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Chapter 9: Problem 1

What is natural convection? How does it differ from forced convection? What force causes natural convection currents?

Short Answer

Expert verified
Natural convection is a process in which fluid motion or heat transfer occurs due to temperature differences within a fluid or between different fluids, without any external force applied. The main difference between natural convection and forced convection lies in the driving force behind fluid motion: In natural convection, buoyancy forces due to density variations caused by temperature differences are responsible, while in forced convection, an external force like a fan or pump drives the fluid motion. The buoyancy force, resulting from differences in fluid density caused by temperature variations, is the force responsible for natural convection currents.

Step by step solution

01

Define Natural Convection

Natural convection is a process where fluid motion or heat transfer occurs due to the temperature difference between different fluids or within a fluid, without any external force applied to cause the motion. In other words, natural convection occurs when the fluid motion is induced by buoyancy forces that result from density variations caused by temperature differences in the fluid.
02

Compare Natural and Forced Convection

The main difference between natural and forced convection is the driving force behind fluid motion or heat transfer. In natural convection, as described earlier, the driving force is the buoyancy force caused by temperature differences in the fluid, leading to density variations. On the other hand, forced convection occurs when an external force, such as a fan, pump, or an object moving through the fluid, drives the fluid motion or heat transfer. Additionally, forced convection usually provides a more uniform and efficient heat transfer compared to natural convection, which can be slower and less predictable due to the lack of control over fluid motion.
03

Identify the Force Causing Natural Convection Currents

The force that causes natural convection currents is the buoyancy force. The buoyancy force is a result of the differences in fluid density caused by temperature variations in the fluid. When a fluid is heated at the bottom, the warmer fluid becomes less dense and rises, while the colder and denser fluid sinks, creating a buoyancy-driven convection current. These natural convection currents are responsible for the fluid motion and heat transfer in natural convection.

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Most popular questions from this chapter

A \(1.5\)-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is \(581 \mathrm{~kg} / \mathrm{m}^{3}\). The tank is exposed to the ambient air at \(25^{\circ} \mathrm{C}\) in calm weather. The outer surface of the tank is polished so that the radiation heat transfer is negligible. Now a crack develops at the top of the tank, and the pressure inside drops to \(1 \mathrm{~atm}\) while the temperature drops to \(-42^{\circ} \mathrm{C}\), which is the boiling temperature of propane at \(1 \mathrm{~atm}\). The heat of vaporization of propane at \(1 \mathrm{~atm}\) is \(425 \mathrm{~kJ} / \mathrm{kg}\). The propane is slowly vaporized as a result of the heat transfer from the ambient air into the tank, and the propane vapor escapes the tank at \(-42^{\circ} \mathrm{C}\) through the crack. Assuming the propane tank to be at about the same temperature as the propane inside at all times, determine how long it will take for the tank to empty if it is not insulated.

Consider two fluids, one with a large coefficient of volume expansion and the other with a small one. In what fluid will a hot surface initiate stronger natural convection currents? Why? Assume the viscosity of the fluids to be the same.

A room is to be heated by a coal-burning stove, which is a cylindrical cavity with an outer diameter of \(32 \mathrm{~cm}\) and a height of \(70 \mathrm{~cm}\). The rate of heat loss from the room is estimated to be \(1.5 \mathrm{~kW}\) when the air temperature in the room is maintained constant at \(24^{\circ} \mathrm{C}\). The emissivity of the stove surface is \(0.85\), and the average temperature of the surrounding wall surfaces is \(14^{\circ} \mathrm{C}\). Determine the surface temperature of the stove. Neglect the heat transfer from the bottom surface and take the heat transfer coefficient at the top surface to be the same as that on the side surface. The heating value of the coal is \(30,000 \mathrm{~kJ} / \mathrm{kg}\), and the combustion efficiency is 65 percent. Determine the amount of coal burned a day if the stove operates \(14 \mathrm{~h}\) a day. Evaluate air properties at a film temperature of \(77^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. Is this a good assumption?

A group of 25 power transistors, dissipating \(1.5 \mathrm{~W}\) each, are to be cooled by attaching them to a black-anodized square aluminum plate and mounting the plate on the wall of a room at \(30^{\circ} \mathrm{C}\). The emissivity of the transistor and the plate surfaces is \(0.9\). Assuming the heat transfer from the back side of the plate to be negligible and the temperature of the surrounding surfaces to be the same as the air temperature of the room, determine the size of the plate if the average surface temperature of the plate is not to exceed \(50^{\circ} \mathrm{C}\). Answer: \(43 \mathrm{~cm} \times 43 \mathrm{~cm}\)

Consider an \(L \times L\) horizontal plate that is placed in quiescent air with the hot surface facing up. If the film temperature is \(20^{\circ} \mathrm{C}\) and the average Nusselt number in natural convection is of the form \(\mathrm{Nu}=C \mathrm{Ra}_{L}^{n}\), show that the average heat transfer coefficient can be expressed as $$ \begin{aligned} &h=1.95(\Delta T / L)^{1 / 4} 10^{4}<\mathrm{Ra}_{L}<10^{7} \\ &h=1.79 \Delta T^{1 / 3} \quad 10^{7}<\mathrm{Ra}_{L}<10^{11} \end{aligned} $$
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