Heat Loss by Free Convection

Ceng 402 Project

Introduction

Free convection is a limiting case of convection in which heat is transported upward by heated fluid which rises. The flow patterns are determined by the buoyancy effect of the heated fluid, as opposed to being determined by some external force as in forced convection. The following correlations are useful for estimating heat losses from various structures. It is assumed that the temperature is constant at *T*_{0} on the surface of the object and at *T*_{inf} far from the surface. The fluid properties such as density, *rho*, and viscosity, *mu*, are to be evaluated at the mean temperature, or film temperature

T_{f} = (T_{0} + T_{inf}) / 2

There are several dimensionless parameters used in calculations involving heat transfer by convection. The Nusselt number *Nu*_{m} for free-convection heat transfer for an object submerged in an infinite fluid is of the form

Nu_{m} = Nu (Gr Pr)

in which *Nu*_{m} is based on the heat-transfer coefficient *h*_{m} for the total surface of the submerged object

Nu_{m} = h_{m} D / k

where *D* is the diameter, and *k* is the thermal conductivity.

The Grashof number *Gr* is another dimensionless parameter

Gr = rho^{2} beta g D^{3} (T_{0} - T_{inf}) / mu^{2}

where *beta* is *1 / T*_{f} for ideal gases, *g* is the gravitational acceleration.

The dimensionless Prandlt number *Pr* is given by

Pr = C_{p} mu / k

where *C*_{p} is the specific heat of the fluid.

For a single sphere of diameter *D* in a large body of fluid, when *Gr*^{1/4}Pr^{1/4} < 200, the Nusselt number is closely represented by

Nu_{m} = 2 + 0.59 Gr^{1/4} Pr^{1/4}

For a long horizontal cylinder in an infinite fluid when *GrPr > 10*^{4}, the Nusselt number is closely represented by

Nu_{m} = 0.518 (Gr Pr)^{1/4}

Diagram:

Free Convection from a Horizontal Cylinder