Solution of Non-Fourier Temperature Field in a Hollow Sphere under Harmonic Boundary Condition

2015 ◽  
Vol 772 ◽  
pp. 197-203 ◽  
Author(s):  
Amin Bahrami ◽  
Siamak Hosseinzadeh ◽  
Ramin Ghasemiasl ◽  
Morteza Radmanesh
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Hollow Sphere ◽  
Separation Of Variables ◽  
Time Dependent ◽  
Separation Of Variables Method ◽  
Method Of Solution ◽  
Duhamel Integral ◽  
Special Case ◽  
General Time

Analytical solution of the axisymmetric two-dimensional non-Fourier temperature field within a hollow sphere is investigated considering Cattaneo-Vernotte constitutive equation with general time-dependent heat flux. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. Duhamel integral is used for applying the time-dependent boundary conditions. The presented solution is applied to special case of harmonic heat flux on outer surface.

scholarly journals A Theorem for Finding Maximum Temperature in Wet Grinding

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
J. L. González-Santander ◽  
G. Martín
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Field ◽  
Integral Form ◽  
Stationary Regime ◽  
Time Dependent ◽  
Maximum Temperature ◽  
Theoretical Computation ◽  
Constant Heat ◽  
Workpiece Surface

We consider the solutions found in the literature for heat transfer in surface grinding, assuming a constant heat transfer coefficient for the coolant acting on the workpiece surface and a constant or linear heat flux profiles entering into the workpiece. From the integral form of the time-dependent temperature field reached in the workpiece, assuming the previous conditions, we prove that the maximum temperature always occurs in the stationary regime on the workpiece surface within the contact zone between the wheel and the workpiece. This result assures a very rapid method for the theoretical computation of the maximum temperature.

A general time-dependent invariant for and integrability of the quadratic system

1994 ◽  
Vol 444 (1922) ◽  
pp. 643-650 ◽  
Keyword(s):  
Direct Method ◽  
First Integral ◽  
Quadratic System ◽  
Time Dependent ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Linear Polynomial ◽  
A Direct Method ◽  
Special Case ◽  
General Time

We derive a general time-dependent invariant (first integral) for the quadratic system (QS) that requires only one condition on the coefficients of the QS. The general invariant could yield asymptotic behaviour of phase-space trajectories. With more conditions imposed on the coefficients, the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method. For the special case of a linear polynomial invariant where one of the variables is analytically invertible, the solution of the QS is reduced to a quadrature.

Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

2015 ◽  
Vol 32 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi ◽  
S. Bakhshandeh
Keyword(s):  
Heat Flux ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Biological Tissues ◽  
Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Duhamel Integral

AbstractIn this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.

scholarly journals Brief note on heat flow with arbitrary heating rates in a hollow cylinder

2011 ◽  
Vol 15 (1) ◽  
pp. 275-280 ◽  
Author(s):  
K.C. Deshmukh ◽  
S.D. Warbhe ◽  
V.S. Kulkarni
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Hollow Cylinder ◽  
Integral Transform ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Time Dependent ◽  
Internal Boundary ◽  
Heating Rates

In this paper the temperature distribution is determined through a hollow cylinder under an arbitrary time dependent heat flux at the outer surface and zero heat flux at the internal boundary due to internal heat generation within it. To develop the analysis of the temperature field, we introduce the method of integral transform. The results are obtained in a series form in-terms of Bessel?s functions.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Existence of a time-dependent heat flux-related ponderomotive effect

1980 ◽  
Vol 23 (8) ◽  
pp. 1532 ◽  
Author(s):  
H. Schamel ◽  
Ch. Sack
Keyword(s):  
Heat Flux ◽  
Time Dependent
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