Heat transfer coefficients for natural convection

Estimate the heat transfer coefficient for natural convection from a horizontal pipe 0.15 m diameter, with a surface temperature of 400 K to air at 294 K... 

Consider the natural-convection equations available. Heat-transfer coefficients for natural convection may be calculated using the equations presented below. These equations are also valid for horizontal plates or discs. For horizontal plates facing upward which are heated or for plates facing downward which are cooled, the equations are applicable directly. For heated plates facing downward or cooled plates facing upward, the heat-transfer coefficients obtained should be multiplied by 0.5. 

TABLE 8.9. Equations for Heat Transfer Coefficients of Natural Convection... 

Convection is the transfer of energy by conduction and radiation in moving, fluid media. The motion of the fluid is an essential part of convective heat transfer. A key step in calculating the rate of heat transfer by convection is the calculation of the heat-transfer coefficient. This section focuses on the estimation of heat-transfer coefficients for natural and forced convection. The conservation equations for mass, momentum, and energy, as presented in Sec. 6, can be used to calculate the rate of convective heat transfer. Our approach in this section is to rely on correlations. 

Previously, Durst and Stephan Q) observed some enhancement in heat transfer coefficients in natural convection in mixtures of n-heptane -- methane as the two-phase region was entered. We reported heat transfer results earlier ( ) for free convection and cross flow about a heated horizontal cylinder in a supercritical n-decane--C02 mixture. These also showed enhancement in the two-phase region relative to single phase. At that time, analysis was hindered by the unavailability of estimates or measurements of some crucial mixture properties. Happily, this situation has been remedied somewhat and we can now draw some conclusions. 

Evaluate the heat loss by natural convection, forced convection, and radiation from a flat plate at a uniform temperature Tm to ambient air or water at a temperature Tm. The temperature difference between the wall and ambient is 100 K. The heat transfer coefficients for natural and forced convection in air are 10 and 200 W/mz-K, and in water are 500 and 10,000 W/m2 -K, respectively. Plot the various heat losses from the plate as a function of Tm/ TW - Tm) for To, = 0,400,800, and 1200 K. Note the effect of convection relative to radiation as a function of temperature. 

Temperature obviously affects the physical properties of the fluids, thus indirectly affecting the transfer coefficients. As in the case of heat transfer in pipes, equations involving viscosity corrections for temperature differences between bulk and interface have been suggested (Eq. 11-14, Table II) and are especially applicable for viscous continuous phases. No correction is needed for water, for instance, especially at > 50. At lower (A Re)c. natural convection is pronounced, especially in liquid systems with low kinematic viscosity. Since the transfer coefficient for natural convection is a function of the Grashof number, one may expect some effects of the temperature gradient. Steinberger and Treybal s equation (Eq. 6) allows for these effects. 

The convection heat transfer coefficient for natural (or free) convection is calculated by ... 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

Consider the criteria requiredfor nucleate boiling. Nucleate boiling occurs when the difference between the temperature of the hot surface and the bulk fluid temperature is above a certain value. At temperature differences less than this value, heat transfer occurs as a result of natural convection. Nucleate-boiling heat-transfer coefficients for a steel tube may be calculated using the equation... 

The equation for nucleate-boiling heat transfer can be rearranged to become a function of AT, the temperature difference between the surface and the fluid. The minimum temperature difference required to effect nucleate boiling will occur when the heat-transfer coefficients for nucleate boiling and natural convection are equal. This will permit solution for the temperature difference AT. 

In many practical applications there is a significant temperature drop between the base of the fin and its tip, and this affects both the natural convection flow and heat transfer. Very little information is available on the coupling between fin conduction and fluid convection, so that attention is restricted to isothermal fins. As a first approximation, the heat transfer coefficient for isothermal fins can be used for the case where the fins are not isothermal, because there is such a weak dependence on the temperature difference. Property values are to be evaluated at 0.5(TW + TJ) unless otherwise indicated. 

Heat transfer coefficients for forced and natural convection in air gaps can be calculated from correlations [43,56]. Substituting, on the basis of the branch Equations 14.23a and b, the (j>i j values into the nodal equations, we get the following system of equations for the network ... 

For the purpose of discussion, it can however, be assumed that at steady state Thotface = Tuquidus in which case h becomes the heat transfer coefficient for a vertical plate undergoing natural convection heating. The magnitude of h is then of the order of 425 [W/m -K] for a cooler immersed in only silicate slag. More precise estimates accounting for different material properties can be made using [20, 23, 24] ... 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

Natural convection heat transfer coefficient for the outside of a pipe... 

From measurements of the local heat transfer from heated vertical surfaces to cryogens in the natural convection regime, it appears that the laminar boundary layer flow undergoes a transition to turbulence when the modified Grashof number (Gr ) is of the order of 10. This agrees with experiments performed with water. For a heat flux of 100 W/m, the wall boundary layer can be expected to be turbulent above a liquid height of 0.3 m in LNG, with an increase in heat transfer coefficient for wall/liquid heat transfer [ 1 ]. 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

---