Free convection heat transfer is sometimes quantified bywriting Equation 4.20 as
An experiment for the configuration shown yields aheat transfer rate per unit length of
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Introduction to Heat Transfer
- 1. A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). + b. Flow shear stress is governed by the following equation ôu Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in tems of the pressure gradient when the shear stress at the bottom plate is zero. Moving plate at Um/s N= N-1 `Fixed plate FIGURE Q1arrow_forwardA rectangular block of height Land horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 Pi(g/em³) Fluid 2 Block P:(g/cm³) Po(g/cm³) (a) Derive a formula for the block density, Pp, in terms of the fluid densities p, and p2, the heights họ. h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) (b) Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes' principle. Prove that these two approaches are equivalent.arrow_forwardCorrect answer pleasearrow_forward
- One model of the glomerular membrane is a microporous membrane in which right cylindrical porespenetrate all the way through the membrane. Assume that the pores have a length of 50 nm and aradius of 3.5 nm. The viscosity of plasma is 0.002 Pa s. The average hydrostatic pressure in theglomerulus is 60 mm Hg, hydrostatic pressure in Bowman’s space is 20 mm Hg and the averageoncotic pressure of glomerular capillary blood is 28 mm Hg.A. Calculate the flow through a single pore assuming laminar flow (use the Poiseuille flowequation).B. How many pores would there have to be to produce a normal GFR?C. If the total aggregate area of the kidneys for filtration is 1.5 m2, what is the density of thepores (number of pores per unit area)D. What fraction of the area is present as pores?arrow_forwardPravinbhaiarrow_forwardThe Colburn equation for heat transfer is: 2/3 0.023 0.2 DG F';u is viscosity, lb h ft; k is thermal conductivity, where C, is heat capacity, Btu lb Btu h ft2 (°F ft); D is pipe diameter, ft; and G is mass velocity per unit area, lb h' ft. The Colburn equation is dimensionally consistent. What are the units and dimensions of the heat transfer coefficient, h?- -1arrow_forward
- fluid mechanicsarrow_forwardThe heat transfer coefficient is a nondimensional parameter which is a function of viscosity ? , specific heat cp (kJ/kg·K), and thermal conductivity k (W/m·K). This nondimensional parameter is expressed as (a) cp/? k (b) k/? cp (c) ? /cpk (d ) ? cp/k (e) cpk/?arrow_forwardIs the pi group 4 already an acceptable form or answer or do you always have to modify it into the Reynold's number?arrow_forward
- A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both speciesarrow_forwardFluid mechanics Iarrow_forwardHW1.1: Equation 2.7 in the text provides the velocity profile, u(y) for a narrow, infinitely long, slit-like microchannel. Use the no-slip boundary conditions (channel walls not moving) to obtain 1 dp - hy} 2n dx the standard solution, u(y)= For an incompressible, Newtonian fluid, with fluid properties as described in the text, shear stress du is typically given by t =n· dy Write-out an expression for the shear stress as a function of y. Calculate shear stress at: (a) y = 0; (b) y = h; and (c) y = h/2.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY