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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

Repeat Prob. 5–99 for the case of implicit formulation.Data from problem 99Consider transient heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The
Consider transient heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, 3, 4, and 5 with a
Consider transient heat conduction in a plane wall with variable heat generation and constant thermal conductivity The nodal network of the medium consists of nodes 0, 1, 2, 3, and 4 with a uniform
Consider one-dimensional transient heat conduction in a composite plane wall that consists of two layers A and B with perfect contact at the interface. The wall involves no heat generation and
Consider transient one-dimensional heat conduction in a pin fin of constant diameter D with constant thermal conductivity. The fin is losing heat by convection to the ambient air at T∞ with a heat
Repeat Prob. 5–104 for the case of implicit formulation.Data from problem 104Consider transient one-dimensional heat conduction in a pin fin of constant diameter D with constant thermal
The roof of a house consists of a 15-cm-thick concrete slab (k = 1.4 W/m · K and α = 0.69 × 10-6 m2/s) that is 18 m wide and 32 m long. One evening at 6 pm, the slab is observed to be at a
A common annoyance in cars in winter months is the formation of fog on the glass surfaces that blocks the view. A practical way of solving this problem is to blow hot air or to attach electric
Repeat Prob. 5–116 using the implicit method with a time step of 1 min.Data from problem 116A common annoyance in cars in winter months is the formation of fog on the glass surfaces that blocks the
Revisit Prob. 5–61 of two-dimensional heat conduction in a square cross section.(a) Develop an explicit finite difference formulation for a two-dimensional transient heat conduction case(b) Find
Quench hardening is a mechanical process in which the ferrous metals or alloys are first heated and then quickly cooled down to improve their physical properties and avoid phase transformation.
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, and 3 with
Consider a 2 cm 3 4 cm ceramic strip (k = 3 W/m · K, ρ = 1600 kg/m3 and cp = 800 J/kg · K) embedded in very high conductivity material as shown in Fig. P5–120. The two sides of the ceramic strip
Can the global (accumulated) discretization error be less than the local error during a step? Explain.
What is the cause of the discretization error? How does the global discretization error differ from the local discretization error?
Why do the results obtained using a numerical method differ from the exact results obtained analytically? What are the causes of this difference?
How is the finite difference formulation for the first derivative related to the Taylor series expansion of the solution function?
Explain why the local discretization error of the finite difference method is proportional to the square of the step size. Also explain why the global discretization error is proportional to the step
What causes the round-off error? What kind of calculations are most susceptible to round-off error?
What happens to the discretization and the round-off errors as the step size is decreased?
Suggest some practical ways of reducing the roundoff error.
What is a practical way of checking if the round-off error has been significant in calculations?
What is a practical way of checking if the discretization error has been significant in calculations?
Starting with an energy balance on the volume element, obtain the steady three-dimensional finite difference equation for a general interior node in rectangular coordinates for T(x, y, z) for the
Starting with an energy balance on the volume element, obtain the three-dimensional transient explicit finite difference equation for a general interior node in rectangular coordinates for T(x, y, z,
Consider one-dimensional transient heat conduction in a plane wall with variable heat generation and variable thermal conductivity. The nodal network of the medium consists of nodes 0, 1, and 2 with
Repeat Prob. 5–134 for the case of implicit formulation.Data from problem 134Consider one-dimensional transient heat conduction in a plane wall with variable heat generation and variable thermal
Consider steady one-dimensional heat conduction in a pin fin of constant diameter D with constant thermal conductivity. The fin is losing heat by convection with the ambient air at T∞ (in °C) with
Consider a large plane wall of thickness L = 0.3 ft and thermal conductivity k = 1.2 Btu/h·ft·°F in space. The wall is covered with a material having an emissivity of ε = 0.80 and a solar
Consider a nuclear fuel element (k = 57 W/m · K) that can be modeled as a plane wall with thickness of 4 cm. The fuel element generates 3 × 107 W/m3 of heat uniformly. Both side surfaces of the
A fuel element (k = 67 W/m · K) that can be modeled as a plane wall has a thickness of 4 cm. The fuel element generates 5 × 107 W/m3 of heat uniformly. Both side surfaces of the fuel element are
Consider steady two-dimensional heat transfer in a long solid bar (k = 25 W/m · K) of square cross section (2 cm × 2 cm) with heat generated in the bar uniformly at a rate of ė = 3 × 106 W/m3.
A two-dimensional bar has the geometry shown in Fig. P5–141 with specified temperature TA on the upper surface and TB on the lower surfaces, and insulation on the sides. The thermal conductivity of
Starting with an energy balance on a disk volume element, derive the one-dimensional transient implicit finite difference equation for a general interior node for T(z, t) in a cylinder whose side
A hot surface at 120°C is to be cooled by attaching 8 cm long, 0.8 cm in diameter aluminum pin fins (k = 237 W/m · K and α = 97.1 × 10-6 m2/s) to it with a center-to-center distance of 1.6 cm.
Solar radiation incident on a large body of clean water (k = 0.61 W/m · K and α = 0.15 × 10-6 m2/s) such as a lake, a river, or a pond is mostly absorbed by water, and the amount of absorption
Reconsider Prob. 5–144. The absorption of solar radiation in that case can be expressed more accurately as a fourth degree polynomial aswhere q̇s is the solar flux incident on the surface of the
A hot brass plate is having its upper surface cooled by impinging jet of air at temperature of 15°C and convection heat transfer coefficient of 220 W/m2 · K. The 10-cmthick brass plate (ρ = 8530
Consider a uranium nuclear fuel element (k = 35 W/m · K, ρ = 19,070 kg/m3 and cp = 116 J/kg · K) of radius 10 cm that experiences a volumetric heat generation at a rate of 4 × 105 W/m3 because of
Starting with an energy balance on the volume element, obtain the two-dimensional transient explicit finite difference equation for a general interior node in rectangular coordinates for T(x, y, t)
A long steel bar has the cross section shown in Fig. P5–149. The bar is removed from a heat treatment oven at Ti = 700°C and placed on the bottom of a tank filled with water at 10°C. To intensify
The unsteady forward-difference heat conduction for a constant area, A, pin fin with perimeter, p, exposed to air whose temperature is T0 with a convection heat transfer coefficient of h isIn order
Air at T0 acts on top surface of the rectangular solid shown in Fig. P5–151 with a convection heat transfer coefficient of h. The correct steady-state finite-difference heat conduction equation for
What is the correct unsteady forward-difference heat conduction equation of node 6 of the rectangular solid shown in Fig. P5–152 if its temperature at the previous time (Δt) is T6*? (a) Τό + 1 =
What is the correct steady-state finite-difference heat conduction equation of node 6 of the rectangular solid shown in Fig. P5–153? (a) T6 = (T₁+T3 + T₂ + ₁)/2 (T5+ T₁+T₂ + T10)/2 = (b)
The height of the cells for a finite-difference solution of the temperature in the rectangular solid shown in Fig. P5–154 is one-half the cell width to improve the accuracy of the solution. The
The height of the cells for a finite-difference solution of the temperature in the rectangular solid shown in Fig. P5–155 is one-half the cell width to improve the accuracy of the solution. If the
Write a two-page essay on the finite element method, and explain why it is used in most commercial engineering software packages. Also explain how it compares to the finite difference method.
Design a fire-resistant safety box whose outer dimensions are 0.5 m × 0.5 m × 0.5 m that will protect its combustible contents from fire which may last up to 2 h. Assume the box will be exposed to
Design a defrosting plate to speed up defrosting of flat food items such as frozen steaks and packaged vegetables and evaluate its performance using the finite difference method. Compare your design
Numerous professional software packages are available in the market for performing heat transfer analysis, and they are widely advertised in professional magazines such as the Mechanical Engineering
A ball bearing manufacturing plant is using air to cool chromium steel balls (k = 40 W/m ∙ K). The convection heat transfer coefficient for the cooling is determined experimentally as a function of
Consider the surface of a metal plate being cooled by forced convection. Determine the ratio of the temperature gradient in the fluid to the temperature gradient in the metal plate at the surface.
A metal plate is being cooled by air (kfluid = 0.259 W/m ∙ K) at the upper surface while the lower surface is subjected to a uniform heat flux of 1000 W/m2. Determine the temperature gradient in
The top surface of a metal plate (kplate = 237 W/m ∙ K) is being cooled by air (kair = 0.243 W/m ∙ K) while the bottom surface is exposed to a hot steam at 100°C with a convection heat transfer
During air cooling of a flat plate (k = 1.4 W/m ∙ K), the convection heat transfer coefficient is given as a function of air velocity to be h 5 27V 0.85, where h and V are in W/m2 ∙ K and m/s,
A metal plate (k = 180 W/m · K, ρ = 2800 kg/m3, and cp = 880 J/kg · K) with a thickness of 1 cm is being cooled by air at 5°C with a convection heat transfer coefficient of 30 W/m2 · K. If the
Air at 5°C, with a convection heat transfer coefficient of 30 W/m2 · K, is used for cooling metal plates coming out of a heat treatment oven at an initial temperature of 300°C. The plates (k = 180
As shown in Fig. P5–81 a T shaped bar (k = 28 W/m · K) in inverted position is attached to a surface maintained at 200°C. The two sides of the bottom portion of the T bar are insulated while the
A long steel strip is being conveyed through a 3-m long furnace to be heat treated at a speed of 0.01 m/s. The steel strip (k = 21 W/m · K, ρ = 8000 kg/m3, and cp = 570 J/kg · K) has a thickness
What is viscosity? What causes viscosity in liquids and in gases? Is dynamic viscosity typically higher for a liquid or for a gas?
What fluid property is responsible for the development of the velocity boundary layer? For what kind of fluids will there be no velocity boundary layer on a flat plate?
What is the physical significance of the Prandtl number? Does the value of the Prandtl number depend on the type of flow or the flow geometry? Does the Prandtl number of air change with pressure?
Will a thermal boundary layer develop in flow over a surface even if both the fluid and the surface are at the same temperature?
What is the physical significance of the Reynolds number? How is it defined for external flow over a plate of length L?
How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher?
What is turbulent thermal conductivity? What is it caused by?
Consider fluid flow over a surface with a velocity profile given asDetermine the shear stress at the wall surface, if the fluid is(a) Air at 1 atm(b) Liquid water, both at 20°C. Also calculate the
Consider a flow over a surface with the velocity and temperature profiles given aswhere the coefficients C1 and C2 are constants. Determine the expressions for the friction coefficient (Cf) and the
Air flowing over a 1-m-long flat plate at a velocity of 7 m/s has a friction coefficient given as Cf = 0.664(Vx/v)-0.5, where x is the location along the plate. Determine the wall shear stress and
Consider a fluid flowing over a flat plate at a constant free stream velocity. The critical Reynolds number is 5 × 105 and the distance from the leading edge at which the transition from laminar to
How is the modified Reynolds analogy expressed? What is the value of it? What are its limitations?
Consider an airplane cruising at an altitude of 10 km where standard atmospheric conditions are 250°C and 26.5 kPa at a speed of 800 km/h. Each wing of the airplane can be modeled as a 25-m × 3-m
A metallic airfoil of elliptical cross section has a mass of 50 kg, surface area of 12 m2, and a specific heat of 0.50 kJ/kg · K. The airfoil is subjected to air flow at 1 atm, 25°C, and 5 m/s
Repeat Prob. 6–85 for an air-flow velocity of 10 m/s.Data from problem 85A metallic airfoil of elliptical cross section has a mass of 50 kg, surface area of 12 m2, and a specific heat of 0.50 kJ/kg
The electrically heated 0.6-m-high and 1.8-m-long windshield of a car is subjected to parallel winds at 1 atm, 0°C, and 80 km/h. The electric power consumption is observed to be 50 W when the
A 5-m × 5-m flat plate maintained at a constant temperature of 80°C is subjected to parallel flow of air at 1 atm, 20°C, and 10 m/s. The total drag force acting on the upper surface of the plate
Air (1 atm, 5°C) with free stream velocity of 2 m/s flowing in parallel to a stationary thin 1 m × 1 m flat plate over the top and bottom surfaces. The flat plate has a uniform surface temperature
Air at 1 atm and 20°C is flowing over the top surface of a 0.2 m × 0.5 m-thin metal foil. The air stream velocity is 100 m/s and the metal foil is heated electrically with a uniform heat flux of
Air at 1 atm is flowing over a flat plate with a free stream velocity of 70 m/s. If the convection heat transfer coefficient can be correlated by Nux = 0.03 Rex0.8 Pr1/3, determine the friction
Metal plates are being cooled with air blowing in parallel over each plate. The average friction coefficient over each plate is given as Cf = 1.33(ReL)-0.5 for ReL < 5 × 105. Each metal plate length
A flat plate is subject to air flow parallel to its surface. The average friction coefficient over the plate is given asThe plate length parallel to the air flow is 1 m. Using EES (or other)
Using a cylinder, a sphere, and a cube as examples, show that the rate of heat transfer is inversely proportional to the nominal size of the object. That is, heat transfer per unit area increases as
Determine the heat flux at the wall of a microchannel of width 1 mm if the wall temperature is 50°C and the average gas temperature near the wall is 100°C for the cases of (a) σT 1.0, y = 1.667,
If (∂T/∂y)w = 80 K/m, calculate the Nusselt number for a microchannel of width 1.2 mm if the wall temperature is 50°C and it is surrounded by (a) Ambient air at temperature 30°C,(b) Nitrogen
A fluid flows at 5 m/s over a wide flat plate 15 cm long. For each from the following list, calculate the Reynolds number at the downstream end of the plate. Indicate whether the flow at that point
Consider the Couette flow of a fluid with a viscosity of m = 0.8 N · s/m2 and thermal conductivity of kf = 0.145 W/m · K. The lower plate is stationary and made of a material of thermal
Engine oil at 15°C is flowing over a 0.3-m-wide plate at 65°C at a velocity of 3.0 m/s. Using EES, Excel, or other comparable software, plot(a) The hydrodynamic boundary layer(b) The thermal
Object 1 with a characteristic length of 0.5 m is placed in airflow at 1 atm and 20°C with free stream velocity of 50 m/s. The heat flux transfer from object 1 when placed in the airflow is measured
A rectangular bar with a characteristic length of 0.5 m is placed in a free stream flow where the convection heat transfer coefficients were found to be 100 W/m2 · K and 50 W/m2· K when the free
In an effort to prevent the formation of ice on the surface of a wing, electrical heaters are embedded inside the wing. With a characteristic length of 2.5 m, the wing has a friction coefficient of
A 15 cm × 20 cm circuit board is being cooled by forced convection of air at 1 atm. The heat from the circuit board is estimated to be 1000 W/m2. If the air stream velocity is 3 m/s and the shear
The transition from laminar flow to turbulent flow in a forced convection situation is determined by which one of the following dimensionless numbers?(a) Grassh of(b) Nusselt(c) Reynolds(d)
In any forced or natural convection situation, the velocity of the flowing fluid is zero where the fluid wets any stationary surface. The magnitude of heat flux where the fluid wets a stationary
The ___________ number is a significant dimensionless parameter for forced convection and the ___________ number is a significant dimensionless parameter for natural convection.(a) Reynolds,
The coefficient of friction Cf for a fluid flowing across a surface in terms of the surface shear stress, ts, is given by (a) 2pV²/Tw (d) 4Tw/pV² W (b) 2Tw/pV² (c) 2Tw/pV²AT (e) None of them
Most correlations for the convection heat transfer coefficient use the dimensionless Nusselt number, which is defined as(a) h/k(b) k/h(c) hLc /k(d) kLc/h(e) k/ρcp
For the same initial conditions, one can expect the laminar thermal and momentum boundary layers on a flat plate to have the same thickness when the Prandtl number of the flowing fluid is(a) Close to
One can expect the heat transfer coefficient for turbulent flow to be ___________ for laminar flow.(a) Less than(b) Same as(c) Greater than
An electrical water (k = 0.61 W/m· K) heater uses natural convection to transfer heat from a 1-cm-diameter by 0.65-m-long, 110 V electrical resistance heater to the water. During operation, the

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