6 Heat Transfer 2: Heat Convection

Dibyakanta Seth

6.1 Introduction

Convection is a mode of heat transfer between a solid surface and the adjacent fluid in motion. Convection het transfer involves both the molecular movement and the bulk transport of the fluid. Higher the velocity of fluid more will be the rate of heat transfer. One common example is the boiling of water in a pan. The heat transfer takes place between the pan surface and the liquid layer adjacent to the surface. Had the water in the pan be still, the mode of heat transfer would have been by conduction.

Mathematical prediction of convective heat transfer is very difficult unlike the conduction and radiation heat transfer. So, the relationships between the variables are better explained with experimental results rather than the theoretical interpretations.

6.2 Newton’s law of cooling

Newton experimentally proved that rate of cooling of a surface depends on the temperature difference between the surface of solid and that of the cooling fluid adjacent to it (Fig 6.1). The generalised equation of heat transfer is applied to express the Newton’s law as

Where, q is the rate of heat transfer (W), hs is called surface heat transfer coefficient or film coefficient (W/m2K), A is the exposed surface area to the liquid, Ts is the temperature of solid surface and T∞ is the bulk temperature of liquid in motion. hs here acts as a conductor of heat transfer in a hypothetical surface film. Comparing the conductance of conduction and convection heat transfer we get

One important interpretation we get here, heat transfer coefficient depends on the thermal conductivity of fluid. Furthermore, since the convection includes the moving fluid the frictional resistance i.e. the viscosity and the fluid velocity affect the heat transfer coefficient.

6.3. Convection types

In convection, if the bulk movement of fluid is caused by buoyancy effect induced due to density difference as a result of temperature variation within the fluid mass, the convection is called natural convection. Boiling of water in a pan is one common example of natural convection. On the other hand, if fluid movement is caused by an external means like pump, fan or the wind, the type of convection is called forced convection. It is obvious that heat transfer in forced convection will be better compared to natural convection.

6.3.1 Natural convection

There are many examples of natural convection in food processing like cooling of cans taken out from a retort exposed to the ambient air, placing some food material in an oven without fan etc. Since, the convection heat transfer is a surface phenomenon that takes place at the interface between the fluid and solid, the controlling factors of heat transfer would be the fluid properties such as density, viscosity, thermal expansion, specific heat at constant pressure and thermal conductivity. The dimensions of surface like diameter and length will affect the heat transfer. The temperature difference between the surface and bulk fluid is the main driving force in convection.

As has been told earlier, experimental results are used to describe the relationship of these factors on heat transfer rate. For simplification, the factors are grouped as different dimensionless numbers named after eminent scientists. These numbers are

The Nusselt number describes about the relative dominance of convection over conduction. When air is blown over a heated surface, the rate of heat transfer increases as a result of increased in Nusselt number. Prandtl number is the ratio of hydrodynamic layer and thermal boundary layer. The thicker the hydrodynamic layer less will be heat transfer and more the thermal boundary layer more will be the heat transfer. Therefore, less the Prandtl number better will be the rate of heat transfer. The Prandtl number for gas is about 0.7 and for water it is around 10.

The power function developed to relate the unit less numbers and the length ration is

K, a, b and c are the proportionality constants. The values of these constants are determined from the experimental results and eventually the Nusselt number is calculated. From the Nusselt number we find out the value of heat transfer coefficient. This value then put to equation (6.1) to calculate rate of heat transfer by convection.

6.3.1.3 Natural convection in horizontal plane

The empirical equations (6.5), (6.6) and (6.7) can be used for horizontal plane but with the replacement of diameter with characteristic length. In all the calculations the fluid properties are measured at film temperature rather than the bulk temperature of fluid.

6.3.2 Forced convection

The movement of fluid past a solid surface is caused by external forces in forced convection heat transfer. One example of forced convection heat transfer in food processing is blast freezer. Since the fluid is constantly drawn from the solid surface the rate of heat transfer is more compared to conduction heat transfer. Different cases of forced convection are discussed as follows.

These equations apply for smooth surfaces. The rough surface helps in maintaining turbulence to some extent, so the rate of heat transfer in rough surface would be more.

6.3.2.3 Heat transfer outside pipe

6.4 Overall heat transfer coefficient

In many heat transfer operations conduction and convection occur simultaneously. For example in shell and tube heat exchanger the steam condenses in shell and heat is given off to the outside tube by convection. The heat from outside surface to inside surface is by conduction and from inside surface to the liquid inside the tube is by means of convection (Fig. 6.2). If we represent the heat transfer in term of resistance, it will be

6.5. Special case of convection heat transfer

6.5.1 Combined conduction and convection heat transfer

6.5.2 Heat transfer from condensing vapour

The condensation is the process of phase transfer from vapour to liquid by giving up the latent heat. Condensation in steam pipeline is an important aspect in food processing to look up for better understanding. If the condensed liquid forms a film over the condensing surface, it is called film condensation. The drop-wise condensation is one where the condensed liquid drops from the condensing surface without spreading on the surface as film. In drop-wise condensation the surface is exposed, thus the rate of heat transfer is more compared to film condensation, may be up to 10 times higher.

The empirical equation for condensation on vertical tubes or plane surfaces is

6.5.3 Heat transfer to boiling liquid

Heating of liquid in a pan causes boiling of liquid. The rate of heat transfer depends on the temperature difference between the liquid and solid surface. If the difference is more than 200C, the heat transfer coefficient decreases because a layer of bubbles formed on the surface of solid covering the surface, thus reduced hs. For temperature difference from 1 to 20 0C, values for hs increases from 1200 to 60000 W/m2K

Sometimes, the rate of heat transfer varies significantly with the resistances offered and not by the change of heat transfer coefficient.

6.6 Critical thickness of insulation

Insulating materials are used to reduce heat loss from the fluid flowing inside a pipe. By adding insulating material the thermal resistance increases, but at the same time the outer diameter of pipe increases which may increase the heat loss. We cannot ascertain whether the heat transfer increase or decrease with the addition of insulating materials. So, a critical diameter is derived beyond which if we add insulation, the heat transfer will decrease. In other words, the minimum thickness given to any heating surface for effective control of heat loss is the critical thickness.

References

1. Transport Processes and Unit Operations (3rd Edition), C. J. Geankoplis, Prentice Hall Inc. Publ., 1993.

2. Unit operations in food processing, R.L. Earle and M.D. Earl, NZIFST (Inc.) Publ., 1983.