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Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

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Abstract

A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article. The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients. The modeled problem, which is resolved into a non-linear partial differential equation (PDE), is made dimensionless and solved by employing the finite difference method (FDM). The results are displayed through graphs and discussed. The effects of amplitude, frequency of oscillation, wet nature, Peclet number, and other relevant quantities on the distribution of temperature through the fin length and with the dimensionless time are investigated. It is deciphered that the periodic heat transfer gives rise to the wavy nature of the fin thermal profile against time. The analysis is beneficial in the design of fin structures for applications like solar collectors, space/airborne applications, and refrigeration industries.

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Abbreviations

A :

dimensionless thermal conductivity parameter

A b :

area of the fin base (m2)

B :

amplitude of the input temperature

C :

fin taper ratio

C T :

temperature ratio

c p :

specific heat at constant pressure (J·kg−1·K−1)

K :

permeability (m2)

L,:

length of the fin (m)

Le,:

Lewis number

N r :

radiative parameter

N c :

convective parameter

Pe :

Peclet number

T :

local fin temperature (K)

T a :

ambient temperature (K)

T b :

base temperature (K)

T bm :

average base temperature (K)

U :

uniform velocity of the fin (m·s−1)

W :

width (m)

X,:

dimensionless length

b 2 :

variable parameter (K−1)

g :

acceleration due to gravity (m·s−2)

h :

heat transfer coefficient (W·m−2·K−1)

h a :

heat transfer coefficient at the ambient temperature Ta (W·m−2·K−1)

h D :

uniform mass transfer coefficient

i fg :

latent heat of water evaporation (J·kg−1)

k eff :

effective thermal conductivity of the material (W·m−1·K−1)

m 0,m 1 :

constants

m 2 :

wet porous parameter

p :

power index of heat transfer coefficient

t * :

time (s)

t(x):

fin thickness at the distance x (m)

t b :

base thickness of the fin (m)

x :

axial coordinate of the fin (m).

ρ f :

density of the ambient fluid (kg·m−3)

τ :

dimensionless time

ν f :

kinematic viscosity of the ambient fluid (m2·s−1)

θ :

non-dimensional temperature

θ a :

dimensionless ambient temperature

ω :

humidity ratio of the saturated air

ψ * :

frequency of oscillation (s−1)

ψ :

dimensionless frequency of oscillation

ω a :

humidity ratio of the surrounding air

φ,:

porosity

α :

thermal conductivity parameter (K−1)

δ,:

a geometrical quantity that defines the tip semi-fin thickness (m)

σ,:

Stefan-Boltzmann constant (W·m−2·K−4)

ε,:

surface emissivity of the fin

β f :

volumetric thermal expansion coefficient of the ambient fluid (K−1).

a:

ambient

b:

base

f:

fluid.

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Acknowledgements

The authors thank Department of Science and Technology, Govt of India for their support under the DST-FIST Programme for HEIs (No. SR/FST/MS-I/2018/23(C)). The author M. L. KEERTHI is thankful to the University Grants Commission, New Delhi, India (No. CSIR-UGC NET DEC. 2019)/(Student ID: 191620111468) for the financial support in the form of UGC-Junior Research Fellowship.

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Authors and Affiliations

  1. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Karnataka, 577451, India

    B. J. Gireesha & M. L. Keerthi

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  1. B. J. Gireesha
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Correspondence to B. J. Gireesha.

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Gireesha, B.J., Keerthi, M.L. Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin. Appl. Math. Mech.-Engl. Ed. 44, 653–668 (2023). https://doi.org/10.1007/s10483-023-2974-6

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  • DOI: https://doi.org/10.1007/s10483-023-2974-6

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