
Supercooled Liquid ◽  
Interface Temperature ◽  
Physical Parameters ◽  
Liquid Droplets ◽  
Differential Formulation ◽  
Air Stream

The freezing phenomena in supercooled liquid droplets are important for many engineering applications. For instance, a theoretical model of this phenomenon can offer insights for tailoring surface coatings and for achieving icephobicity to reduce ice adhesion and accretion. In this work, a mathematical model and hybrid numerical–analytical solutions are developed for the freezing of a supercooled droplet immersed in a cold air stream, subjected to the three main transport phenomena at the interface between the droplet and the surroundings: convective heat transfer, convective mass transfer and thermal radiation. Error-controlled hybrid solutions are obtained through the extension of the generalized integral transform technique to the transient partial differential formulation of this moving boundary heat transfer problem. The nonlinear boundary condition for the interface temperature is directly accounted for by the choice of a nonlinear eigenfunction expansion base. Also, the nonlinear equation of motion for the freezing front is solved together with the ordinary differential system for the integral transformed temperatures. After comparisons of the solution with previously reported numerical and experimental results, the influence of the related physical parameters on the droplet temperatures and freezing time is critically analysed.

Coupled FEM-BEM Approach for Axisymetrical Heat Transfer Problems

2008 ◽  
Vol 273-276 ◽  
pp. 740-745
Author(s):  
Gennady Mishuris ◽  
Michał Wróbel
Keyword(s):  
Heat Transfer ◽  
Half Space ◽  
Integral Transform ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Nonlocal Boundary ◽  
Fem Analysis ◽  
Nonlocal Boundary Conditions ◽  
Problem Solution ◽  
Infinite Domain

This work deals with a stationary axisymmetrical heat transfer problem in a combined domain. This domain consists of half-space joined with a bounded cylinder. An important feature of the problem is the possible flux singularity along the edge points of the transmission surface. Domain decomposition is used to separate the subdomains. The solution for an auxiliary mixed boundary value problem in the half space is found analytically by means of Hankel integral transform. This allows us to reduce the main problem in the infinite domain to another problem defined in the bounded subdomain. In turn, the new problem contains a nonlocal boundary conditions along the transmission surface. These conditions incorporate all basic information about the infinite sub-domain (material properties, internal sources etc.). The problem is solved then by means of the Finite Element Method. In fact it might be considered as a coupled FEM-BEM approach. We use standard MATLAB PDE toolbox for the FEM analysis. As it is not possible for this package to introduce directly a non-classical boundary condition, we construct an appropriate iterative procedure and show the fast convergence of the main problem solution. The possible solution singularity is taken into account and the corresponding intensity coefficient of the heat flux is computed with a high accuracy. Numerical examples dealing with heat transfer between closed reservoir (filled with some substance) and the infinite foundation are discussed.

Uncoupling the Conjugate Heat Transfer Problem in a Horizontal Plate Under the Influence of a Laminar Flow

2003 ◽  
Author(s):  
Ricardo S. Va´squez ◽  
Antonio J. Bula
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Conjugate Heat Transfer ◽  
Energy Equation ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Interface Temperature ◽  
Horizontal Plate ◽  
Steady State Condition ◽  
Heated Body

The conjugate heat transfer process of cooling a horizontal plate in steady state condition is studied. The model considers both solid and fluid regions in Cartesian coordinates. The problem was solved analytically, considering the fluid flowing in a laminar condition and hydrodynamically developed before any interaction with the heated body. The height of the fluid considered was enough to allow the generation of a thermal boundary layer without any restriction. The conservation of mass, momentum and energy equations were considered to turn the problem into a non dimensional form. The heated body presented a constant heat flux at the bottom side, and convective heat transfer at the top side in contact with the fluid. The other two boundary conditions are adiabatic. The energy equation was considered in the solid to turn it into a non dimensional form. The interface temperature was obtained from a regression using the Chebyshev polynomial approximation. As the problem deals with the cooling of a electronics components, the solution presents the mathematical solution of the energy equation for the solid, including the isothermal lines. The non dimensional form allows a thorough analysis of the problem, considering the influence of the different parameters in the conjugate heat transfer problem. The solution is compared with numerical solution of different problems, and the parameters considered are Reynolds number, plate thickness, Prandtl number, and solid thermal conductivity. The results obtained present isothermal lines, local Nusselt number, and average Nusselt number.

Experimental Study of Droplet Evaporation in a High-Temperature Air Stream

1983 ◽  
Vol 105 (2) ◽  
pp. 384-388 ◽  
Author(s):  
M. Renksizbulut ◽  
M. C. Yuen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Liquid Droplets ◽  
Transfer Number ◽  
Number Range ◽  
Transfer Rates ◽  
Hot Air ◽  
Air Stream ◽  
Stream Density ◽  
Freely Suspended

Heat transfer rates to simulated and freely suspended liquid droplets were measured in an atmospheric hot air tunnel. The experiments were limited to water, methanol, and heptane droplets in a Reynolds number range of 25 to 2000, and a mass transfer number range of 0.07 to 2.79. The present experimental data together with data by others can best be correlated by Nuf(1+Bf).7 = 2 + 0.57 ReM1/2 Prf1/3, where properties are evaluated at film conditions except for the density in the Reynolds number which is the free-stream density. Thus the data shows that at higher temperatures, evaporation reduces heat transfer rates directly by a factor of (1 + Bf).7. Indirectly, evaporation affects heat transfer rates through the changes in both the composition and temperature of the surrounding gaseous medium.

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.

A Technique with a Correction Term for Unsteady State Heat Transfer Problem with Moving Boundary

2016 ◽  
Vol 13 (02) ◽  
pp. 1640010 ◽  
Author(s):  
R. P. Niu ◽  
G. R. Liu ◽  
M. Li
Keyword(s):  
Heat Transfer ◽  
Moving Boundary ◽  
Transfer Problem ◽  
Correction Term ◽  
Heat Transfer Problem ◽  
Unsteady State ◽  
The Finite Element Method ◽  
State Heat ◽  
Time Marching ◽  
Previous Step

The paper proposes a general formulation for simulating unsteady state heat transfer problem with moving boundaries. The method is equipped with a correction term based on the finite element method. In dealing with the unsteady behavior, forward time marching is performed using the finite difference method. We introduce a correction term to effectively deal with the moving boundary effects, which directly uses the nodal temperature at the previous step in the time marching process. A mathematical study has been conducted to examine the theoretical basis. Finally, intensive numerical experiments are conducted to demonstrate effectiveness and stability of the proposed procedure.

scholarly journals On the Thermal Performance of a Microparallel Channels Heat Exchanger

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Ivana Fernandes de Sousa ◽  
Carolina Palma Naveira Cotta ◽  
Daduí Cordeiro Guerrieri ◽  
Manish K. Tiwari
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Exchanger ◽  
Theoretical Analysis ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Coolant Fluid ◽  
Differential Formulation ◽  
Micro Heat Exchanger ◽  
Conjugated Heat Transfer

Abstract This paper presents the experimental and theoretical analysis of a micro heat exchanger designed for the waste heat recovery from a high concentration photovoltaic (HCPV) system. A test bench was built to analyze the thermal behavior of a heat exchanger targeted to work in a similar condition of an existing HCPV panel. A high power heater was encapsulated inside a copper cartridge, covered by thermal insulation, leading to dissipated heat fluxes around 0.6 MW/m2, representative of the heat flux over the solar cell within the HCPV module. The experimental campaign employed water as the coolant fluid and was performed for three different mass flow rates. An infrared camera was used to nonintrusively measure the temperature field over the micro heat exchanger external surface, while thermocouples were placed at the contact between the heat exchanger and the heater, and at the water inlet and outlet ports. In the theoretical analysis, a hybrid numerical–analytical treatment is implemented, combining the numerical simulation through the comsolmultiphysics finite elements code for the micro heat exchanger, and the analytical solution of a lumped-differential formulation for the electrical heater cartridge, offering a substantial computational cost reduction. Such computational simulations of the three-dimensional conjugated heat transfer problem were critically compared to the experimental results and also permitted to inspect the adequacy of a theoretical correlation based on a simplified prescribed heat flux model without conjugation effects. It has been concluded that the conjugated heat transfer problem modeling should be adopted in future design and optimization tasks. The analysis demonstrates the enhanced heat transfer achieved by the microthermal system and confirms the potential in reusing the recovered heat from HCPV systems in a secondary process.

The Effect of Subcooled Liquid on Laminar Film Boiling

1962 ◽  
Vol 84 (2) ◽  
pp. 149-155 ◽  
Author(s):  
E. M. Sparrow ◽  
R. D. Cess
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Transfer Problem ◽  
Film Boiling ◽  
Physical Parameters ◽  
Two Phase ◽  
Fixed Temperature ◽  
Subcooled Liquid ◽  
Flow And Heat Transfer ◽  
Parameter Ranges

Heat-transfer results for film boiling in the presence of a subcooled liquid have been determined analytically for the case of the isothermal vertical plate. The two-phase flow and heat-transfer problem which arises has been formulated exactly within the framework of boundary-layer theory, and free convection within the liquid has been accounted for. At a fixed temperature difference between surface and saturation, the effect of subcooling is to increase the heat transfer from the plate surface, with the magnitude of the increase being controlled by five physical parameters. Graphical presentation of the heat-transfer results is made for parametric values which correspond to water, but this information may be applied to other fluids having similar parameter ranges. For large subcooling, the heat transfer is essentially equal to that for pure free convection (no boiling), and the limits for this condition are given.

scholarly journals A new integral transform with an application in heat-transfer problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 677-681 ◽  
Author(s):  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Integral Transform ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
First Time

In this paper, an new integral transform J[?(?)] =1/? ?0??(?)e??? d? is proposed for the first time. The integral transform is used to solve the differential equation arising in heat-transfer problem.

scholarly journals MHD Flow of a Viscous Fluid over an Exponentially Stretching Sheet in a Porous Medium

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Iftikhar Ahmad ◽  
Muhmmad Sajid ◽  
Wasim Awan ◽  
Muhammad Rafique ◽  
Wajid Aziz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Transfer Problem ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Exponentially Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

Radiation effects on magnetohydrodynamic (MHD) boundary-layer flow and heat transfer characteristic through a porous medium due to an exponentially stretching sheet have been studied. Formulation of the problem is based upon the variable thermal conductivity. The heat transfer analysis is carried out for both prescribed surface temperature (PST) and prescribed heat flux (PHF) cases. The developed system of nonlinear coupled partial differential equations is transformed to nonlinear coupled ordinary differential equations by using similarity transformations. The series solutions for the transformed of the transformed flow and heat transfer problem were constructed by homotopy analysis method (HAM). The obtained results are analyzed under the influence of various physical parameters.

Sign in / Sign up

Export Citation Format

Share Document