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Indirect measurement of the heat conductivity and specific heat coefficients of homogeneous fluid

Indirekte Messung der Wärmeleitfähigkeit und der spezifischen Wärmekapazität homogener Fluide

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Abstract

The coefficients of heat conductivityk and of specific heatc p have been determined as parameters of a system of differential equations of balance and boundary conditions. The values of the coefficientsk andc p are obtained by solving the inverse convection problem. The inverse convection problem includes a system of differential equations resulting from the mass, momentum and energy balances, the boundary conditions and an additional condition consisting of satisfying the postulate of the minimum squares of differences of the temperatures computed numerically and those measured at given points in the measurement tube.

Zusammenfassung

Die Koeffizientenk undc p der Wärmeleitfähigkeit und der spezifischen Wärmekapazität wurden als Parameter eines Systems von Differenzialgleichungen bestimmt, und zwar durch Lösung des inversen Wärmeleitungs-problems. Neben der Erhaltungssätzen für Masse, Impuls und Energie sowie den Randbedingungen geht das Prinzip der kleinsten Quadrate bezüglich der Temperaturdifferenz aus Berechnungs- und Meßwerten (an bestimmten Punkten des Versuchsrohres) in das Auswerteschema ein.

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Abbreviations

AL:

dimensionless fluid thermal conductivity,k/k s

Bi :

Biot numberαd/k s

c p :

specific heat at constant pressure

d :

inside diameter of tube, 2R

k :

thermal conductivity of the fluid

L o :

dimensionless flange thickness,l o /2R

L k :

dimensionless length tube,l k /2R

L q :

dimensionless length of resistance heater,l q /2R

Me:

power of direct current supplying the resistance heater

p :

pressure

Pe :

Peclet number,Re Pr

Pr :

Prandtl number,vρc p /k

q :

dimensionless power of heater,Me d/(πk s t p dzl q )

r⋆:

radial coordinate

r :

dimensionless radial coordinate,r⋆/2R

r k :

flange radius

r z :

outside radius of tube

R :

inside radius of tube

R k :

dimensionless flange radius,r k /2R

R z :

dimensionless outside radius of tube,r z /2R

Re :

Reynolds number,du/v

t :

temperature

T :

dimensionless temperature, (t−t o )/t p

TS:

dimensionless temperature of external surface of test tube, 103(t s (r)−t o )/t p

u :

fluid average axial velocity

U :

dimensionless fluid axial velocity,v x /u

V :

dimensionless fluid radial velocity,v r /u

w :

wall thickness

X :

dimensionless axial coordinate,x/2R

α :

heat transfer coefficient

ν :

kinematic viscosity

ρ :

fluid density

o :

inlet

p :

surrounding medium

r :

radial direction

s :

solid

x :

axial direction

z :

outside

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Rup, K. Indirect measurement of the heat conductivity and specific heat coefficients of homogeneous fluid. Heat and Mass Transfer 31, 323–328 (1996). https://doi.org/10.1007/BF02184045

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Keywords

  • Boundary Condition
  • Differential Equation
  • Convection
  • Heat Conductivity
  • Energy Balance