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Investigation of Heat Transfer in a Porous Annulus with Pulsating Pressure Gradient by Homotopy Analysis Method

  • Research Article - Mechanical Engineering
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Abstract

The present research derives analytical expressions for the heat transfer in a porous annulus with pulsating pressure gradient imposed across the annulus. The governing partial and coupled equations are transformed to ordinary ones by utilizing the similarity variables and then solved analytically using Homotopy Analysis Method (HAM). The analytic solution is expressed in the form of series, and its convergence is analyzed. The resulting temperature distribution, Nusselt number and entropy generation profiles are shown graphically for the different values of the parameters of the problem. A numerical solution has also been obtained to verify the solution by HAM. Good agreement is observed between the two methods.

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Abbreviations

a and b :

a < b Radii

C(η):

Amplitude of the fluctuating component of temperature

f(η):

Radial velocity

k :

Thermal conductivity

M(η):

Steady component of temperature

N(η):

Fluctuating component of temperature

Nu:

Nusselt number

P:

Pressure

Pr:

Prandtl number

Re:

Reynolds number

Res :

Residual

T :

Temperature

t :

Time

u :

Velocity component in the positive direction of r

V 1 :

Constant suction velocity at r = a

V 2 :

Constant suction velocity at r = b

w :

Velocity component in the positive direction of z

α :

Dimensionless parameter characterizing frequency

ϕ :

Phase

φ(r,t):

Arbitrary function of r and t

ν :

Kinematic viscosity

ρ :

Density

σ :

Entropy generation

ω :

Frequency of pulsation of pressure gradient

ζ :

Square of radius ratio

Ω :

Ratio of the rates at which the mass transfer takes place at the two boundaries

*:

Dimensionless

i :

Inner cylinder

o :

Outer cylinder

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Authors and Affiliations

  1. Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran

    M. M. Rashidi, N. Kavyani & M. Keimanesh

  2. Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology, Sector # 7, Banur, Distt Patiala, Punjab, 140601, India

    S. C. Rajvanshi & B. S. Saini

  3. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    I. Pop

Authors
  1. M. M. Rashidi
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  2. S. C. Rajvanshi
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  3. N. Kavyani
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  4. M. Keimanesh
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  5. I. Pop
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  6. B. S. Saini
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Correspondence to I. Pop.

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Rashidi, M.M., Rajvanshi, S.C., Kavyani, N. et al. Investigation of Heat Transfer in a Porous Annulus with Pulsating Pressure Gradient by Homotopy Analysis Method. Arab J Sci Eng 39, 5113–5128 (2014). https://doi.org/10.1007/s13369-014-1140-5

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  • DOI: https://doi.org/10.1007/s13369-014-1140-5

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