Analysis of the feasibility of describing unsteady heat conduction processes in dense disperse systems by differential equations accounting for phase interaction characteristics

1970 ◽  
Vol 18 (5) ◽  
pp. 559-565 ◽  
Author(s):  
O. M. Todes ◽  
N. V. Antonishin ◽  
L. E. Simchenko ◽  
V. V. Lushchikov
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Phase Interaction ◽  
Disperse Systems ◽  
Unsteady Heat Conduction

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.

The Numerical Method of Lines facilitates the instruction of unsteady heat conduction in simple solid bodies with convective surfaces

2020 ◽  
pp. 030641902091042
Author(s):  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Method Of Lines ◽  
Adjoint System ◽  
One Dimensional ◽  
First Order ◽  
The Method Of Lines ◽  
Unsteady Heat Conduction

The present study on engineering education addresses the Method of Lines and its variant the Numerical Method of Lines as a reliable avenue for the numerical analysis of one-dimensional unsteady heat conduction in walls, cylinders, and spheres involving surface convection interaction with a nearby fluid. The Method of Lines transforms the one-dimensional unsteady heat conduction equation in the spatial and time variables x, t into an adjoint system of first-order ordinary differential equations in the time variable t. Subsequently, the adjoint system of first-order ordinary differential equations is channeled through the Numerical Method of Lines and the powerful fourth-order Runge–Kutta algorithm. The numerical solution of the adjoint system of first-order ordinary differential equations can be carried out by heat transfer students employing appropriate routines embedded in the computer codes Maple, Mathematica, Matlab, and Polymath. For comparison, the baseline solutions used are the exact, analytical temperature distributions that are available in the heat conduction literature.

Real-time estimation of thermal boundary of unsteady heat conduction system using PID algorithm

2020 ◽  
Vol 153 ◽  
pp. 106395 ◽  
Author(s):  
Shibin Wan ◽  
Peng Xu ◽  
Kun Wang ◽  
Jia Yang ◽  
Shan Li
Keyword(s):  
Heat Conduction ◽  
Real Time ◽  
Time Estimation ◽  
Conduction System ◽  
Pid Algorithm ◽  
Real Time Estimation ◽  
Unsteady Heat Conduction

The Lumped Capacitance Model for Unsteady Heat Conduction in Regular Solid Bodies With Natural Convection to Nearby Fluids Engages the Nonlinear Bernoulli Equation

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Natural Convection ◽  
Heat Equation ◽  
Biot Number ◽  
Bernoulli Equation ◽  
Convective Coefficient ◽  
Unsteady Heat Conduction ◽  
The Mean ◽  
Capacitance Model ◽  
Solid Bodies

For the analysis of unsteady heat conduction in solid bodies comprising heat exchange by forced convection to nearby fluids, the two feasible models are (1) the differential or distributed model and (2) the lumped capacitance model. In the latter model, the suited lumped heat equation is linear, separable, and solvable in exact, analytic form. The linear lumped heat equation is constrained by the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1, where the mean convective coefficient h¯ is affected by the imposed fluid velocity. Conversely, when the heat exchange happens by natural convection, the pertinent lumped heat equation turns nonlinear because the mean convective coefficient h¯ depends on the instantaneous mean temperature in the solid body. Undoubtedly, the nonlinear lumped heat equation must be solved with a numerical procedure, such as the classical Runge–Kutta method. Also, due to the variable mean convective coefficient h¯ (T), the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1 needs to be adjusted to Bil,max=h¯max(V/S)/ks < 0.1. Here, h¯max in natural convection cooling stands for the maximum mean convective coefficient at the initial temperature Tin and the initial time t = 0. Fortunately, by way of a temperature transformation, the nonlinear lumped heat equation can be homogenized and later channeled through a nonlinear Bernoulli equation, which admits an exact, analytic solution. This simple route paves the way to an exact, analytic mean temperature distribution T(t) applicable to a class of regular solid bodies: vertical plate, vertical cylinder, horizontal cylinder, and sphere; all solid bodies constricted by the modified lumped Biot number criterion Bil,max<0.1.

scholarly journals Asymptotic Periodicity for a Class of Partial Integrodifferential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Alejandro Caicedo ◽  
Claudio Cuevas ◽  
Hernán R. Henríquez
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integral Equations ◽  
Integrodifferential Equations ◽  
Materials With Memory ◽  
Asymptotic Periodicity ◽  
With Memory ◽  
Equations With Delay

We study the existence of S-asymptotically ω-periodic solutions for a class of abstract partial integro-differential equations and for a class of abstract partial integrodifferential equations with delay. Applications to integral equations arising in the study of heat conduction in materials with memory are shown.

Solution to shape identification problem of unsteady heat-conduction fields

2003 ◽  
Vol 32 (3) ◽  
pp. 212-226 ◽  
Author(s):  
Eiji Katamine ◽  
Hideyuki Azegami ◽  
Yasuhiro Matsuura
Keyword(s):  
Heat Conduction ◽  
Identification Problem ◽  
Shape Identification ◽  
Unsteady Heat Conduction
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