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

scholarly journals Analytical study of joint heat transfer between a gasdynamic boundary layer and an anisotropic strip

2020 ◽  
Vol 12 (S) ◽  
pp. 233-243
Author(s):  
Thant ZIN HEIN ◽  
Boris A. GARIBYAN ◽  
Sergey N. VAKHNEEV ◽  
Olga V. TUSHAVINA ◽  
Vladimir F. FORMALEV
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heat Fluxes ◽  
Aerodynamic Heating ◽  
Arbitrary Boundary ◽  
Coupled Heat Transfer

When solving the problems of coupled heat transfer between viscous flows and streamlined bodies under the conditions of aerodynamic heating of aircraft, it is necessary to overcome significant difficulties. They associated primarily with determining the boundary conditions. The paper investigates the joint (coupled) heat transfer between a heat and gas dynamic boundary layer and an anisotropic strip under conditions of aerodynamic heating based on the obtained analytical solution of the second initial boundary value problem of thermal conductivity in an anisotropic strip with arbitrary boundary conditions. Since the system of equations of the gasdynamic boundary layer is essentially nonlinear, mainly numerical methods are used to solve it. For an incompressible boundary layer near the critical point of a blunt wedge, an analytical solution is obtained to determine the components of the velocity vector, density, temperature, and heat fluxes. The closed-form solution to the conjugate problem was received in the form of a Fredholm integral equation of second kind. The results of numerical experiments are obtained and analyzed.

scholarly journals Conjugate heat transfer numerical study of the ejector by means of SU2 solver

2021 ◽  
Vol 2088 (1) ◽  
pp. 012004
Author(s):  
D V Brezgin ◽  
K E Aronson ◽  
F Mazzelli ◽  
A Milazzo
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Conjugate Heat Transfer ◽  
Numerical Study ◽  
Working Fluid ◽  
Static Pressure Distribution ◽  
Flow Parameters ◽  
Permeable Walls ◽  
Solid Bodies

Abstract In this paper, the test supersonic ejector with conjugate heat transfer in solid bodies has been studied numerically. An extensive numerical campaign by means of open-source SU2 solver is performed to analyze the fluid dynamics of the ejector flowfield accounting for the heat conduction in solids. The fluid domain simulation is carried out by employing compressible RANS treatment whilst the heat distribution in solids is predicted by simultaneous solving the steady heat conduction equation. The working fluid is R245fa and all simulations are performed accounting for real gas properties of the refrigerant. Experimental data against numerical results comparison showed close agreement both in terms mass flow rates and static pressure distribution along the walls. Within the CFD trials, the most valuable flow parameters at a wall vicinity are compared: distribution across the boundary layer of the temperature and the turbulent kinetic energy specific dissipation rate, boundary layer displacement and momentum thicknesses. A comprehensive analysis of the simulation results cases with adiabatic walls against cases with heat permeable walls revealed the actual differences of the flow properties in the wall vicinity. However, the ejector performance has not changed noticeably while accounting for the heat conduction in solids.

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
A. Amiri Delouei ◽  
M. Norouzi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Function Technique ◽  
Conductive Heat ◽  
Fiber Reinforced ◽  
Legendre Series

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

Inverse Determination of Steady Heat Convection Coefficient Distributions

1998 ◽  
Vol 120 (2) ◽  
pp. 328-334 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Measurement Data ◽  
Cost Effective ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Simple Modification ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions

An inverse Boundary Element Method (BEM) procedure has been used to determine unknown heat transfer coefficients on surfaces of arbitrarily shaped solids. The procedure is noniterative and cost effective, involving only a simple modification to any existing steady-state heat conduction BEM algorithm. Its main advantage is that this method does not require any knowledge of, or solution to, the fluid flow field. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object, while the heat transfer coefficients on boundaries exposed to a moving fluid can be partially or entirely unknown. Over-specified boundary conditions or internal temperature measurements on other, more accessible boundaries are required in order to compensate for the unknown conditions. An ill-conditioned matrix results from the inverse BEM formulation, which must be properly inverted to obtain the solution to the ill-posed problem. Accuracy of numerical results has been demonstrated for several steady two-dimensional heat conduction problems including sensitivity of the algorithm to errors in the measurement data of surface temperatures and heat fluxes.

scholarly journals ANALYTICAL SOLUTION OF A 2D TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN´S FUNCTIONS

2020 ◽  
Vol 19 (1) ◽  
pp. 66
Author(s):  
J. R. F. Oliveira ◽  
J. A. dos Santos Jr. ◽  
J. G. do Nascimento ◽  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
...  
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transient Heat Conduction Problem

Through the present work the authors determined the analytical solution of a transient two-dimensional heat conduction problem using Green’s Functions (GF). This method is very useful for solving cases where heat conduction is transient and whose boundary conditions vary with time. Boundary conditions of the problem in question, with rectangular geometry, are of the prescribed temperature type - prescribed flow in the direction x and prescribed flow - prescribed flow in the direction y, implying in the corresponding GF given by GX21Y22. The initial temperature of the space domain is assumed to be different from the prescribed temperature occurring at one of the boundaries along x. The temperature field solution of the two-dimensional problem was determined. The intrinsic verification of this solution was made by comparing the solution of a 1D problem. This was to consider the incident heat fluxes at y = 0 and y = 2b tending to zero, thus making the problem one-dimensional, with corresponding GF given by GX21. When comparing the results obtained in both cases, for a time of t = 1 s, it was seen that the temperature field of both was very similar, which validates the solution obtained for the 2D problem.

scholarly journals APPROXIMATE ANALYTICAL SOLUTION OF THE PROBLEM OF CONJUGATE HEAT TRANSFER BETWEEN THE BOUNDARY LAYER AND THE ANISOTROPIC STRIP

2019 ◽  
Vol 16 (32) ◽  
pp. 572-582
Author(s):  
Vladimir F. FORMALEV ◽  
Sergey A. KOLESNIK ◽  
Ekaterina L. KUZNETSOVA
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Integral Transform ◽  
External Boundary ◽  
Interface Boundary ◽  
Heat Flows ◽  
Anisotropic Heat Conduction ◽  
Longitudinal Variable

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed.

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

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