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Numerical Simulation of Flow Through Equilateral Triangular Duct Under Constant Wall Heat Flux Boundary Condition

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Abstract

The force convective heat transfer in an equilateral triangular duct of different wall heat flux configurations was analysed for the laminar hydro-dynamically developed and thermally developing flow by the use of finite volume method. Unstructured meshing was generated by multi-block technique and set of governing equations were discretized using second-order accurate up-wind scheme and numerically solved by SIMPLE Algorithm. For ensuring accuracy, grid independence study was also done. Numerical methodology was verified by comparing results with previous work and predicted results showed good agreement with them (within error of ±5 %). The different combinations of constant heat flux boundary condition were analysed and their effect on heat transfer and fluid flow for different Reynolds number was also studied. The results of different combinations were compared with the case of force convective heat transfer in the equilateral triangular duct with constant heat flux on all three walls.

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Abbreviations

A:

Cross sectional area of the duct (m2)

a:

Side length of the equilateral triangular duct (m)

cp :

Specific heat capacity of air at constant pressure

Dh :

Hydraulic diameter \( \left( { = 4\frac{A}{\text{P}}} \right)\) (m)

f :

Fanning friction factor [dimensionless]

g:

Proportionality factor of Newton’s second law of motion

h:

Height of equilateral triangular duct

\( \bar{h} \) :

Local convective heat transfer coefficient (W/m2K)

havg :

Average convective heat transfer coefficient (W/m2K)

k:

Thermal conductivity of the air (W/m K)

L:

Length of the duct (m)

Nu:

Nusselt number, \( \left( { = {\text{h}}\frac{{D_{h} }}{k}} \right) \) [dimensionless]

m:

Mass flow rate through the duct (kg/s)

P:

Perimeter of the equilateral triangular duct, (= 3.a) m

p:

Pressure (Pa)

Q:

heat carried by the air (J/s)

Re:

Reynolds Number, \( \left( { = \frac{{\rho uD_{h} }}{\mu }} \right) \) [dimensionless]

Tfi :

Fluid temperature at the inlet of the duct (K)

Tfo :

Fluid temperature at the exit of the duct (K)

Tb :

Bulk/Mean temperature of the fluid at the arbitrary cross section along the fluid flow (K)

Tw :

Circumferential duct wall temperature (K)

u, v, w:

velocity components in x, y, and z- directions respectively (m/s)

xfd,h :

Hydrodynamic length (m)

x, y, z:

Coordinate direction (m)

\( \alpha \) :

Thermal diffisivity (m2/s)

\( \mu \) :

Fluid viscosity (Ns m−2)

\( \rho \) :

Fluid density (kg/m3)

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Authors and Affiliations

  1. National Institute of Technology Hamirpur, Hamirpur, 177005, Himachal Pradesh, India

    Rajneesh Kumar, Anoop Kumar & Varun Goel

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  1. Rajneesh Kumar
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  2. Anoop Kumar
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  3. Varun Goel
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Correspondence to Rajneesh Kumar.

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Kumar, R., Kumar, A. & Goel, V. Numerical Simulation of Flow Through Equilateral Triangular Duct Under Constant Wall Heat Flux Boundary Condition. J. Inst. Eng. India Ser. C 98, 313–323 (2017). https://doi.org/10.1007/s40032-016-0290-5

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  • DOI: https://doi.org/10.1007/s40032-016-0290-5

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