scholarly journals Investigation of the boundary layer zone with an aerodynamic flow around an axisymmetric spindle-shaped body for solving conjugate problems of heat and mass transfer

2021 ◽  
Vol 2131 (2) ◽  
pp. 022028
Author(s):  
T Novoselova ◽  
L Tolmacheva ◽  
A Palii ◽  
J Akopdjanyan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Surface Region ◽  
The Body ◽  
Temperature Fields ◽  
Similarity Coefficients ◽  
Near Surface ◽  
Shaped Body

Abstract The article discusses the possibility of calculating the thickness of the boundary layer when flowing around an axisymmetric spindle-shaped body without using empirical similarity coefficients. For this, the use of physical analogy of processes is proposed. The necessary flow conditions are described. The two-dimensional Laplace equation is solved for the near-surface region of the laminar flow around the body, obtained by rotating a curve of a given shape. When solving the problems of conjugate heat transfer, the regularities of the interaction of the flow with the body surface are taken into account, which, as a result, is reduced to the joint solution of the boundary layer equations describing the flow field and the heat conduction equations describing the propagation of temperature fields inside and outside the body. In view of the complexity or impossibility of the analytical solution of such problems, it is customary to resort to numerical methods for solving these equations. Even the numerical solution of the conjugate heat transfer problem is associated with a huge number of calculations, the availability of computing power and significant time costs. Therefore, it is customary to solve such problems in a quasi-stationary approximation, which imposes certain restrictions on the scope of application

Analytical Solution of the Problem of Conjugate Heat Transfer between a Gasdynamic Boundary Layer and Anisotropic Strip

2020 ◽  
pp. 44-59
Author(s):  
V.F. Formalev ◽  
S.A. Kolesnik ◽  
B.A. Garibyan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Conjugate Heat Transfer ◽  
Heat Fluxes ◽  
The Body ◽  
Conductivity Tensor

The paper focuses on the problem of conjugate heat transfer between the thermal-gas-dynamic boundary layer and the anisotropic strip in conditions of aerodynamic heating of aircraft. Under the assumption of an incompressible flow which takes place in the shock layer behind the direct part of the shock wave, we found a new analytical solution for the components of the velocity vector, temperature distribution, and heat fluxes in the boundary layer. The obtained heat fluxes at the interface between the gas and the body are included as boundary conditions in the problem of anisotropic heat conduction in the body. The study introduces an analytical solution to the second initial-boundary value problem of heat conduction in an anisotropic strip with arbitrary boundary conditions at the interfaces, with heat fluxes which are obtained by solving the problem of a thermal boundary layer used at the interface. An analytical solution to the conjugate problem of heat transfer between a boundary layer and an anisotropic body can be effectively used to control, e.g. to reduce, heat fluxes from the gas to the body if the strip material chosen is such that the longitudinal component of the thermal conductivity tensor is many times larger than the transverse component of the thermal conductivity tensor. Such adjustment is possible due to an increase in body temperature in the longitudinal direction, and, consequently, a decrease in the heat flow from the gas to the body, as well as due to a favorable change in the physical characteristics of the gas. Results of numerical experiments are obtained and analyzed

Some Boundary Layer-Porous Wall Coupling Effects in Laminar Flows With Surface Injection

1970 ◽  
Vol 92 (3) ◽  
pp. 257-266
Author(s):  
D. A. Nealy ◽  
P. W. McFadden
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Balance ◽  
Transfer Problem ◽  
Porous Wall ◽  
Laminar Flows ◽  
Stream Velocity ◽  
Axial Conduction ◽  
Boundary Layer Development ◽  
Layer Development

Using the integral form of the laminar boundary layer thermal energy equation, a method is developed which permits calculation of thermal boundary layer development under more general conditions than heretofore treated in the literature. The local Stanton number is expressed in terms of the thermal convection thickness which reflects the cumulative effects of variable free stream velocity, surface temperature, and injection rate on boundary layer development. The boundary layer calculation is combined with the wall heat transfer problem through a coolant heat balance which includes the effect of axial conduction in the wall. The highly coupled boundary layer and wall heat balance equations are solved simultaneously using relatively straightforward numerical integration techniques. Calculated results exhibit good agreement with existing analytical and experimental results. The present results indicate that nonisothermal wall and axial conduction effects significantly affect local heat transfer rates.

scholarly journals Numerical Simulation of Secondary Flow in Gas Turbine Disc Cavities, Including Conjugate Heat Transfer

1996 ◽  
Author(s):  
Y.-H. Ho ◽  
M. M. Athavale ◽  
J. M. Forry ◽  
R. C. Hendricks ◽  
B. M. Steinetz
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Conjugate Heat Transfer ◽  
Gas Flow ◽  
Numerical Study ◽  
Labyrinth Seal ◽  
Temperature Fields ◽  
Heat Transfer Analysis ◽  
Flow Rates ◽  
Turbine Disc

A numerical study of the flow and heat transfer in secondary flow elements of the entire inner portion of the turbine section of the Allison T-56/501D engine is presented. The flow simulation included the interstage cavities, rim seals and associated main path flows, while the energy equation also included the solid parts of the turbine disc, rotor supports, and stator supports. Solutions of the energy equations in these problems usually face the difficulty in specifications of wall thermal boundary conditions. By solving the entire turbine section this difficulty is thus removed, and realistic thermal conditions are realized on all internal walls. The simulation was performed using SCISEAL, an advanced 2D/3D CFD code for predictions of fluid flows and forces in turbomachinery seals and secondary flow elements. The mass flow rates and gas temperatures at various seal locations were compared with the design data from Allison. Computed gas flow rates and temperatures in the rim and labyrinth seal show a fair 10 good comparison with the design calculations. The conjugate heat transfer analysis indicates temperature gradients in the stationary intercavity walls, as well as the rotating turbine discs. The thermal strains in the stationary wall may lead to altered interstage labyrinth seal clearances and affect the disc cavity flows. The temperature, fields in the turbine discs also may lead to distortions that can alter the rim seal clearances. Such details of the flow and temperature fields are important in designs of the turbine sections to account for possible thermal distortions and their effects on the performance. The simulation shows that the present day CFD codes can provide the means to understand the complex flow field and thereby aid the design process.

scholarly journals A finite element analysis on combined convection and conduction in a channel with a thick walled cavity

2014 ◽  
Vol 24 (8) ◽  
pp. 1888-1905 ◽  
Author(s):  
M.M. Rahman ◽  
Hakan Oztop ◽  
S. Mekhilef ◽  
R. Saidur ◽  
A. Chamkha ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Mixed Convection ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Element Analysis ◽  
Content Type ◽  
Combined Convection

Purpose – The purpose of this paper is to examine the effects of thick wall parameters of a cavity on combined convection in a channel. In other words, conjugate heat transfer is solved. Design/methodology/approach – Galerkin weighted residual finite element method is used to solve the governing equations of mixed convection. Findings – The streamlines, isotherms, local and average Nusselt numbers are obtained and presented for different parameters. It is found heat transfer is an increasing function of dimensionless thermal conductivity ratio. Originality/value – The literature does not have mixed convection and conjugate heat transfer problem in a channel with thick walled cavity.

A Two-Dimensional Conjugate Heat Transfer Model for Forced Air Cooling of an Electronic Device

1989 ◽  
Vol 111 (1) ◽  
pp. 41-45 ◽  
Author(s):  
A. Zebib ◽  
Y. K. Wo
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Electronic Device ◽  
Transfer Problem ◽  
Maximum Temperature ◽  
Transfer Model ◽  
Air Cooling ◽  
Two Dimensional ◽  
Component Design ◽  
Forced Air

Thermal analysis of forced air cooling of an electronic component is modeled as a two-dimensional conjugate heat transfer problem. The velocity field in a constricted channel is first computed. Then, for a typical electronic module, the energy equation is solved with allowance for discontinuities in the thermal conductivity. Variation of the maximum temperature with the average air velocity is presented. The importance of our approach in evaluating possible benefits due to changes in component design and the limitations of the two-dimensional model are discussed.

scholarly journals Two conjugate convection boundary-layers of counter forced flow

2018 ◽  
Vol 22 (2) ◽  
pp. 835-846
Author(s):  
Mohamed Mosaad
Keyword(s):  
Heat Transfer ◽  
Boundary Layers ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Forced Flow ◽  
Relative Importance ◽  
Counter Flow ◽  
Wide Range ◽  
Convection Boundary ◽  
Laminar Forced Convection

In this study, the conjugate heat transfer problem of two laminar forced convection boundary-layers of counter flow on the opposite sides of a conductive wall is analyzed by employing the integral method. The analysis is conducted in a dimensionless framework to generalize the solution. The dimensionless parameters affecting the thermal interaction between the two convection layers are deduced from the analysis. These parameters give a measure of the relative importance of interactive heat transfer modes. Mean Nusselt number data are obtained for a wide range of the main affecting parameters.

scholarly journals Solving bio-heat transfer multi-layer equation using Green’s Functions method

2021 ◽  
Vol 2090 (1) ◽  
pp. 012150
Author(s):  
de Oliveira Eduardo Peixoto ◽  
Gilmar Guimaräes
Keyword(s):  
Heat Transfer ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
The Body ◽  
Mathematical Background ◽  
Number Of Layers ◽  
Pennes Equation ◽  
Transfer Problems

Abstract An analytical method using Green’s Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes’ Equation, is presented. Mathematical background on how treating Pennes’ equation and its μ2T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ2T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green’s Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.

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.

Non-Darcian Boundary Layer Flow and Forced Convective Heat Transfer Over a Flat Plate in a Fluid-Saturated Porous Medium

1990 ◽  
Vol 112 (1) ◽  
pp. 157-162 ◽  
Author(s):  
A. Nakayama ◽  
T. Kokudai ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Similarity Solution ◽  
Temperature Fields ◽  
Solid Boundary ◽  
Local Similarity ◽  
Viscous Term ◽  
Inertia Term

The local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium. The full boundary layer equations, which consider the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables deduced from a scale analysis. The results from this local similarity solution are found to be in good agreement with those obtained from a finite difference method. The effects of the convective inertia term, boundary viscous term, and porous inertia term on the velocity and temperature fields were examined in detail. Furthermore, useful asymptotic expressions for the local Nusselt number were derived in consideration of possible physical limiting conditions.

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