STEADY HEAT FLOW II: NUMERICAL METHODS

1965 ◽  
pp. 105-127
Author(s):  
H. SCHUH
Keyword(s):  
Numerical Methods ◽  
Heat Flow ◽  
Steady Heat

The combustion of wood. Part I

1946 ◽  
Vol 42 (2) ◽  
pp. 166-182 ◽  
Author(s):  
C. H. Bamford ◽  
J. Crank ◽  
D. H. Malan
Keyword(s):  
Thermal Decomposition ◽  
Temperature Distribution ◽  
Heat Flow ◽  
Thermal Breakdown ◽  
Interesting Problem ◽  
Considerable Time ◽  
Simple Manner ◽  
Thermal Changes ◽  
Wood Part ◽  
Steady Heat

The combustion of wood presents an interesting problem in non-steady heat flow. When wood is heated, the temperature distribution at a given time may be calculated by means of the well-known conduction equation together with the relevant boundary conditions, provided that the temperature is nowhere sufficiently high to cause appreciable thermal decomposition. When this condition does not apply, the calculation becomes much more complicated, since, as has been recognized for a considerable time, the decomposition is exothermic. The general problem, therefore, is to calculate temperatures and rates of decomposition inside a mass of material, the thermal breakdown of which is accompanied by a heat change, given an initial set of conditions, and a known rate of supply of heat to the surface. The theoretical part of this paper aims at solving this problem for the case of sheets of wood heated in a comparatively simple manner. The treatment is, however, general and may be applied to other materials which undergo thermal changes without melting, if the relevant thermal and other constants are inserted.

Momentum transfer and heat flow in liquid helium II

1939 ◽  
Vol 35 (1) ◽  
pp. 114-122 ◽  
Author(s):  
J. F. Allen ◽  
J. Reekie
Keyword(s):  
Thermal Conductivity ◽  
Hydrostatic Pressure ◽  
Heat Flow ◽  
Momentum Transfer ◽  
Liquid Helium ◽  
Liquid Flow ◽  
Glass Capillary ◽  
Considerable Part ◽  
Helium Ii ◽  
Steady Heat

It has been found by one of the authors (1) in collaboration with Dr H. Jones that a flow of heat in liquid He ii is accompanied by what seems to be a transfer of momentum. The effect can be seen when the channel through which the heat and liquid flow consists of a smooth-walled glass capillary, such as shown in Fig. 1a. Due to the high thermal conductivity of He ii, a considerable part of the heat put into the reservoir is carried down through the capillary to the bath. When a steady heat flow exists, a flow of liquid takes place in the opposite direction, and the level of the liquid in the reservoir is seen to be higher than that in the bath. Smooth capillaries, however, produce a rise in level of only 1 or 2 cm. at most, since the viscosity of the liquid is small and hydrostatic pressure pulls the accumulated liquid in the reservoir back through the capillary. When the heat flow is large, violent surging is observed in the reservoir, but there is no further rise in level.

scholarly journals On steady heat flow problem involving Yang-Srivastava-Machado fractional derivative without singular kernel

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 717-721 ◽  
Author(s):  
Ai-Min Yang ◽  
Yang Han ◽  
Jie Li ◽  
Wei-Xing Liu
Keyword(s):  
Heat Flow ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Flow Problem ◽  
Singular Kernel ◽  
Sumudu Transform ◽  
Steady Heat

In this article, we present a new application for the Yang-Srivastava-Machado fractional derivative without singular kernel to the steady heat flow problem. The Sumudu transform is used to find the analytical solution of the fractional-order heat flow.

scholarly journals A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow

2016 ◽  
Vol 20 (2) ◽  
pp. 753-756 ◽  
Author(s):  
Xiao-Jun Yang ◽  
H.M. Srivastava ◽  
Tenreiro Machado
Keyword(s):  
Heat Flow ◽  
Fractional Derivative ◽  
Singular Kernel ◽  
Steady Heat
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