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Determination of heat transfer parameters by use of finite integral transform and experimental data for regular geometric shapes

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Abstract

This article offers a study on estimation of heat transfer parameters (coefficient and thermal diffusivity) using analytical solutions and experimental data for regular geometric shapes (such as infinite slab, infinite cylinder, and sphere). Analytical solutions have a broad use in experimentally determining these parameters. Here, the method of Finite Integral Transform (FIT) was used for solutions of governing differential equations. The temperature change at centerline location of regular shapes was recorded to determine both the thermal diffusivity and heat transfer coefficient. Aluminum and brass were used for testing. Experiments were performed for different conditions such as in a highly agitated water medium (T = 52 °C) and in air medium (T = 25 °C). Then, with the known slope of the temperature ratio vs. time curve and thickness of slab or radius of the cylindrical or spherical materials, thermal diffusivity value and heat transfer coefficient may be determined. According to the method presented in this study, the estimated of thermal diffusivity of aluminum and brass is 8.395 × 10−5 and 3.42 × 10−5 for a slab, 8.367 × 10−5 and 3.41 × 10−5 for a cylindrical rod and 8.385 × 10−5 and 3.40 × 10−5 m2/s for a spherical shape, respectively. The results showed there is close agreement between the values estimated here and those already published in the literature. The TAAD% is 0.42 and 0.39 for thermal diffusivity of aluminum and brass, respectively.

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Abbreviations

A:

Constant

b:

Thickness of sample (m)

Cp :

Specific heat (J/kg-K)

d:

Probe diameter(m)

D:

Sample diameter (m)

H:

Heat transfer coefficient (W/m2 –K)

Jo, J1 :

0th and 1st Order of first kind of Bessel functions

K:

Thermal conductivity (W/m-K)

L:

An operator for Finite Integral Transforms method

M:

Mass of sample (kg)

m:

Slopes of temperature ratio vs time curves, l/s

n:

A characteristic number (n = 0 for infinite slab, n = 1 for infinite cylinder, and n = 2 for sphere)

q:

Heat flux (w?m2)

Q:

Rate of heat transfer (w)

r:

Sistance from the center, m

R:

Radius of an infinite cylinder or a sphere, m

T:

Temperature (°C)

Ti :

Initial temperature (°C)

T∞ :

Medium temperature

x:

distance from the center(m)

α:

Thermal diffusivity (m2/s)

ρ:

Density, kg/m3

ϕ:

Dimensionless temperature ratio

θ:

The temperature difference with ambient temperatures(T- T∞)(°C)

ξ:

Characteristic length (m)

λ:

Root of Eqs. (43)–(45)

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Acknowledgements

The author is grateful to Fars Technological and Environmental Research Center and the Shiraz University of Technology for supporting this work.

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Authors and Affiliations

  1. Department of Petroleum and Gas Engineering, Shiraz University of Technology, Shiraz, Iran

    Mohammad Reza Talaghat & Seyyed Mohammad Jokar

  2. Fars Technological and Environmental Research Center, Shiraz, Iran

    Mohammad Reza Talaghat

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  1. Mohammad Reza Talaghat
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  2. Seyyed Mohammad Jokar
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Correspondence to Mohammad Reza Talaghat.

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Talaghat, M.R., Jokar, S.M. Determination of heat transfer parameters by use of finite integral transform and experimental data for regular geometric shapes. Heat Mass Transfer 53, 3529–3544 (2017). https://doi.org/10.1007/s00231-017-2067-7

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