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Heat Transfer Performance on Longitudinal Porous Fins with Temperature-Dependent Heat Generation, Heat Transfer Coefficient and Surface Emissivity

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Abstract

Analytical and numerical analyses have been performed to study the problem of the porous fin with temperature-dependent heat generation, heat transfer coefficient and thermal emissivity. This study is performed using Darcy’s model to formulate the heat transfer equation. The partial differential equations have been transformed into an ordinary differential equation using a similarity transformation. The powerful analytical methods called collocation method, the least square method and homotopy analysis method have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem. Also, temperature fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of natural convection parameter Nc, radiation parameter Nr and porosity Sh parameter on the heat transfer rate. As an important outcome, these proposed methods are able to solve a large class of nonlinear problems effectively, more easily and accurately; and thus, it has been widely applicable in engineering and physics.

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Abbreviations

A :

Cross-sectional or profile area

d :

Diameter of fin

h :

Convection heat transfer coefficient

h b :

Convection heat transfer coefficient at the base

k :

Thermal conductivity

K :

Permeability of the porous fin

L :

Fin length

P :

Fin perimeter

q ideal :

Ideal fin heat transfer rate

q :

Fin heat transfer rate

C p :

Specific heat

Ra :

Rayleigh number

Rd :

Radiation–conduction parameter

V w :

Average velocity of the fluid passing through the fin at any point

Nc :

Convection–conduction parameter

Nr :

Surface radiation

Kr :

Thermal conductivity ratio

T :

Temperature

x :

Height coordinate

δ :

Fin thickness

\(\dot{m}\) :

Mass flow rate

CM:

Collocation method

LSM:

Least square method

HAM:

Homotopy analysis method

G :

Generation number

ɛ g :

Internal heat generation parameter

θ a :

Characterize the temperatures of convection

θ s :

Characterize the temperatures of radiation sinks

m :

Convection heat transfer coefficient

α :

Thermal diffusivity

\(\bar{\varepsilon }\) :

Porosity

ε :

Emissivity

ε a :

Emissivity of fin at the radiation sink temperature

ρ :

Density of the fluid

ρ ε :

Electrical density

θ :

Dimensionless temperature

θ b :

Dimensionless radiation ambient temperature

λ :

Variation of surface emissivity

eff:

Porous properties

f :

Fluid properties

b:

Base of fin

s:

Solid properties

a:

Ambient conditions

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

    H. A. Hoshyar & D. D. Ganji

  2. Young Researchers Club, Sari Branch, Islamic Azad University, Sari, Iran

    I. Rahimipetroudi

Authors
  1. H. A. Hoshyar
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  2. I. Rahimipetroudi
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  3. D. D. Ganji
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Correspondence to H. A. Hoshyar.

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Hoshyar, H.A., Rahimipetroudi, I. & Ganji, D.D. Heat Transfer Performance on Longitudinal Porous Fins with Temperature-Dependent Heat Generation, Heat Transfer Coefficient and Surface Emissivity. Iran J Sci Technol Trans Mech Eng 43, 383–391 (2019). https://doi.org/10.1007/s40997-017-0126-9

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  • DOI: https://doi.org/10.1007/s40997-017-0126-9

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