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Thermal stresses and efficiency analysis of a radial porous fin with radiation and variable thermal conductivity and internal heat generation

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Abstract

The porous fin of radial profile is considered in the current analysis along with the radiation and thermal-dependent internal heat generation condition. In addition, two different cases have been examined based on the linear dependency and exponential dependency of thermal conductivity on temperature. The Darcy’s law is used to study the porous nature of fin. The modeled governing equation is a second-order nonlinear ordinary differential equation and is solved via Runge–Kutta–Fehlberg fourth–fifth-order method. The important terms are grouped as dimensionless parameters and discussed their influence on the heat transfer rate and thermal stresses of the fin. The thermal stresses like radial stress and tangential stress are addressed comprehensively and interpreted graphically. Also, the fin efficiency is defined and discussed graphically. It is found that the tangential stress shows higher compression near fin base region and larger tensile stress near tip radius.

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Abbreviations

A:

Thermal conductivity parameter

Cp :

Specific heat at constant pressure (J kg-1 K-1)

CT :

Temperature ratio

Da :

Darcy number

E :

Young’s modulus

G :

Generation number

K :

Permeability (m2)

Nr :

Radiation–conduction parameter

R :

Dimensionless radius

R* :

Ratio of tip radius to base radius

Ra :

Rayleigh number

T :

Local fin temperature (K)

T ∞ :

Ambient temperature (K)

T b :

Base temperature (K)

b2 :

Variable parameter (K-1)

g:

Acceleration due to gravity (m s-2)

h :

Heat transfer coefficient (W m-2 K-1)

k 0 :

Thermal conductivity of the material (W m-1 K-1)

q :

Heat transfer rate (W)

r :

Fin radius (m)

r b :

Base radius (m)

r t :

Tip radius (m)

t :

Fin thickness (m)

ρ f :

Density of the ambient fluid (kg m-3)

νf :

Kinematic viscosity (m2 s-1)

ν:

Poisson’s ratio

θ :

Non-dimensional temperature

ϕ :

Porosity

σ :

Stefan-Boltzmann constant (W m-2 K-4)

σ r ,σ ϕ :

Radial and tangential stress

ε :

Surface emissivity of fin

ε r ,ε ϕ :

Radial and tangential strain

α :

Linear coefficient of thermal expansion

β f :

Volumetric thermal expansion coefficient

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Acknowledgement

The authors thank the Department of Science and Technology, Government of India for their support under DST-FIST programme for HEIs. (Grant No. SR/FST/MS-I/2018/23(C)).

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Authors and Affiliations

  1. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shimoga, India

    G. Sowmya & B. J. Gireesha

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  1. G. Sowmya
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  2. B. J. Gireesha
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Correspondence to B. J. Gireesha.

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Sowmya, G., Gireesha, B.J. Thermal stresses and efficiency analysis of a radial porous fin with radiation and variable thermal conductivity and internal heat generation. J Therm Anal Calorim 147, 4751–4762 (2022). https://doi.org/10.1007/s10973-021-10801-7

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