THERMAL ENERGY TRANSPORT. quiz #1

Transcription

1 THERMAL ENERGY TRANSPORT quiz #1 1. Express the following principles in terms of appropriate quantities. Make an appropriate sketch. a) Conservation of Mass (i) Lumped form (ii) Integral form b) Momentum Principle (i) Lumped form (ii) Integral form c) Conservation of Energy (i) Lumped form (ii) Integral form (assume W & f only) 2. Express the following constitutive relations in terms of appropriate quantities. Include appropriate sketch and list all restrictions. a) Newton's Law of Viscous Shear b) Fourier's Model for Conduction 3. Express the definition of the convective heat transfer coefficient, h. List the units of h in English and SI.

2 4. Formulate, but do not solve, the governing differential equation for one-dimensional steady-state conduction through a plane wall.

3 THERMAL ENERGY TRANSPORT quiz #2 1. List are the three steps of von Karman's Integral technique. 2. What are the advantages and disadvantages of this technique? 3. Make a sketch of flow over a flat plate. Include the concept of a viscous boundary layer and label completely. 4. Express the implicit definition of the viscous boundary layer thickness. 5. Assuming a linear velocity profile, determine a functional relationship for the velocity, u(x,y). 6. Determine the overall drag coefficient for this problem if the plate is L long and it is known that 1/ 2 δ = 2 3( µ x ρu. v f )

4 7. Utilizing von Karman's integral technique, apply the momentum principle to the viscous boundary layer and determine an integral/differential equation. Show that it is: δv (x) s(x) u d 2 d v v 0 = µ + ρu dy + ρu f (v n) y=δv (x) y dx dx y= 0 y= 0 s= 0 dy

5 THERMAL ENERGY TRANSPORT quiz #3 Thermal Boundary Layer Theory 1. Write down the expression for the implicit definition of the thickness of the thermal boundary layer, δ T (x). 2. For flow over a flat plate, formulate an expression for the convective heat transfer coefficient, h, in terms of the thermal boundary layer thickness, δ T (x), if the fluid temperature is assumed to be linear in the y-direction. Show all work. 3. Sketch out the appropriate thermodynamic system to which the conservation of energy principle should be applied in order to determine a model for the thermal boundary layer thickness, δ T (x). 4. Starting with the lumped parameter formulation of the conservation of energy principle, simplify this form of the equation (with explanation) to where only the terms appropriate for application to the above TD system are left. Do not actually apply to the TD system.

6 5. Apply only the heat transfer term to the above TD system, and show what it reduces to when x 0. Show all your work. 6. If the viscous BL thickness δ 12µ x ρu 1/ 2 v (x) = ( ) f, find an expression for h. Think! 7. Find an expression for the overall Nusselt number, Nu L for a plate of length L. Show all work.

7 THERMAL ENERGY TRANSPORT quiz #4 Natural and Combined Convection 1. The viscous and thermal boundary layers are usually assumed to be the same thickness. Physically, why is this reasonable? 2. What modeling technique have we used in modeling boundary layer theory and what are the basic steps? 3. Why is the momentum equation more difficult to solve for natural convection than for pure forced convection? 4. What is the local Richardson number, Ri x, and physically, what is it a measure of? 5. Plot a graph of Nu x /Re x 1/2 as a function of the Richardson number, Ri x. Plot the forced and natural convection asymptotes. Also, plot the assisting flow solution and the opposing flow solution where forced convection initially dominates.

8 6. If δ T (x) = b o x 1/4 where bo = c{pr[ρ 2 gβ(t w -T f )/µ 2 ]} -1/4, and assuming the temperature distribution is a 2nd order plolynomial, show that the average Nusselt number can be expressed as Nu L = c o (PrGr L ) 1/4. 7. A vertical solar collector plate has a known incoming uniform solar heat flux, f q,s, W/m 2. The back of the plate is well insulated so that the only heat transfer from the plate is natural convection. Knowing that Nu L = c 1 {(T w -T f )L 3 } 1/4, formulate a model for the temperature of the plate, T w.

9 THERMAL ENERGY TRANSPORT quiz #6 Extended Surfaces 1. Sketch a diagram of an optimum fin, including coordinate system and appropriate parameters and system quantities. 2. For the optimum fin, what is meant by equal utilization of material? 3. Find the temperature distribution and superimpose it just below the sketch. 4. Obtain expressions for both the heat dissipated by the fin, and the fin effectiveness. 5. Stating all assumptions necessary, show that the D.E. governing the optimal fin is: d dx A dt hp ( ) ( dx k T T f ) = 0 6. From the above D.E., obtain the D.E. governing the diameter, D(x), of the fin. 7. Solve the above D.E. for D = D(x).

10 Physics of Radiation 1. Define thermal radiation: THERMAL ENERGY TRANSPORT quiz #7 2. Define monochromatic intensity of radiation. 3. Draw and label an appropriate sketch for monochromatic intensity of radiation from one surface to another. What are its units (SI)? 4. Which electromagnetic waves have a higher energy (circle the correct answer): a) visible/infra-red b) x-ray/radar. 5. Circle the EM bands that compose what we call thermal radiation (circle all that apply): AM radio, gamma-ray, x-ray, infra-red, TV(UHF), visible, UV, cosmic-ray, AM radio, radar 6. What wavelength (high or low) would be best for use in detecting flying objects and why? 7. Define a differential solid angle. Include appropriate sketch.

11 8. What is the solid angle for one-half of a hemisphere (show you work)? 9. Express the total power of radiation in terms of monochromatic intensity. What are the units (SI)? 10. Which theory describes (insert first letter of appropriate theory in the brackets): absorption ( ); emission ( ); transmission ( ); reflection ( )? 11. If h is Planck s constant, write expressions for both the energy and momentum of a photon. 12. Define, in terms of an appropriate sketch and symbol, the monochromatic transmissivity.

12 ADVANCED THERMAL ENERGY TRANSPORT Quiz #8 1. Define monochromatic intensity of radiation. 2. Consider the radiation configuration factor; FA 1 A 2 a) Define it with appropriate nomenclature b) Define it in words c) Write down a model for how it can be computed (derive if you can t remember it). d) How is it related to FA 2 A 1? e) What assumptions are involved? 3. Write down the most general expression for net radiation exchange between two gray surfaces.

13 4. If the solar constant at the surface of the Earth, S c is known, utilize your answer in 3) above to find an expression for the heat transfer rate from the Sun to the Earth. 5. If A 2 is black and A 1 is gray in 2) above, derive an expression for the net heat transfer rate between the two surfaces, in terms of the configuration factor,, and other appropriate parameters. FA 1 A 2