INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA END OF SEMESTER EXAMINATION SEMESTER II 2012/2013 SESSION KULLIYYAH OF ENGINEERING Program
: ENGINEERING
Level of Study
: UG3
Time Duration
: 2.30 p.m. – 5.30 p.m. : 3 Hr
Date
: 05/06/2013
Sections
: 1 and 2
Course Code : BTE 3215 Course Title
: Heat and Mass Transfer
This Question Paper Consists of fourteen (14) Printed Pages (including Cover Page) with five (5) Questions in Part A and four (4) Questions in Part B INSTRUCTION(S) TO CANDIDATES DO NOT OPEN UNTIL YOU ARE ASKED TO DO SO
Attempt All Questions in Part A. (Total marks = 50) In Part B: Q6 is Compulsory. Answer any Two (2) questions from Q7, Q8, Q9 and Q10. (Total marks = 50) Answers should be clear and intelligible. Whenever appropriate, justify your answer. No books, notes and programmable calculators are permitted. For specific instructions, please refer to the appropriate section. A list of formulae and material properties are attached at the end of the question paper.
Any form of cheating or attempt to cheat is a serious offence which may lead to dismissal.
BTE 3215 Heat and Mass Transfer
Part A: Answer ALL. Total marks for Part A = [50 marks] Q1 [10 Marks] a) What is the physical significance of Prandtl number? Is it possible to consider Pr as fluid property? Explain how. (5 marks) b) Consider a hot baked potato. Will the potato cool faster or slower when we blow the warm air coming from our lungs on it instead of letting it cool naturally in the cooler air in the room? Explain using Newton’s law of cooling. (5 marks) Q2 [10 Marks] a) Explain briefly the advantages of lumped capacitance analysis and the circumstances under which this is a suitable approach. (5 marks) b) What are the characteristics of a blackbody? Does such a thing actually exist in nature? What is the principal role of a blackbody behavior in radiation analysis? (5 marks) Q3 [10 Marks] a)
Your friend asserts that, in a heat exchanger, it is impossible for the exit temperature of the cold fluid to be greater than the exit temperature of the hot fluid when both fluids are single phase fluids. What is your response? Explain using diagrams. (5 marks)
b) Consider air (O2 and N2) in a closed, cylindrical container with its axis vertical and with opposite ends maintained at different temperatures. If the bottom surface is colder than the top surface, does mass transfer occur? Explain using Fick’s Law. (5 marks) Q4 [10 Marks] a) Explain the variation of convective heat transfer coefficient in the thermally developing region and in the fully developed temperature profile region for both external flow on a flat plate and internal flow in a tube. Show the variation of h versus x for both cases. (5 marks) b) How does dropwise condensation differ from film condensation? Which mode of condensation is characterized by larger heat transfer rates? Why? (5 marks)
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BTE 3215 Heat and Mass Transfer
Q5 [10 Marks] Consider a hemispherical furnace of diameter, D = 5 m with a flat base as shown in Figure 1. The dome of the furnace is black, and the base has an emissivity of 0.7. The base and the dome of the furnace are maintained at uniform temperature of 400 K and 1000 K, respectively. Determine; a) The view factors F12 and F21.
(5 marks)
b) The net rate of radiation heat transfer from the dome to the base surface during steady operation. (5 marks)
Figure 1
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BTE 3215 Heat and Mass Transfer
Part B: Q6 is Compulsory. Answer any Two (2) questions from Q7, Q8, Q9 and Q10.Total marks for this part = [50 marks] Q6 [20 Marks] A house built on a riverside is to be cooled in summer by utilizing the cool water of the river, which flows at an average temperature of 15°C. A 15 m long section of a circular duct of 20 cm diameter passes through the water as shown in Figure 2. Air enters the underwater section of the duct at Tm,i = 35 °C and velocity, u∞ = 3 m/s. Assume the surface of the duct is at the temperature of the water (Ts = 15°C). Air 35 °C, 3 m/s
Figure 2 Assuming the bulk mean temperature of air to be 300 K, and using properties of air at 1 atm and 300 K and determine a) The convective heat transfer coefficient h.
(6 marks)
b) The outlet temperature of air Tm,o as it leaves the underwater portion of the duct. (6 marks) c) The pressure loss through the pipe and the minimum power required to overcome the resistance to flow. (8 marks) Q7 [15 Marks] Air at 50°C and 3 atm flows over a 100 cm x 100 cm flat-plate held at a constant temperature of 204°C. Determine, a) air speed that will assure laminar flow over the entire plate.
(5 marks)
b) the thickness of boundary layer at a distance of 40 mm from the leading edge. (5 marks)
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BTE 3215 Heat and Mass Transfer
c) if the emissivity of the plate is 0.8, determine total heat transfer during this flow. (5 marks) Q8 [15 Marks] A thin-walled container with a hot process fluid at 50 °C is placed in quiescent, cold water path at 10 °C as sown in Figure 3. Heat transfer at the inner and outer surfaces of the container may be approximated by free convection from a vertical plate. If the surface temperature on the cold water side is 34 °C, determine
Figure 3 a) the Rayleigh number RaL.
(5 marks)
b) Nusselt number NuL.
(5 marks)
c) Estimate the convection heat rate per unit thickness of the wall.
(5 marks)
Q9 [15 Marks] A counterflow, concentric tube heat exchanger is used to cool an industrial product ( = 860 kg/m3, Pr = 500, k = 0.138 W/m∙K , = 32.6 x10-3 N∙s/m2 ). The flow rate of cooling water through the inner tube ( Di = 2 cm) is 0.5 kg/s, while the flow rate of the industrial product through the outer annulus (D0 = 3 cm) is 0.8 kg/s. The product enters at 100 °C. The water enters at 34 °C and leaves at 60 °C. Determine a) Convective heat transfer coefficient of the cooling water.
(5 marks)
b) The overall heat transfer coefficient of this heat exchanger. (Hint : Take Nui = 5.45 for Di/D0 = 0.667 by interpolation)
(5 marks)
c) How long must the tube be if the outlet temperature of the product is to be 70 °C? (5 marks) Q10 [15 Marks] Ethanol (species A) is diffusing through a 4 mm stagnant film of water (species B). The ethanol concentrations of the entrance and the exiting planes are maintained at 0.1 and 0.02 mol/m3, respectively. If the water film temperature is 283 K, determine a) The mass diffusivity of ethanol in water at 283 K.
(5 marks)
b) The steady state molar flux of the ethanol.
(5 marks)
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BTE 3215 Heat and Mass Transfer
c) The concentration profile as a function of position x within the liquid film. (5 marks)
Some useful equations and constants: 1. Heat equation T T T T k k k q c p x x y y z z t
1 T 1 T T T k kr 2 k q c p r r r r z z t
2. Stefan-Boltzmann constant = 5.67X10-8 W/m2∙K4 3. Thermal entry length for laminar flow x fd ,t D
0.05 Re D Pr lam
4. Internal forced convection for constant surface temperature condition, To Ts Tm , o PL exp h Ti Ts Tm ,i m c p
Tlm
Ts = constant
To Ti T ln o Ti
p f
u m 2 L 2D
P p V
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BTE 3215 Heat and Mass Transfer
5. Natural Convection for vertical plate: RaL
g Ts T L3 Nu L 0.825
For all RaL,
2
0.387 RaL
1
6
1 0.492 / Pr 169
8 27
6. Heat Exchanger -NTU Method Cr
Cmin , Cmax
q qmax
NTU
,
UA , Cmin
qmax Cmin (Th ,i Tc ,i )
5. Fick’s Law of Diffusion (stationary medium approximation) N A, x CDAB A
DAB p 1T
3
dx A dx
xA C A
2
2C A 2 C A 2 C A N 1 C A A 2 2 2 x y y z DAB DAB t
6. Radiation Exchange: The Two-Surface Enclosure
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C
BTE 3215 Heat and Mass Transfer
(T14 T24 ) q12 q1 q2 1 1 1 1 2 1 A1 A1F12 2 A2
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BTE 3215 Heat and Mass Transfer
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