# Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model

## Abstract

Calculation of free convection from bodies of arbitrary shape has been investigated previously. The Body Gravity Function (BGF) which accounts for the geometry of each body shape was considered to be a constant value. In the present study, it is shown that BGF is not a constant value in a wide range of Rayleigh number. Instead, its value changes as Rayleigh number increases. Therefore, by analytical modeling of *Dynamic BGF* and derivation of a new parameter called *Body Fluid Function*, a novel method is proposed to calculate laminar free convection heat transfer from isothermal convex bodies of arbitrary shape. Results for 24 different body shapes are compared with the available experimental and numerical data. Excellent agreement shows that the present simple method accurately predicts laminar free convection heat transfer from isothermal convex bodies of arbitrary shape in the whole range of laminar flow and for fluids of any Prandtl number.

### List of symbols

*A*Total surface area

- \( \tilde{A} \)
Fraction of sectional area defined by Eq. 7

- BFF
Body fluid function defined by Eq. 18

*C*Universal correction factor defined by Eq. 24

- \( F(\Pr ) \)
Prandtl number function defined by Eq. 2

*G*Body gravity function based on characteristic length \( \sqrt A \)

*G*_{dyn}Dynamic body gravity function

- Gr
Grashof number

- \( G^{\prime}_{\text{low}} \)
Modified lower bound

*h*Convection heat transfer coefficient

*h*_{x},*h*_{ω}Scale factors

*k*Thermal conductivity

*N*Number of distinct surfaces of a body shape

- \( {\text{Nu}}_{\sqrt A } \)
Nusselt number based on characteristic length \( \sqrt A \)

- \( {\text{Nu}}_{\sqrt A }^{0} \)
Conduction limit based on characteristic length \( \sqrt A \)

- P
Local perimeter of body with respect to gravity vector, m

- Pr
Prandtl number

*R*Thermal resistance

- \( {\text{Ra}}_{\sqrt A } \)
Rayleigh number based on characteristic length \( \sqrt A \)

- θ
The angle between normal to the surface and the gravity vector

*x*,*ω*Surface coordinate lines

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