# Results for: “Laxmi Publications”

70 eBooks

## he9-1 |
Mahesh M. Rathore | Laxmi Publications | |||||

Internal Flow 9 9.1. Flow Inside Ducts. 9.2. Hydrodynamic Considerations—Mean velocity um—Hydrodynamic entry length—Velocity profile in fully developed region—Friction factor—Pressure drop and friction factor in fully developed flow. 9.3. Thermal Considerations—The mean temperature or bulk temperature. 9.4. The Heat Transfer in Fully Developed Flow. 9.5. General Thermal Analysis—Constant surface heat flux—Constant surface temperature. 9.6. Heat Transfer in Laminar Tube Flow. 9.7. Flow Inside a Non-circular Duct. 9.8. Thermally Developing, Hydrodynamically Developed Laminar Flow. 9.9. Heat Transfer in Turbulent Flow Inside a Circular Tube—Analogy between heat and momentum transfer in turbulent flow through tube—Correlation for turbulent flow. 9.10. Heat Transfer to Liquid Metal Flow in Tube. 9.11. Summary—Review Questions—Problems—References and Suggested Reading. 9.1. FLOW INSIDE DUCTS The flow of fluid through the tubes and ducts for transporting cooling and heating fluids, etc., is of engineering importance. Most heat exchangers involve the heating or cooling of fluids flowing in the tubes. The fluid in such applications is forced to flow by a fan or pump through a tube that is sufficiently long to accomplish desired heating or cooling. Pressure drop and heat flux are associated with forced flow through the tubes and friction factor and heat transfer coefficient are used to determine the pumping power and length of tube. See All Chapters |
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## LAX20-2 |
Dr. A.J. Nair | Laxmi Publications | |||||

$� PRINCIPLES OF BIOTECHNOLOGY AND GENETIC ENGINEERING n Since the microcarrier culture is well mixed, it is easy to monitor and control different environmental conditions such as pH, PO2, PCO2, etc. n Cell sampling is easy. n Since the beads settle down easily, cell harvesting and downstream processing of products is easy. n Microcarrier cultures can be relatively easily scaled-up using conventional equipment such as fermentors that have been suitably modified. Because of the many advantages of the technique itself, it has gained great popularity. Thus, a large variety of microcarriers are available on the market. FIGURE 20.4 Vero cells cultured on cytodex microcarriers. 6. Fixed-bed reactors. Microcarriers, macrocarriers, or encapsulated beads could be used in fixed-bed reactors. The cells are immobilized in a matrix and the culture fluid is circulated in a closed loop. There is no agitation system. If the bed of immobilized cells is disturbed by the circulating medium, it is said to be a fluidized-bed reactor. Such a process achieves a high degree of aeration and agitation. See All Chapters |
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## 13 |
Parmananda Gupta | Laxmi Publications | |||||

148 DIFFERENTIAL GEOMETRY AND CALCULUS OF VARIATIONS Example 4. Find the extremal of the functional z a −a (λy + 1 2 µy″2) dx which satisfy the boundary conditions y(– a) = 0, y′(– a) = 0, y(a) = 0, y′(a) = 0. z FGH IJ K 1 µy″ 2 dx . −a 2 1 2 Let F(x, y, y′, y″) = λy + µy″ 2 d d2 Fy ′ + F =0 The Euler-Poisson equation is Fy − dx dx 2 y ″ Here Fy = λ, Fy′ = 0, Fy″ = µy″ Sol. Given functional is ∴ (1) λ− ⇒ a λy + d d2 (0) + (µy″ ) = 0 ⇒ dx dx 2 µ d4 y dx 4 +λ =0 ⇒ ...(1) d4 y λ =– 4 µ dx d3 y λ = − x + c1 3 µ dx ⇒ d2y ⇒ dx 2 =− λ x2 + c1x + c2 µ 2 dy λ x3 x2 =− + c1 + c2x + c3 2 dx µ 6 ⇒ λ x4 x3 x2 + c3x + c4 + c1 + c2 6 2 µ 24 This is the equation of the extremals. The boundary conditions are y(– a) = 0, y′(– a) = 0, y(a) = 0, y′(a) = 0 ⇒ y= − y(– a) = 0 ⇒ − λa4 c1a 3 c2 a2 – c3a + c4 = 0 − + 24µ 6 2 − ...(4) λa4 c1 a3 c2 a2 + + + c3a + c4 = 0 24µ 6 2 ...(5) λa3 c1a 2 + + c2a + c3 = 0 6µ 2 ...(6) − y′(a) = 0 ⇒ c1 a3 – 2c3a = 0 ⇒ c1a2 + 6c3 = 0 3 (4) + (6) ⇒ c1a2 + 2c3 = 0 Solving (7) and (8), we get c1 = 0, c3 = 0 (3) – (5) ⇒ (4) (3) ⇒ – λa 3 + 0 – c2a + 0 = 0 6µ ⇒ − λa 4 a2 −0+ 24µ 2 ...(3) λa 3 c1 a2 – c2a + c3 = 0 See All Chapters |
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## 5up4-6 |
M. Goyal | Laxmi Publications | |||||

232 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Difference table is ∆2 f(x) ∆ f(x) u x f(x) –1 10 2854 0 14 3162 ∆3 f(x) 308 74 382 1 18 3544 2 22 3992 –8 66 448 Bessel’s formula is RS f (0) + f (1) UV + FG u − 1IJ ∆ f (0) + u (u − 1) RS ∆ 2! T 2 W H 2K T 2 f(u) = f (− 1) + ∆2 f (0) 2 FG H UV W (u − 1) u − + ∴ f (.25) = 3! ∆3 f (−1) FG 3162 + 3544 IJ + (.25 – .5) (382) + (.25) (.25 − 1) FG 74 + 66 IJ H 2 K H 2 K 2 + Hence IJ K 1 u 2 = 3250.875 y15 = 3250.875. (.25 − 1) (.25 − .5) (.25) (– 8) 6 ASSIGNMENT 1. Apply Bessel’s formula to find the value of y2.73 given that y2.5 = 0.4938, y2.6 = 0.4953, y2.7 = 0.4965, y2.8 = 0.4974, y2.9 = 0.4981, y3.0 = 0.4987. 2. Find the value of y if x = 3.75, given that x: 2.5 3.0 3.5 4.0 4.5 5.0 y: 24.145 22.043 20.225 18.644 17.262 16.047. Use Bessel’s formula. 3. Apply Bessel’s formula to find u62.5 from the following data: 4. 5. x : 60 61 62 63 64 65 ux : 7782 7853 7924 7993 8062 8129. Apply Bessel’s formula to find the value of f(12.2) from the following table: x : 0 5 10 15 20 25 30 f(x) : 0 0.19146 0.34634 0.43319 0.47725 0.49379 0.49865 Following table gives the values of ex for certain equidistant values of x. Find the value of ex when x = 0.644 using Bessel’s formula: x : ex See All Chapters |
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## ch-12 |
Rehana Khan | Laxmi Publications | |||||

LINKAGE 12 MAPPING G ENE IN PRO AND E UKARYOTES AND The frequency of crossing over, thus appears to be closely related to physical distance between genes. When one knows all the genes, linkage groups and number of linkage groups of a species, it becomes possible for him that by adopting the crossing over as a tool he may determine the relative distance between the genes in a linkage group and also their order and may give diagrammatic representation of chromosomes showing the gene as points separated by distances proportional to the amount of crossing over. Such a diagrammatic, graphical representation of relative distance between linked genes of a chromosome is called linkage or genetic map. MAPPING GENES IN BACTERIA The most commonly used bacterium for genetic and molecular analysis is Escherichia coli (E. coli), which is found most commonly in animal (including human) intestines. It is a good subject for study since it can be grown on a simple defined medium and can be handled with simple microbiological techniques. See All Chapters |