National Institute of Technology 2007 B.Tech Chemical Engineering Transport Phenomena - Question Paper
Transport Phenomena
Time: three Hrs Max Marks:100
4th May, 2007
1. A spherical aggregate of bacterial cells, presumed to be homogeneous are of the radius R. Under certain circumstances, the oxygen metabolism rate of the bacterial cells is almost zero order with respect to oxygen concentration and may be approximated by an effective volumetric reaction rate ro2 = -k0. The diffusion may be defined by Fick’s legal regulations with an effective pseudo binary diffusivity for oxygen in the bacterial medium D02-M. Neglect transient and convection effects because the oxygen solubility is very low in the system. Let ?0 be the oxygen mass concentration at the aggregate surface. describe the subsequent dimensionless quantities:
If N is large enough, then an oxygen free core may exist in the aggregate such that x>0
a) Establish the pseudo steady state oxygen concentration distribution. (10)
b) Derive the expression from which the dimensionless oxygen free core radius may be determined as a function of N. (05)
c) For what value of N does an oxygen free core exist? (05)
2. Determine the steady state temperature distribution T® In a solid sphere of radius R in which heat is generated at a uniform rate of g0 W/m3 and heat is dissipated from the surface by convection into a medium at a temperature at infinity with a heat transfer coefficient h. Determine the expressions for the temperature at the centre of the sphere and the heat flux at the boundary surface. (15)
3. A Stormer Viscometer consists essentially of 2 concentric cylinders, the inner of which rotates while the outer is held stationary. Viscosity is determined by measuring the rate of rotation of the inner cylinder under the application of a known torque. Develop an expression for the velocity distribution in this type of apparatus, as a function of applied torque, for laminar flow of a Newtonian Fluid. Neglect end effects. (20)
4. Starting from the fundamentals derive the formula of thermal energy. discuss the physical significance of every term in this formula. (25)
5. A fluid of constant p and u is contained in a very long horizontal pipe of length L and radius R. Initially the fluid is at rest. At time t = 0, a pressure gradient is impressed on the system. Determine how the velocity profile modifications with time. (20)
TIME: 3 Hrs
A spherical aggregate of bacterial cells, assumed to be homogeneous are of the radius R. Under certain circumstances, the oxygen metabolism rate of the bacterial cells is almost zero order with respect to oxygen concentration and may be approximated by an effective volumetric reaction rate ro2~ -ko- The diffusion may be described by Ficks law with an effective pseudo binary diffusivity for oxygen in the bacterial medium D02-M Neglect transient and convection effects because the oxygen solubility is very low in the system. Let p0 be the oxygen mass concentration at the aggregate surface. Define the following dimensionless quantities:
TV = M
- r.
and
10
a)
b) c)
05
05
Po / R /PoDq2-M
enough, then an oxygen free core may exist in the aggregate such that % = 0 for < 0
Establish the pseudo-steady-state oxygen concentration distribution X-
Derive an expression from which the dimensionless oxygen-free core radius 0 may be determined as a function of N.
For what value of N does an oxygen-free core exist?
If N is large
Determine the steady state temperature distribution T(r) in a solid sphere of radius R in which heat is generated at a uniform rate of go W/m3 and heat is dissipated from the surface by convection into a medium at a temperature Too with a heat transfer coefficient h. Determine the expressions for the temperature at the centre of the sphere and the heat flux at the boundary surface.
15
A Stormer viscometer consists essentially of two concentric cylinders, the inner of which rotates while the outer is held stationary. Viscosity is determined by measuring the rate of rotation of the inner cylinder under the application of a known torque. Develop an expression for the velocity distribution in this kind of apparatus, as a function of applied torque, for laminar flow of a Newtonian fluid. Neglect end ects.
20
Starting from the fundamentals derive the equation of thermal energy. Explain the physical significance of each term in this equation.
25
"01 constant p and jlx is contained in a very long horizontal pipe of length L and radius R. Initially the fluid is at rest. At til
* * * * *
t /V./
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| Earning: Approval pending. |
