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A novel contactless transient method for measuring local values of heat transfer coefficient

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Abstract

This paper presents a new non-contact transient method for measuring the heat transfer coefficient. The proposed method is based on measuring the temperature response of the surface temperature to the heat flux irradiating the same surface, which is affected by the heat transfer coefficient on the back of the surface. The theoretical solution of this problem together with the measured experimental data then enables an evaluation to be made of the local value of the heat transfer coefficient and the corresponding integral value. We present the theoretical foundations, a description of the required experimental setup, the methodology for evaluating the heat transfer coefficient, and an error analysis. The results of forced convection inside the tubes and the incident geometry of the impinging jets in comparison with the experimental results from the literature are presented as validation experiments. Very good agreement is demonstrated and the experimental results obtained by the proposed method lie in the standard range of 10%.

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Abbreviations

a :

thermal diffusivity (m2/s)

A,B,C,D :

model constants (−)

Bi:

Biot number (−)

c p :

specific heat capacity (J/kg K)

C 1,C 2 :

integration constants

d :

inner diameter (m)

E :

error (%)

f :

friction factor (−)

h :

heat transfer coefficient (W/m2 K)

H :

Heaviside function (−)

K :

function (−)

L :

dimension (m)

m,n :

exponents (−)

Nu:

Nusselt number (−)

\(\overline {\text {Nu}}\) :

overall Nusselt number (−)

Pr:

Prandtl number (−)

q :

heat flux rate (W/m2)

\(\dot {Q}\) :

heat flux (W)

r :

radius (m)

r/d :

radial dimensionless coordinate (−)

Re:

Reynolds number (−)

s :

Laplace variable (−)

S :

surface (m2)

t :

time (s)

T :

temperature (∘C, K)

\(\overline {T}\) :

image of temperature (−)

ΔT :

temperature difference (∘C, K)

u :

velocity (m/s)

U :

voltage (V)

x,y,z :

coordinates (−)

z/d :

axial dimensionless coordinate (−)

δ :

wall thickness (m)

𝜖 :

emissivity (−)

λ :

thermal conductivity (W/m K)

λ c :

roots of equation

μ :

dynamic viscosity (Pa s)

ν :

kinematic viscosity (m2/s)

ρ :

density (kg/m3)

subscripts

A:

analytical

f:

fluid

found:

found value

char:

characteristic

L:

liquid

MAX:

maximum

MIN:

minimum

N:

normalized

SET:

set value

x:

at the distance x

w:

wall

0:

initial, at the distance z = 0

∗:

dimensionless

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Acknowledgements

Authors acknowledge support from the Grant Ag. of the Czech Technical University in Prague, grant SGS18/129/ OHK2/2T/12 and support from the EU Operational Programme Research, Development and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague.

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  1. Faculty of Mechanical Engineering, Department of Process Engineering, Czech Technical University in Prague, Technická 4, 166 00, Prague 6, Czech Republic

    Stanislav Solnař, Martin Dostál & Tomáš Jirout

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  1. Stanislav Solnař
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Correspondence to Stanislav Solnař.

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Solnař, S., Dostál, M. & Jirout, T. A novel contactless transient method for measuring local values of heat transfer coefficient. Heat Mass Transfer 57, 1025–1038 (2021). https://doi.org/10.1007/s00231-020-03008-3

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