# Analysis of natural convection heat transfer through staggered pin finned horizontal base plate within a rectangular enclosure

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## Abstract

An experimental study of natural convection heat transfer from heat staggered Pin fin array within air filled rectangular enclosure has been performed experimentally. It has been done to analyze the effects of several inducing parameters on system performance. The study has been done at wide ranges of influencing parameters such as Rayleigh number (328,042 ≤ Ra ≤ 794,323) and fin spacing (25 mm ≤ S ≤ 100 mm) and at a given fin height (L = 25 mm). The present study reported that the average Nusselt number (Nu) always increases by increasing Ra. While, by decreasing in fin spacing Nu increases initially up to an extreme value then tends to decrease. The fin effectiveness decreases continuously by increasing in Rayleigh number. It has been found that by decreasing in fin spacing, fin effectiveness increases initially up to a maximum value, beyond which it tends to decrease with further decrease in fin spacing. The correlations are developed for Nu as a function of dimensionless number (S/H) and Rayleigh numbers (Ra) and verified with experimental data.

### Nomenclature

- A
Effective surface area available for heat transfer [m

^{2}]- a
Length of the enclosure [m]

- b
Enclosure width [m]

- g
Acceleration due to gravity [ms

^{−2}]- H
Height of the enclosure [m]

- h
Averageconvectionheattransfercoefficient[W/m

^{2}.K]- K
Thermal conductivity [W/m.K]

- L
Fin height [m]

- Nu
Nusselt number [−]

- P
_{r} Prandtl number [−]

- Q
Heat transfer rate [W]

- Ra
Rayleigh number [−]

- R
Resistance of the heat source [ohms]

- S
Fin spacing [m]

- T
Temperature [K]

- T′
Plate thickness [m]

- Ta
Ambient temperature [K]

- T
_{c} Average temperature of the enclosure top surface [K]

- T
_{h} Average temperature of the heated finned plate [K]

- T
_{f} Film temperature [K]

- V
Voltage supplied [V]

- x
Thickness [m]

### Greek letters

- ε
_{fin} Fin effectiveness [−]

- ε'
Equivalent emissivity

- β
Coefficient of volume expansion [K

^{−-1}]- ν
Kinematic viscosity of air fluid [m

^{2}/s]- σ
Stefan Boltzmann constant [W/m

^{2}.K^{4}]- f*
Equivalent view factor of finned plate [−]

### Subscripts

- a
Air

- b
Bare surface

- cd
Conduction

- cv
Convection

- f
Finned surface

- opt
Optimum

- rd
Radition

- wl
Glass wall

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