# Numerical and experimental investigation of multi-mode heat transfer in a square cavity with and without triangular fins

## Abstract

Numerical and experimental studies on laminar natural convection and radiation in a differentially heated cavity with/without triangular fins are presented. The square cavity is filled with air (Pr = 0.71). The top and bottom walls are adiabatic, while the active (hot) and cold walls are isothermal. Triangular conductive fins made of highly conductive material are placed on the heated and cooled vertical surfaces of a square cavity. The effects of pertinent parameters on fluid flow and heat transfer characteristics are studied. The governing differential equations, assuming laminar flow, are solved using the commercial software FLUENT. Experiments have been carried out for three different configurations viz square cavity without fins, square cavity with two fins on vertical walls and square cavity with continuous fins on vertical walls. Rayleigh number varies from 1.18 × 10^{5} to 2.15 × 10^{5} for the first experiment (square cavity without fins). The other two experiments with fins have been conducted for six different heat inputs. The numerical results have been validated against the experimental results obtained. It is concluded that the triangular fins on isothermal walls enhance the heat transfer in the cavity. Natural convection is influenced by wall surface emissivity. The square cavity with continuous fins is more effective than square cavity with two fins on vertical isothermal walls.

### Keywords

Natural convection Radiation Square cavity Traingular fins### Nomenclature

- ᅟ
ᅟ

### Notations

*A*Area,

*m*^{2}*AR*Aspect ratio,

*L*/*H*, 1 in present study*b*Triangular fin width,

*m**F*_{ij}View factor from the

*i*^{ t h }element to*j*^{ t h }element of the enclosure*g*Acceleration due to gravity,

*m*/*s*^{2}*G*Irradiation,

*W*/*m*^{2}*h*Heat transfer coefficient,

*W*/*m*^{2}*K**H*Cavity height,

*m**H*_{f}^{∗}Dimensionless fin position,

*y*_{ p }/*H**J*Radiosity,

*W*/*m*^{2}*k*Thermal conductivity,

*W*/*m**K**L*Cavity length,

*m**L*_{c}Characteristics length (the heated perimeter coming in contact with air),

*m**L*_{f}Fin length,

*m**L*_{f}^{∗}Dimensionless fin length,

*L*_{ f }/*L*- \( {Nu}_{c}^{\prime} \)
Convective Nusselt number at hot wall

*N**u*_{c}Average convective Nusselt number at hot wall

- \( {Nu}_{r}^{\prime} \)
Radiative Nusselt number at hot wall

*N**u*_{r}Average radiative Nusselt number at hot wall

*N**u*_{t}Total Nusselt number at hot wall

*p*Pressure,

*P**a**P*Dimensionless pressure, \((p-p_{\infty })L^{2}/\rho \alpha ^{2} \)

*P**r*Prandtl number,

*ν*/*α**q*Heat flux,

*W*/*m*^{2}*Q*_{in}Total heat input,

*W**R**a*Rayleigh number (

*g**β*△*T**L*^{3})/*ν**α**T*Temperature,

*K*- △
*T* Temperature difference (

*T*_{ h }–*T*_{ c }) for radiation and (*T*_{ h }−*T*_{ m }) for convection,*K**T*_{m}Mean temperature, (

*T*_{ h }+*T*_{ c })/2,*K**u*,*v*Fluid velocities,

*m*/*s**U*,*V*Dimensionless fluid velocities,

*u**L*/*α*,*v**L*/*α**W*_{f}Depth of the fin,

*m**x*,*y*Cartesian coordinates

*X*,*Y*Dimensionless cartesian coordinates,

*x*/*L*,*y*/*L**y*_{b}Half width of the fin,

*m*

### Greek Symbols

*α*Thermal diffusivity of air,

*m*^{2}/*s**ε*Emissivity of wall

*ν*Kinematic viscosity of air,

*m*^{2}/*s**θ*Dimensionless temperature, (

*T*−*T*_{ c })/(*T*_{ h }−*T*_{ c })*σ*Stefan Boltzmann constant,

*W*/*m*^{2}*K*^{4}

### Subscripts

- Al
Aluminum

- c
Convective

- C
Cold

- f
Fluid

- h
Hot

- in
Input

- l
Loss

- m
Mean

- r
Radiative

- s
Solid

- t
Total

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