Transient heat transfer in superfluid helium

Conference · Thu Jan 01 04:00:00 EST 1981

OSTI ID:5333121

Dresner, L

According to the Goerter-Mellink law, the heat flux in superfluid helium is proportional to the cube root of the temperature gradient. If we use this proportionality in place of Fourier's linear law to derive an equation of heat conduction, we obtain a non-linear partial differential equation. Such equations are usually difficult to solve because we cannot superpose solutions to obtain others. In spite of this, the problem of this paper, the constant-flux problem, can be solved because its temperature profiles are self-similar. Self-similarity means that the temperature profile at one time can be obtained from that at a different time by suitable (different) stretching of the distance and temperature axes of the latter profle. The self-similarity of the temperature profiles is connected with the invariance of the non-linear partial differential equation to certain groups of transformations. We reduce the partial differential equation of heat conduction to an ordinary differential equation, the appropriate solution of which we find without extensive computation. The reduction involves the similarity variables ..delta..T/..sqrt..t and z/..sqrt..t, where ..delta..T is the temperature rise at a distance z from the heated face at a time t after the (constant) heating has begun. Use of these variables should, and does, reduce all of the experimental temperature profiles reported by van Sciver to a single, universal curve. We obtain this curve as well by solving the differential equation; agreement is excellent. In fact agreement with all the experimental data reported by van Sciver is excellent, so that the Goerter-Mellink law seems to be a very successful basis for describing transient heat transfer in superfluid helium.

• Research Organization: Japan Atomic Energy Research Inst., Tokai, Ibaraki
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 5333121
• Report Number(s): CONF-810835-48-DRAFT; ON: DE84007588
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
DIFFERENTIAL EQUATIONS
EQUATIONS
EVEN-EVEN NUCLEI
FLUIDS
HEAT FLUX
HELIUM 4
HELIUM II
HELIUM ISOTOPES
ISOTOPES
LIGHT NUCLEI
MATHEMATICAL MODELS
NUCLEI
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FLUIDS
STABLE ISOTOPES
SUPERFLUIDITY
TEMPERATURE GRADIENTS
TRANSFORMATIONS