Thermomechanical Parameters Due to Fire in Unsteady Heat-Conduction Analysis

1980 ◽  
pp. 135-140 ◽  
Author(s):  
Dietrich Hartmann
Keyword(s):  
Heat Conduction ◽  
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.

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

Electrical Simulation Experiment and the Analysis of Thermal Conductivity of Materials

2014 ◽  
Vol 989-994 ◽  
pp. 599-602
Author(s):  
Wen Bo Li ◽  
Yin Gai Jin ◽  
Shuang Yin ◽  
Pei Yan Chen
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Simulation Experiment ◽  
Simulation Method ◽  
Measuring Method ◽  
Electrical Simulation ◽  
Conductive Plate ◽  
Electric Simulation ◽  
Unsteady Heat Conduction ◽  
Different Shapes

s: Jilin university innovation experiment Electrical Simulation Experiment and the Analysis of Thermal Conductivity of Materials aims to solve the problem of thermocouple measuring tenderness in error. Thermocouple is used to measure temperature when measuring unsteady heat conduction in laboratory. The improved measuring method of unsteady heat conduction puts the breakthrough on the electric simulation method. The text bench is constructed by different shapes of conductive plate which is made of the graphite conductive paint, and voltmeter is refitted by diodes and controlled transformer. Through the test bench, we finished the simulation of unsteady heat conduction under the similar thermal conductive boundary conditions. Finally, the error analysis of experiment and the advantages of electric simulation method are given in this paper.

TRANSIENT HEAT CONDUCTION FROM SPHEROIDS

2014 ◽  
Vol 38 (3) ◽  
pp. 373-389 ◽  
Author(s):  
Rajai Alassar ◽  
Mohammed Abushosha ◽  
Mohammed El-Gebeily
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Dimensionless Temperature ◽  
Legendre Functions ◽  
Axis Ratio ◽  
Spheroidal Wave Functions ◽  
Implicit Finite Difference Scheme ◽  
Unbounded Medium ◽  
Unsteady Heat Conduction ◽  
Limiting Case

We study the unsteady heat conduction from a spheroid (prolate or oblate) initially heated and then left to cool in an unbounded medium of constant temperature. We present two solutions of the problem. The first makes use of the spheroidal wave functions as basis. The second, which is numerical, is obtained by expanding the dimensionless temperature in terms of Legendre functions and then solving the resulting set of differential equations in the radial direction using an implicit finite difference scheme. The two solutions are further verified by comparing them to the limiting case of a sphere. We study the effect of the axis ratio on the time development of temperature inside the spheroid and the heat flux across the surface.

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