# Heat and Mass Transfer Unit-1 Conduction

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1 1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature gradient in that direction. - A dt dx dt - KA where A are in m 2 dx dt dx - Temperature gradient in K/m K Thermal conductivity W/mK. 2. Define Thermal Conductivity. Thermal conductivity is defined as the ability of a substance to conduct heat. 3. Write down the equation for conduction of heat through a slab or plane wall. Heat transfer T overall Where T = T 1 T 2 R L R - Thermal resistance of slab KA L = Thickness of slab, K = Thermal conductivity of slab, A = Area 4. Write down the equation for conduction of heat through a hollow cylinder. Heat transfer T overall Where, T = T 1 T 2 R R 1 r 2 in 2 LK r1 thermal resistance of slab L Length of cylinder, K Thermal conductivity, r 2 Outer radius, r 1 inner radius 5. State Newton s law of cooling or convection law. Heat transfer by convection is given by Newton s law of cooling = ha (T s - T ) Where A Area exposed to heat transfer in m 2, h - heat transfer coefficient in W/m 2 K

2 T s Temperature of the surface in K, T - Temperature of the fluid in K. 6. Write down the general equation for one dimensional steady state heat transfer in slab or plane wall with and without heat generation T T T 1 T x y z t T T T q 1 T x y z K t 7. Define overall heat transfer co-efficient. The overall heat transfer by combined modes is usually expressed in terms of an overall conductance or overall heat transfer co-efficient U. Heat transfer = UA T. 8. Write down the equation for heat transfer through composite pipes or cylinder. Heat transfer T R overall, Where, T = T a T b, r r 2 1 In In L2 r1 r2 2 L har1 K1 K2 hbr R. 9. What is critical radius of insulation (or) critical thickness? Critical radius = r c Critical thickness = r c r 1 Addition of insulating material on a surface does not reduce the amount of heat transfer rate always. In fact under certain circumstances it actually increases the heat loss up to certain thickness of insulation. The radius of insulation for which the heat transfer is maximum is called critical radius of insulation, and the corresponding thickness is called critical thickness. 10. Define fins (or) extended surfaces. It is possible to increase the heat transfer rate by increasing the surface of heat transfer. The surfaces used for increasing heat transfer are called extended surfaces or sometimes known as fins. 11. State the applications of fins. The main applications of fins are 1. Cooling of electronic components 2. Cooling of motor cycle engines. 3. Cooling of transformers 4. Cooling of small capacity compressors

3 12. Define Fin efficiency. The efficiency of a fin is defined as the ratio of actual heat transfer by the fin to the maximum possible heat transferred by the fin. fin fin max 13. Define Fin effectiveness. Fin effectiveness is the ratio of heat transfer with fin to that without fin Fin effectiveness = with fin without fin 1. Define convection. Unit-2 Convection Part-A Convection is a process of heat transfer that will occur between a solid surface and a fluid medium when they are at different temperatures. 2. Define Reynolds number (Re) & Prandtl number (Pr). Reynolds number is defined as the ratio of inertia force to viscous force. Re Inertia force Viscous force Prandtl number is the ratio of the momentum diffusivity of the thermal diffusivity. Momentum diffusivity Pr Thermal diffusivity 3. Define Nusselt number (Nu). It is defined as the ratio of the heat flow by convection process under an unit temperature gradient to the heat flow rate by conduction under an unit temperature gradient through a stationary thickness (L) of metre. conv Nusselt number (Nu) =. cond

4 4. Define Grash of number (Gr) & Stanton number (St). It is defined as the ratio of product of inertia force and buoyancy force to the square of viscous force. Inertia force Buyoyancy force Gr 2 (Viscous force) Stanton number is the ratio of nusselt number to the product of Reynolds number and prandtl number. Nu St Re Pr 5. What is meant by Newtonian and non Newtonian fluids? The fluids which obey the Newton s Law of viscosity are called Newtonian fluids and those which do not obey are called non Newtonian fluids. 6. What is meant by laminar flow and turbulent flow? Laminar flow: Laminar flow is sometimes called stream line flow. In this type of flow, the fluid moves in layers and each fluid particle follows a smooth continuous path. The fluid particles in each layer remain in an orderly sequence without mixing with each other. Turbulent flow: In addition to the laminar type of flow, a distinct irregular flow is frequency observed in nature. This type of flow is called turbulent flow. The path of any individual particle is zig zag and irregular. Fig. shows the instantaneous velocity in laminar and turbulent flow. 7. What is meant by free or natural convection & forced convection? If the fluid motion is produced due to change in density resulting from temperature gradients, the mode of heat transfer is said to be free or natural convection. If the fluid motion is artificially created by means of an external force like a blower or fan, that type of heat transfer is known as forced convection. 8. Define boundary layer thickness. The thickness of the boundary layer has been defined as the distance from the surface at which the local velocity or temperature reaches 99% of the external velocity or temperature. 9. What is the form of equation used to calculate heat transfer for flow through cylindrical pipes? Nu = (Re) 0.8 (Pr) n

5 n = 0.4 for heating of fluids n = 0.3 for cooling of fluids 10. What is meant by Newtonian and non Newtonian fluids? The fluids which obey the Newton s Law of viscosity are called Newtonian fluids and those which do not obey are called non Newtonian fluids. Unit-3 1. What is meant by Boiling and condensation? The change of phase from liquid to vapour state is known as boiling. The change of phase from vapour to liquid state is known as condensation. 2. Give the applications of boiling and condensation. Boiling and condensation process finds wide applications as mentioned below. 1. Thermal and nuclear power plant. 2. Refrigerating systems 3. Process of heating and cooling 4. Air conditioning systems 3. What is meant by pool boiling? If heat is added to a liquid from a submerged solid surface, the boiling process referred to as pool boiling. In this case the liquid above the hot surface is essentially stagnant and its motion near the surface is due to free convection and mixing induced by bubble growth and detachment. 4. What is meant by Film wise and Drop wise condensation? The liquid condensate wets the solid surface, spreads out and forms a continuous film over the entire surface is known as film wise condensation. In drop wise condensation the vapour condenses into small liquid droplets of various sizes which fall down the surface in a random fashion. 5. Give the merits of drop wise condensation? In drop wise condensation, a large portion of the area of the plate is directly exposed to vapour. The heat transfer rate in drop wise condensation is 10 times higher than in film condensation. 6. What is heat exchanger?

6 A heat exchanger is defined as an equipment which transfers the heat from a hot fluid to a cold fluid. 7. What are the types of heat exchangers? The types of heat exchangers are as follows 1. Direct contact heat exchangers 2. Indirect contact heat exchangers 3. Surface heat exchangers 4. Parallel flow heat exchangers 5. Counter flow heat exchangers 6. Cross flow heat exchangers 7. Shell and tube heat exchangers 8. Compact heat exchangers. 8. What is meant by Direct heat exchanger (or) open heat exchanger? In direct contact heat exchanger, the heat exchange takes place by direct mixing of hot and cold fluids. 9. What is meant by Indirect contact heat exchanger? In this type of heat exchangers, the transfer of heat between two fluids could be carried out by transmission through a wall which separates the two fluids. 10. What is meant by Regenerators? In this type of heat exchangers, hot and cold fluids flow alternately through the same space. Examples: IC engines, gas turbines. 11. What is meant by Recuperater (or) surface heat exchangers? This is the most common type of heat exchangers in which the hot and cold fluid do not come into direct contact with each other but are separated by a tube wall or a surface. 12. What is meant by parallel flow and counter flow heat exchanger? In this type of heat exchanger, hot and cold fluids move in the same direction. In this type of heat exchanger hot and cold fluids move in parallel but opposite directions. 13. What is meant by shell and tube heat exchanger?

7 In this type of heat exchanger, one of the fluids move through a bundle of tubes enclosed by a shell. The other fluid is forced through the shell and it moves over the outside surface of the tubes. 14. What is meant by compact heat exchangers? There are many special purpose heat exchangers called compact heat exchangers. They are generally employed when convective heat transfer coefficient associated with one of the fluids is much smaller than that associated with the other fluid. 15. What is meant by LMTD? We know that the temperature difference between the hot and cold fluids in the heat exchanger varies from point in addition various modes of heat transfer are involved. Therefore based on concept of appropriate mean temperature difference, also called logarithmic mean temperature difference, also called logarithmic mean temperature difference, the total heat transfer rate in the heat exchanger is expressed as = U A (T)m Where U Overall heat transfer coefficient W/m 2 K A Area m 2 (T) m Logarithmic mean temperature difference. 16. What is meant by Fouling factor? We know the surfaces of a heat exchangers do not remain clean after it has been in use for some time. The surfaces become fouled with scaling or deposits. The effect of these deposits the value of overall heat transfer coefficient. This effect is taken care of by introducing an additional thermal resistance called the fouling resistance. 17. What is meant by effectiveness? The heat exchanger effectiveness is defined as the ratio of actual heat transfer to the maximum possible heat transfer. Effectiveness Actual heat transfer = Maximum possible heat transfer Unit-4 Radiation max 1. Define emissive power [E] and monochromatic emissive power. [E b ] The emissive power is defined as the total amount of radiation emitted by a body per unit time and unit area. It is expressed in W/m 2. The energy emitted by the surface at a given length per unit time per unit area in all directions is known as monochromatic emissive power. 2. What is meant by absorptivity, reflectivity and transmissivity?

8 Absorptivity is defined as the ratio between radiation absorbed and incident radiation. Reflectivity is defined as the ratio of radiation reflected to the incident radiation. Transmissivity is defined as the ratio of radiation transmitted to the incident radiation. 3. What is black body and gray body? Black body is an ideal surface having the following properties. A black body absorbs all incident radiation, regardless of wave length and direction. For a prescribed temperature and wave length, no surface can emit more energy than black body. If a body absorbs a definite percentage of incident radiation irrespective of their wave length, the body is known as gray body. The emissive power of a gray body is always less than that of the black body. 4. State Planck s distribution law. The relationship between the monochromatic emissive power of a black body and wave length of a radiation at a particular temperature is given by the following expression, by Planck. 5 C1 Eb C2 T e 1 Where E b = Monochromatic emissive power W/m 2 = Wave length m c 1 = W m 2 c 2 = mk 5. State Wien s displacement law. The Wien s law gives the relationship between temperature and wave length corresponding to the maximum spectral emissive power of the black body at that temperature. mas T = c3 Where c 3 = [Radiation constant] T = 2.9 mas mk 6. State Stefan Boltzmann law. [April 2002, M.U.]

9 The emissive power of a black body is proportional to the fourth power of absolute temperature. E b b b T E = T Where E = Emissive power, w/m 4 4 = Stefan. Boltzmann constant = W/m K T = Temperature, K 2 7. Define Emissivity. It is defined as the ability of the surface of a body to radiate heat. It is also defined as the ratio of emissive power of any body to the emissive power of a black body of equal temperature. E Emissivity E 8. State Kirchoff s law of radiation. b This law states that the ratio of total emissive power to the absorbtivity is constant for all surfaces which are in thermal equilibrium with the surroundings. This can be written as E1 E2 E It also states that the emissivity of the body is always equal to its absorptivity when the body remains in thermal equilibrium with its surroundings. 1 = E 1 ; 2 = E 2 and so on. 9. Define intensity of radiation (I b ). It is defined as the rate of energy leaving a space in a given direction per unit solid angle per unit area of the emitting surface normal to the mean direction in space. I n Eb 10. State Lambert s cosine law. It states that the total emissive power E b from a radiating plane surface in any direction proportional to the cosine of the angle of emission E b cos 11. What is the purpose of radiation shield?

10 Radiation shields constructed from low emissivity (high reflective) materials. It is used to reduce the net radiation transfer between two surfaces. 12. Define irradiation (G) and radiosity (J) It is defined as the total radiation incident upon a surface per unit time per unit area. It is expressed in W/m 2. It is used to indicate the total radiation leaving a surface per unit time per unit area. It is expressed in W/m What is meant by shape factor? The shape factor is defined as the fraction of the radiative energy that is diffused from on surface element and strikes the other surface directly with no intervening reflections. It is represented by F ij. Other names for radiation shape factor are view factor, angle factor and configuration factor. Unit-5 Mass Transfer 1. What is mass transfer? The process of transfer of mass as a result of the species concentration difference in a mixture is known as mass transfer. 2. Give the examples of mass transfer. Some examples of mass transfer. 1. Humidification of air in cooling tower 2. Evaporation of petrol in the carburetor of an IC engine. 3. The transfer of water vapour into dry air. 3. What are the modes of mass transfer? There are basically two modes of mass transfer, 1. Diffusion mass transfer 2. Convective mass transfer 4. What is molecular diffusion? The transport of water on a microscopic level as a result of diffusion from a region of higher concentration to a region of lower concentration in a mixture of liquids or gases is known as molecular diffusion. 5. What is Eddy diffusion?

11 When one of the diffusion fluids is in turbulent motion, eddy diffusion takes place. 6. What is convective mass transfer? Convective mass transfer is a process of mass transfer that will occur between surface and a fluid medium when they are at different concentration. 7. State Fick s law of diffusion. The diffusion rate is given by the Fick s law, which states that molar flux of an element per unit area is directly proportional to concentration gradient. m a D A where, ab a 2 D ab Diffusion coefficient of species a and b, m / s a dc dx ma kg -mole Molar flux, 2 A s-m dc dx concentration gradient, kg/m 8. What is free convective mass transfer? 3 If the fluid motion is produced due to change in density resulting from concentration gradients, the mode of mass transfer is said to be free or natural convective mass transfer. Example : Evaporation of alcohol. 9. Define forced convective mass transfer. If the fluid motion is artificially created by means of an external force like a blower or fan, that type of mass transfer is known as convective mass transfer. Example: The evaluation if water from an ocean when air blows over it. 10. Define Schmidt Number. It is defined as the ratio of the molecular diffusivity of momentum to the molecular diffusivity of mass. Molecular diffusivity of momentum Sc Molecular diffusivity of mass 11. Define Scherwood Number. It is defined as the ratio of concentration gradients at the boundary.

12 hmx Sc D ab hm Mass transfer coefficient, m/s 2 D ab Diffusion coefficient, m / s x Length, m

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