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Heat Convection. Convection Latin: com (together) + vehere (to carry); the bulk movement of thermal energy in fluids
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Heat Convection • Convection Latin: com (together) + vehere (to carry); the bulk movement of thermal energy in fluids • Convection is the flow of heat through a bulk, macroscopic movement of matter from a hot region to a cool region, as opposed to the microscopic transfer of heat between atoms involved with conduction. • Suppose we consider heating up a local region of air. As this air heats, the molecules spread out, causing this region to become less dense than the surrounding, unheated air. For reasons discussed in the previous section, being less dense than the surrounding cooler air, the hot air will subsequently rise due to buoyant forces - this movement of hot air into a cooler region is then said to transfer heat by convection.
Heating a pot of water on a stove is a good example of the transfer of heat by convection. When the stove is first turned on heat is transferred first by conduction between the element through the bottom of the pot to the water. However, eventually the water starts bubbling - these bubbles are actually local regions of hot water rising to the surface, thereby transferring heat from the hot water at the bottom to the cooler water at the top by convection. At the same time, the cooler, more dense water at the top will sink to the bottom, where it is subsequently heated. These convection currents are illustrated in the following figure.
Heated air rises, cools, then falls. Air near heater is replaced by cooler air, and the cycle repeats.
Consider now two regions separated by a barrier, one at a higher pressure relative to the other, and subsequently remove the barrier, as in the following figure. These convection currents are illustrated in the following figure.
Natural/Free Convection Occur due to density differences caused by temperature gradients within the system and may cause either laminar or turbulent flow of fluid.
Natural/Free Convection Warm land is cooled during the day, while cooler land is warmed at night.
Very hot, low-density air is buoyed upward, carrying thermal energy with it.
Forced Convection Forced convection involves use of some mechanical means, such as a pump or a fan, to induce the movement of the fluid.
Forced Convection Hot room air is forced outside, while cooler air replaces it. Hot piston cylinders in automobile engine are cooled by water forcedaround them.
The velocity of fluid reduces to zero at the surface of the plate due to the viscous action. Thus, heat transfer in the boundary layer, where velocity is zero, must occur due to conduction. Away from the wall, heat transfer to fluid is due to convection. In practice, it is difficult to determine the thickness of the boundary layer. The rate of heat transfer is expressed by Newton’s law of cooling, which accounts for the overall effect of convection. q = hA(Tp – Ta)
Ta Tp Heat convection • Heat transfer to a heated flat plate exposed to a fluid. Newton’s law of cooling q = -hAdT q = hA(Tp – Ta) When Tp > Ta h = convective or surface heat transfer coefficient
Some approximate values of h High value of h reflects a high rate of heat transfer. Forced convection offers a high value of h than free convection
Example The rate of heat flux from a metal plate is 1000 W/m2. The surface temperature of the plate is 120°C, and ambient temperature is 20°C. Estimate the convective heat transfer coefficient.
Radiation • The third and last form of heat transfer we shall consider is that of radiation, which in this context means light (visible or not). This is the means by which heat is transferred, for example, from the sun to the earth through mostly empty space - such a transfer cannot occur via convection nor conduction, which require the movement of material from one place to another or the collisions of molecules within the material.
Thermal radiation There are many types of electromagnetic radiation; thermal radiation is only one. Thermal radiation lies in the range from about 0.1-100 m, while visible-light portion is about 0.35-0.75 m. Thermal radiation
Radiation • Often the energy of heat can go into making light, such as that coming from a hot campfire. This light, being a wave, carries energy, and so can move from one place to another without requiring an intervening medium. When this light reaches you, part of the energy of the wave gets converted back into heat, which is why you feel warm sitting beside a campfire. Some of the light can be in the form of visible light that we can see, but a great deal of the light emitted is infrared light, whose longer wavelength is detectable only with special infrared detectors. The hotter the object is, the less infrared light is emitted, and the more visible light. For example, human beings, at a temperature of about 37oCelsius, emit almost exclusively infrared light, which is why we don't see each other glowing in the dark. On other hand, the hot filament of a light bulb emits considerably more visible light.
Radiation • Heat transfer by electromagnetic waves • Does not need a material medium • Black body: perfect absorber perfect emitter (at all wavelengths)
Radiation • Occur between two surfaces by the emission and later absorption of electromagnetic radiation • Energy radiated (or emitted) from a surface is proportional to the absolute temperature raised to the fourth power and surface characteristics.
Radiation Speed of light
Radiated Power from Blackbody • When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant.
The radiated power in a given wavelength interval Δλ at wavelength λ can be approximated by
Stefan-Boltzmann Law of Radiation • By considering the radiation as such a gas, the principles of quantum-statistical thermodynamics can be applied to derive an expression for energy density of radiation per unit volume and per unit wavelength. When the energy density is integrated over all wavelengths, the total energy emitted is proportional to absolute temperature to the fourth power.
Stefan-Boltzmann Law of Radiation The energy radiated by a blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature and is given by qemitted = AT4 = emissivity (0-1) = Stefan-Boltzmann constant = 5.67 x 10-8 J/(s-m2-K4)A = surface area of objectT = Kelvin temperature
The Stefan-Boltzmann Law The total power per unit area from a blackbody radiator can be obtained by integrating the Planck radiation formula over all wavelengths. The radiated power per unit area as a function of wavelength is so the integrated power is It is helpful to make the substitution
The Stefan-Boltzmann Law Making the substitution gives Making use of the standard form integral gives the final form of the Stefan-Boltzmann law
= 0.8 Example How much energy is radiated by this object in ten minutes? --------------------------------------------------- t = 10 x 60 seconds = 600 s Q = radiant energy = q.t q = A T4 Q = (0.8)(5.67x10-8)(5)(500)4 x (600) = 8.5 x 106 J q = sAT4
Blackbody radiation • The materials which obey this law appear black to the eye; they do not reflect any radiation. • Thus a blackbody is also considered as one which absorbs all radiation incident upon it. Therefore; Eb = T4 where Eb is called emissive power of a black body.
Absorption and Emission of Radiation Incident energy Energy out = Energy in Emitted energy/Incident energy = Emissivity = .
Black Bodies Summer clothing: white reflects radiant energy better than black. Until equilibrium is reached, white stripes on roads are at a lower temperature than unpainted asphalt. Wrap an ice-cube in black cloth and another in aluminum foil and place both in the sunshine. What will happen?
Example: How much does the human body radiate? • Body temperature = 37 C = 37 +273 = 310 K, Estimate surface area A = 1.5 m2 = 0.70q = A T4 = (0.70)(5.67 x 10-8)(1.5 m2)(310)4 = 550 watts (5 light bulbs)------------------------------------------------------------------------The sun provides about 1000 watts per square meter at the Earth's surface. 30 % is reflected byhuman skin. 700 watts is absorbed per square meter.
Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing radiation from hot objects is called the Stefan-Boltzmann law:
If object at temperature T is surrounded by an environment at temperature T0(heat transfer surface of the object enclosed by a much larger surface or environment), the net heat flow or net radiant exchange is: qnet = A [T4 - T04] Example: Standing outdoors on hot August day:Body temperature: 37 C = 37 +273 = 310 K, Air temperature: 37 C = 310 K qnet= A [T4 - T04] = A [3104 - 3104] = 0
Example: Standing outdoors on a cold Februarymorning:Body temperature = 37 C = 37 +273 = 310 K, Air temperature = 0 C = 273 KA = 1.5 m2 = 0.70qnet = A [T4 - T04] = (0.70)(5.67 x 10-8)(1.5 m2)(3104 - 2734) = 219 watts
Radiation shape factor • Consider 2 black surfaces, we wish to obtain a general expression for the energy exchange between these surfaces when they are maintained at different temperatures. The problem becomes essentially one of determinating the amount of energy which leaves one surface and reaches the other. To solve this problem the radiative shape factors are used. • Radiation shape factor = view factor = angle factor = configuration factor = Fm-n = fraction of energy leaving surface m which reaches surface n. • Energy leaving surface 1 and arriving at surface 2 = Eb1A1F12 • Energy leaving surface 2 and arriving at surface 1 = Eb2A2F21
Since the surfaces are black, all the incident radiation will be absorbed, and net energy exchange is Eb1A1F12 - Eb2A2F21 = q1-2 If both surface are at the same temperature, they can be no heat exchange or q1-2 = 0. Also Eb1 = Eb2 A1F12 = A2F21 Therefore: q = A1 (T14-T24) . FA1A2
