Me 1351

Heat and Mass Transfer.(me1351) 1. Define thermal conductivity of a material? The amount of energy conducted through a body of unit area and unit thickness in unit time when the difference in temperature between the faces causing heat flow is unit temperature difference. 2. Write down the Fourier conduction equation: (∂2T / ∂X2) + (∂2T /∂Y2) + (∂2T /∂Z2) = (1/α) ((∂t /∂ι) ▼2T = (1/α) ((∂t /∂ι) 3. Define overall heat transfer coefficient : The overall heat transfer coefficient in the heat transmitted per unit area per unit time per degree temp difference between the bulk fluids on each side of the metal. It is denoted by U. 4. Give an expression for conduction heat transfer through a furnace wall of three Layers:

Soln:

5. What are the factors affecting the thermal conductivity? i. ii. iii. iv.

Material structure Moisture content Density of the material Pressure and temperature.

6. Define thermal diffusivity? It is the ratio of its thermal conductivity k to the thermal storage capacity ρc. α = (k/ρc). It indicates the rate at which heat is distributed in the material. 7. Define thermal Resistance: Heat transfer may be analogy with the flow of electricity in an electrical resistance. As the flow of electric current in the electrical resistance is

directly proportional to the potential difference heat flow is directly proportional to temp diff (dt), the driving force for heat conduction through a medium As per ohm’s law current (I) = Potential difference (dv)/ electrical resistance. As per Fourier equation heat flow rate Q = temp diff (dt)/ (dx/KA) Comparing to (1) & (2) I is analogous to Q , dv is analogous to dt , R is analogous to (dx/KA). The Quantity (dx/KA) is called the thermal conduction resistance. 8. Draw the diagram of electrical analogy for the composite layer of three concentric Cylinders indicating the values of their thermal resistance.

where Ka , Kb , Kc , are the thermal conductivities of 3 cylinders respectively. 9. State fouriers law of heat conduction. The rate of flow of heat through a simple homogeneous solid is directly proportional to the area of the section at right angles to the direction of heat flow and to change of temperature with respect to the length of the heat flow. Q α A. (dt/dx) Q = -K.A (dt/dx) 10. Define and distinguish between steady state , unsteady state and transient state of heat transfer . Steady State: It refers to the condition which prevails in a heat conducting medium where temperature at fixed points do not change with time. Unsteady State: It designates a phenomenon which is time dependent . Conduction of heat in unsteady refers to the transient conditions where in the heat flow and the temp distribution at any point of the system vary continuously with time

11. Give the example of heat generation application? • • • •

Fuel rods – nuclear reactor Electrical conductors Chemical and combustion processes Drying and setting of concrete.

12. Write down the formula used for finding heat loss through a sphere by conduction? Q= 4лkr1r2(t1-t2)/(r2-r1) 13. Discuss on thermal conductivity of insulators? In insulating materials the thermal conductivity may vary from sample to sample due to variations in structure , composition , density , and porosity. 14. What is critical thickness of insulation? The thickness up to which heat flow increase and after which heat flow decreases is termed as critical thickness. Critical thickness or radius = (k/h0) = rc 15. In the case of liquids and gases heat transfer takes place according to? Convection 16. Unit for thermal conductivity is?

17. Materials having different values of thermal conductivities are known as? Non isotropic material. 18. Draw the electrical analogy diagram for the composite layers of sphere indicating the values of their thermal resistance..

19. Give the reasons for low and high thermal conductivity in insulating and conducting material? Reason: K may vary from sample to sample due to variations in structure, composition and porosity. Conducting Materials: In metals the molecules are closely packed. Molecular activity is rather small and so thermal conductivity is substantially due to the flow of free electrons. 20. How conduction and convective heat transfer occurs in solids and liquids respectively? Conduction: It is the transfer of heat from one part of a substance to another part of the same substance or from one substance to another in physical contact with it, without displacement of molecules forming the substance. In solids conduction takes place by • Lattice vibration • Transport of free electrons. Convection: It is the transfer of heat within the fluid by mixing of one portion of the fluid with another. 21. When heat transferred by molecular collision it is referred to as heat transfer by? Conduction. 22. Write the equation for calculating the heat transfer through a hollow cylinder with variable thermal conductivity. Q = - K0(1+βt).(2лrL(dt/dr)) 23. Write the electrical analogy circuit for a composite plane wall having 4 layers of different material.

24. Material in which thermal conductivity do not vary with respect to axis is called? Isotropic material. 25. Write down the general heat conduction equation for an unsteady state 3-D heat flow through a plane wall. (∂2T / ∂X2) + (∂2T /∂Y2) + (∂2T /∂Z2)+(q/k) = (1/α) ((∂t /∂ι) 26. What are the three ways in which heat may be transferred? • • •

Conduction Convection Radiation

27. Write steady state conduction equation for variable thermal conductivity. Q = - K0(1+βt).(dt/dx).A 28. Give the expression for temperature distribution across a plane wall for one dimensional steady state conduction. (∂2T /∂X2)+(q/k) =0. 29. Define log mean area for a cylinder and a sphere: Cylinder: It is an expression for the heat flow through a hollow cylinder of the same form as that for a plane wall .Then thickness will be equal to (r2-r1) and the area A will be an equivalent area Am. Am = (A0 –Ai)/(ln(A0/Ai) = 2лL(r2-r1)/(ln(r2/r1)). Sphere: Am2 = Ai*A0 Am = (Ai*A0)0.5 = 4лr1r2 rm = (r1r2)0.5

30. Give the general expression for heat flow in three dimensions in cylindrical coordinates. (∂2t / ∂r2) +(1/r) (∂t /∂r) + (1/r2)(∂2t /∂φ2)+ (∂2t / ∂x2) +(q/k) = (1/α) ((∂t /∂ι) 31. Cork is a good (insulator) because it has porous body. 32.

Derive the unit of thermal conductivity:

33.

Define efficiency of fin η fin=Actual heat transferred by the fin[Q fin] maximum head that would be transferred if whole surface of the fin is maintained at the base temp[Qmax]

34.

Define effectiveness of fin Effectiveness of fin is the ratio of the fin heat transfer to the heat transfer rate that would exist without a fin Є fin=Q with fin Q without fin

35.

What is the advantage of insulating the fin at its end. If the tip of the fin is insulated there is no heat loss from the end of the fin.

36.

Name some good conductors of heat. Silver, copper, aluminium and cast iron.

37.

Mention four application of fin. Finned surface are used in I. Economizers for steam power plants II. Radiators of automobiles III. Air cooled engine cylinder heads IV. Transformer and electronic components etc.

38.

Define Newtonian heating or cooling? The process in which the internal resistance is assumed negligible in comparison with its surface resistance is called the Newtonian heating or cooling process.

39.

Define lumped system? In lumped system the whole solid, whole energy at any time is a function of its temperature and total heat capacity is treated as one lump. The temperature in this process is considered to be uniform at a given time.

40.

What is mean by unsteady heat conduction? If there is an abrupt change in its surface temperature, the body attains an equilibrium temperature or a steady state after some period. During this period the temperature varies with time and the body is said to be in an unsteady or transient state.

41.

Define error function and its significance? erf [

]

is known as Gaussian error function. It is defined

by erf [

]

= (2/л).0∫z e-n2 dn.

With erf (0)=0,erf(α)=1. 42. What is the shape of steady state conduction in cylindrical wall? Shape Factor S = (2лL)/(ln(r0/r1) 43. Define conduction shape factor? In order to solve the problem in 2-D,3-D conduction heat transfer we need to construct a potential field consisting of curvilinear squares and thereafter count the number of temperature increment and heat flow lanes. 44. Define Biot Number and what are its significance? Bi = (hlc)/k Where, h= convective heat transfer coefficient lc = characteristic length. Significance: • It gives an indication of the ratio of internal resistance to surface resistance. • When Bi is small it indicates that the system has a small internal (conduction) resistance.

45. Define periodic variation in transient state? In periodic transient state temperatures under go periodic changes which are either regular or irregular but definitely cyclic. Example: The temperature variations in • Cylinder of an IC engine • Building during a period of 24 hours. 46. Name any numerical methods in the solution of transient heat conduction in solids. • Relaxation method • Newton raphson method. 47. Define semi-infinite solid and infinite solids.

Infinite Solid: A solid which extends itself infinitely in all directions of space is termed as an infinite solid.

Semi-infinite Solid: If an infinite solid is split in the middle by a plane , each half is known as semi-infinite solid. 48. Define fourier number. Fourier number F0 = (α ι)/ Lc2 It signifies the degree of penetration of heating or cooling effect through a solid. 49. Define time constant for a thermocouple. The quantity (ρ Vc / h As) (which has units of time) is called time constant and is denoted by ι.

Ι = (ρ Vc)/(h As) = (k/αh) (V/As) 50. Define response of a thermocouple. It is defined as the time required for the thermocouple to attain the source temperature.

UNIT 2 1. 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. 2. 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. Velocity Turbulent flow

Laminar flow Time

Turbulent flow : In addition to the laminar type of flow, a distinct irregular flow is frequently 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. 3. What

is hydrodynamic boundary layer ? In hydrodynamic boundary layer, velocity of the fluid is less99% thanof free stream velocity. 4. What is thermal boundary layer ? In thermal boundary layer, temperature of the fluid is less thanof99% free stream temperature. 5. Define convection . Convection is a process of heat transfer that will occur between solid surface and a fluid medium when they are at different temperatures. 6. State Newton's law of convection. the equation

Heat transfer from the moving fluid to solid surface is given by Q = h A (Tw - T∞) this equation is referred to as Newton's

law of cooling. Where h - Local heat transfer coefficient in W/m2 K A - Surface area in m2

Tw - Surface (or) wall temperature in K T∞ - Temperature of fluid in K

7. What is meant by free or natural 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. 8. What is forced convection? If the fluid motion is artificially created by means of an y external force like a blower or fan, that type of heat transfer is known as forced convection. 9. According to Newton's law of cooling the amount of heat transfer from a solid surface of area A at a temperature T w , a fluid at a temperature T∞ is given by _____________ = Q hA (T w - T∞) 10. Indicatethe concept or significance of boundary layer. In the boundary layer concept the flow field over a body is divided into two regions:

•

A thin region near the body called the boundary layer where the velocity and the temperature gradients are large. • The region outside the boundary layer where the velocity and the temperature gradients are very nearly equal to their free stream values.

UNIT 3 1. What is meant by pool boiling? If heat is added to a liquid from a submerged solid surface, the boiling process is 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. 2. What is mean t by Film 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 3. What is meant by Drop 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.

4. What is heat exchanger? A heat exchanger is defined as equipment which transfers the heat from a hot fluid to a cold fluid. 5. 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 6. What is meant by parallel flow heat exchanger? In this type of heat exchanger, hot and cold fluids move in the same direction. 7. What is meant by counter flow heat exchanger? In this type of heat exchanger, hot and cold fluids move in parallel but opposite directions. 8. 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. 9. What is meant by Fouling Factor? We know, the surfaces of heat exchangers do not remain clean after it has been in use for some time. The surfaces become fouled with scaling or deposits. Tube effect of these deposits affecting the value of overall heat transfer co-efficient. This effect is taken care of by introducing an additional thermal resistance called the fouling resistance. 10. What is meant by Effectiveness? The heat exchanger effectiveness is defined as the ratio of actual heat transfer to the maximum possible heat transfer. Actual heat transfer Effectiveness є = __________________________

Maximum possible heat transfer

UNIT 4 1. Define Radiation. The heat transfer from one body to another without any transmitting medium is known as radiation. It is an electromagnetic wave phenomenon. 2. Define emissive power The emissive power is defined as the total amount of radiation emitted by a body per unit time and unit area. 2 It is expressed in W/m

3. Define monochromatic emissive power Ebλ 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. 4. What is meant by absorptivity Absorptivity is defined as the ratio between radiation a b so rb e and d incident radiation. Radiation absorbed

Absorbitivity, α=_______________________________ Incident radiation 5. What is meant by reflectivity? Reflectivity is defined as the ratio of radiation reflected to the incident radiation Reflectivity, p =Radiation reflected Incident radiation 6. What is Black body? Black body is an ideal surface having the following properties. I. A black body absorbs all incident radiation, regardless of wave length and direction.

2. For a prescribed temperature and wave length, no surface can emit more energy than black body. 7. 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. Amax T = c3 Where c3=2.9 x 10-3 mK 8. Define Emissivity. It is defined as the ability of the surface of a body to radiate h e a. tIt 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,s= Eb 9. What is meant by gray 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 t h a of t the black body. 10. Define irradiation (G). It is defined as the total radiation incident upon a surface per unit time per unit area. It is expressed in W/m2. UNIT 5 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 are 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? When one of the diffusion fluids is in turbulent motion, e d d y diffusion takes place

6. What is convective mass transfer? Convective mass transfer is a process of mass transfer that will occur between a surface and a fluid medium when they are at different concentrations. 7. What is free convective mass transfer? 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.

8.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 evaporation of water from an ocean when air blows over it. 9. 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 10. . Give two examples of convective mass transfer. 1. Evaporation of alcohol 2. Evaporation of water from an ocean when air blows over it