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Chapter 14 Solutions
Fundamentals of Heat and Mass Transfer
- An iron-carbon alloy initially containing 0.268 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1040°C. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0.0 wt% C. At what position will the carbon concentration be 0.201 wt% after a 7 h treatment? The value of D at 1040°C is 2.5 × 10-¹1 m²/s. erf(z) erf(z) 0.55 0.5633 1.3 0.025 0.0282 0.60 0.6039 1.4 0.9523 0.0564 0.65 0.6420 1.5 Z 0.00 0.05 0.15 0.0000 0.10 0.1125 0.70 0.6778 0.20 Z 0.1680 0.75 0.7112 1.7 0.2227 0.80 0.7421 1.8 0.45 0.4755 1.1 0.50 0.5205 Z 1.6 1.2 0.9103 erf(z) 0.9340 2.8 0.9661 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.30 0.3286 0.90 0.7970 2.0 0.9953 0.35 0.3794 0.95 0.8209 2.2 0.40 0.4284 1.0 0.8427 2.4 0.9763 0.9838 0.9891 0.9981 0.8802 2.6 0.9998 0.9993 0.9999arrow_forwardAn iron-carbon alloy initially containing 0.240 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1100°C. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0.0 wt% C. At what position will the carbon concentration be 0.180 wt% after a 7 h treatment? The value of D at 1100°C is 3.7 × 10-11 m2/s.arrow_forwardA diffusion couple of two metals, A and B, was fashioned as shown in Figure 5.1. After a 26 hour heat treatment at 1170°C (and subsequent cooling to room temperature) the concentration of A is 4.0 wt% at the 11-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, only at 701°C for 26 hours, at what position (in mm) will the composition be 4.0 wt% A? The preexponential and activation energy values for the diffusion of A in B are 2.4 x 10-4 m²/s and 154 kJ/mol, respectively. i mmarrow_forward
- Q3) Pulverized coal pellets, which may be approximated as carbon spheres of radius R = 1.5 mm, are burned in a pure oxygen atmosphere at 1400K and 1.2 atm. Oxygen is transferred to the particle surface by diffusion, where it is consumed in the reaction, C(s) + O2(g) → CO2(g). The reaction rate is first order and of the form R = -k.Co2 at r = R where k = 0.12 m/s. This is the reaction rate per unit surface area of the carbon pellets. Neglecting change in R, determine the steady-state O2 molar consumption rate in mol/s. At 1400K, the binary diffusion coeffici for O2 and CO2 is 1.6x104 m2/s.arrow_forward34) Hydrogen is allowed to diffuse through a palladium plate that is 0.015m thick at 500°C. The concentrations of carbon at the two faces are 0.65 and 0.30 kg/m3, which are maintained constant. The diffusion coefficient at this temperature is 6.13x1011 m²/s. Calculate the diffusion flux in units of kg/m2s.arrow_forwardConsider a sheet of Iron which is maintained in an atmosphere filled with nitrogen and is permitted to achieve and steady state diffuseion. The thickness of the sheet is 6.5mm. The diffusion coefficient of nitrogen in iron is 1.9 × 10 -11 m 2 /s at 675 0 C.arrow_forward
- The viscosity values for the H2 and Freon-12 gas mixtures at 25 ° C and 1 atm pressure and the mole fractions of the mixture are given in the table below. For H2 and Freon-12, calculate the viscosity values of the mixture for 3 different compositions using pure viscosity values. H2 Mol Frac. 0,00 0,25 0,50 0,75 1,00 Viscosity (µ) x 106 (poise) 124,0 128,1 131,9 135,1 88,4arrow_forwardA copper–nickel diffusion couple similar to that shown in Figure 5.1a is fashioned. After a 700-h heat treatment at 1100C (1373 K), the concentration of Cu is 2.5 wt% at the 3.0-mm position within the nickel. At what temperature must the diffusion couple be heated to produce this same concentration (i.e., 2.5 wt% Cu) at a 2.0-mm position after 700 h? The preexponential and activation energy for the diffusion of Cu in Ni 2.7*10^-5(m^2/s) and 256 kJ/mol.arrow_forwardA membrane is to be manufactured to the following specifications. At 700°C the leak rate of hydrogen at steady state is not to exceed 103 mol cm2 hr' when the concentrations of hydrogen are maintained at Chigh = 7.7 × 1019 atoms cm³ on one side of the membrane and Clow effectively zero on the other side. Determine the minimum thickness, {, of iron foil that will meet these requirements. The diffusion coefficient of atomic hydrogen in iron, DH, at 700°C is 3.091x104 cm? s. Express your answer in units of cm.arrow_forward
- Carbon is allowed to diffuse through a steel plate 10mm thick. The concentrations of carbon at the two faces are 0.85???3 and 0.40???3 which are maintained constant. If the preexponential and activation energy are 5.0 × 10 ―7 ?2??? and 77,000 ????, compute the temperature at which the diffusion flux is 6.3 × 10 ―10 ???2 ∙ ???arrow_forwardThermo-fluid Mechanics I want a quick solutionarrow_forwardANSWER THERMOFLUIDS QUESTIONSarrow_forward
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