Non-Fourier heat conduction in a plane slab with prescribed boundary heat flux Heat and Mass Transfer 31 (1996) 443-450

1997 ◽  
Vol 32 (6) ◽  
pp. 521-521 ◽  
Author(s):  
A. Barletta ◽  
E. Zanchini
Keyword(s):  
Mass Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Heat And Mass Transfer ◽  
Fourier Heat Conduction ◽  
Plane Slab

scholarly journals Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jiawei Fu ◽  
Keqiang Hu ◽  
Linfang Qian ◽  
Zengtao Chen
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Intensity Factor ◽  
Functionally Graded ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Flux Intensity ◽  
Cylindrical Crack ◽  
Heat Flux Intensity ◽  
Fourier Heat Conduction

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

Comprehesive Solution of Heat Conduction Problem Using Mathematical Model of Heat and Mass Transfer in Permafrost Soils

2014 ◽  
Vol 50 (6) ◽  
pp. 262-266 ◽  
Author(s):  
L. A. Duginov ◽  
N. B. Kutvitskaya ◽  
M. A. Magomedgadzhieva ◽  
E. A. Melˈnikova ◽  
M. Kh. Rozovskii
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Heat And Mass Transfer ◽  
Heat Conduction Problem ◽  
Permafrost Soils

scholarly journals Heat and mass transfer in the process of heat treatment and drying of natural leather with the convective method of energy supply

2021 ◽  
Vol 66 (1) ◽  
pp. 84-92
Author(s):  
A. O. Ol’shanskii ◽  
A. M. Gusarov ◽  
S. V. Zhernosek
Keyword(s):  
Heat Transfer ◽  
Heat Treatment ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Unsteady Heat Conduction

In the work, the authors investigated the possibility of using the results of analytical solutions of the linear differential equations of unsteady heat conduction with constant heat transfer coefficients to calculate the temperature of the material during heat treatment of leathers. Heat treatment of natural leathers as heat-sensitive materials is carried out under mild temperature conditions and high air moisture contents, the temperature does not undergo significant changes, and the heat transfer coefficients change almost linearly. When using analytical solutions, the authors made the assumptions that for small temperature gradients over the cross section of a thin body, the thermal transfer of matter can be neglected and for values of the heat and mass transfer Biot criteria less than unity, the main factor, limiting heat and mass transfer, is the interaction of the evaporation surface of the body with the environment; so, in solving the differential heat equation we can restrict ourselves to one first member of an infinite series. In this case, a piecewise stepwise approximation of all thermophysical characteristics with constant values of these coefficients at the calculated time intervals was applied, which made it possible to take into account the change in the transfer coefficients throughout the entire heat treatment process. Processing of experimental data showed that in low-intensity processes with reliable values of the transfer coefficients, it is possible to use the results of solutions of differential equations of unsteady heat conduction in heat transfer calculations. The results of the study of heat transfer during drying of leather confirm the laws of temperature change established experimentally. Together with experimental studies of drying processes, analytical studies are of great practical importance in the development of new methods for calculating heat and mass transfer in wet bodies.

Mesoscopic Heat Conduction and Onset of Periodicity

2003 ◽  
Author(s):  
Kal Renganathan Sharma
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Time Domain ◽  
Heat Conduction Equation ◽  
Higher Order ◽  
Heat Propagation ◽  
Conduction Equation ◽  
Transient Temperature ◽  
Higher Order Terms ◽  
Fourier Heat Conduction

Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q/∂t2−τr3/3!∂3q/∂t3−…(2) This was obtained by a Taylor series expansion in time domain. Manifestation of higher order terms in the modified Fourier’w law as periodicity in the time domain is considered in this study. When a CWT is maintained at one end of a medium of length L where L is the distance from the isothermal wall beyond which there is no appreciable temperature change from the initial condition during the duration of the study the transient temperature profile is obtained by the method of Laplace transforms. The space averaged heat flux is obtained and upon inversion from Laplace domain found to be a constant for the the case obeying Fourier’s law; 1 − exp(−τ) using the Cattaneo and Vernotte non-Fourier heat conduction equation, and upon introduction of the second derivative in time of the heat flux the expression becomes, 1 − exp(−τ)(Sin(τ) + Cos(τ)). Thus the periodicity in time domain is lost when the higher order terms in the generalized Fourier expression is neglected.

Heat Transfer and Air Diffusion Phenomena in a Bed of Polymer Powder Using Apparent Heat Capacity Method: Application to the Rotational Molding Process

2007 ◽  
Author(s):  
M. Boutaous ◽  
E. Pe´rot ◽  
A. Maazouz ◽  
P. Bourgin ◽  
P. Chantrenne
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat Flux ◽  
Phase Change ◽  
Heat And Mass Transfer ◽  
Granular Media ◽  
Transfer Model ◽  
Melting Front ◽  
Polymer Powder ◽  
Air Diffusion

The process of rotational moulding consists in manufacturing plastic parts by heating a polymer powder in a biaxial rotating mould. In order to optimise the production cycle of this process, a complete simulation model has to be used. This model should describe the phenomena of heat and mass transfer in a moving granular media with phase change, coalescence, sintering, air evacuation and crystallization during the cooling stage. This paper focus on the study of heat and mass transfer in a quiescent polymer powder during the heating stage. An experimental device has been built. It consists in an open plane static mold on which an initial thickness, e, of a polymer powder is deposited. This powder is then heated until it melts. An inverse heat conduction method is used to determine the heat flux and temperature at the interface between the mold and the powder. This interfacial heat flux is taken as a boundary condition in a numerical heat transfer model witch takes into account the heat transfer in granular media with phase change, coalescence, sintering, air bubbles evacuation and rheological behaviour of the polymer. For the numerical simulation of the heat transfer, the apparent specific heat method is used. This approach allows to solve the same energy equation for all the material phases, so one do not have to calculate the melting front evolution. This fine modelling, close to the real physical phenomena makes it possible to estimate the temperature profile and the evolution of the polymer powder characteristics (phase change, air diffusion, viscosity, evolution of the thermophysical properties of the equivalent homogeneous medium, thickness reduction, air volume fraction...). Several results are then presented, and the influence of different parameters, like the thermal contact resistance, the process initial conditions and the polymer’s rheological characteristics are studied and commented. Indeed the predictions of the temperature rises in the polymer bed, agree well with the experimental measurements.

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