(Aktu Btech) Heat and Mass Transfer Important Unit-3 Forced and Natural Convection

B.Tech AKTU Quantum Book will take you deep into the area of Heat and Mass Transport. To be successful in this subject, keep track of important notes, frequently asked questions, and critical insights. Unit-3 Forced and Natural Convection

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Important Questions For Heat and Mass Transfer:
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Q1. Explain the concept of boundary layer. 

Ans.

• 1. The boundary layer is the layer that lies next to the boundary. Every time there is relative motion between the border and the fluid, a boundary layer is generated.
• 2. A layer of fluid that comes into touch with the boundary surface and sticks to it causes the condition of no slip to occur when a genuine fluid (viscous fluid) flows through a stationary solid boundary.
• 3. As a result, the layer of fluid that is unable to move away from the boundary surface experiences retardation. This retarded layer then causes the adjacent layers of fluid to experience their own retardation, which leads to the development of a small region immediately adjacent to the boundary surface where the flow velocity of the fluid increases quickly from zero at the boundary surface and approaches the velocity of the main stream.
• 4. According to boundary layer theory, the extensive fluid medium around bodies moving in fluids can be divided into following two regions: 
  • i. The boundary layer, which is a thin layer next to the boundary and is where the viscous shear occurs.
  • ii. A area outside the boundary layer where the behaviour of the flow is very similar to that of an ideal fluid and the possibility for Theory is now applicable.

Q2. Derive an expression for Nusselt number for turbulent flow over flat plate using Colburn analogy.

Ans. 1. As we know that, the inter-relationship between fluid friction and Newton’s law of viscosity is given as,

2. Heat flow along Y-direction follows the Fourier equation 

3. When Pr is unity, temperature and velocity profile are identical (for

most of the gases, 0.6 < Pr < 1.0)

5. Separating the variables and integrating within the limits : 

7. Substituting eq. (3.6.5) and eq. (3.6.6) in eq. (3.6.4), we get

8. It represents the Nusselt number divided by the product of the Reynolds and Prandtl number, i.e., 

Eq. (3.6.7) is called the Reynolds analogy. 

9. Further in case of laminar boundary layer on a flat plate, we have

Eq. (3.6.10) shows the inter-relationship between heat and momentum transfer and designated as Colburn analogy. 

12. For Pr = 1, the Reynolds and Colburn analogies are same. 

Q3. What do you understand by mixed boundary layer ?

Ans. 1. Fig. shows flow over a plate. 

• 2. If the length of the plate is more than the distance x, calculated from equation, Ux/v = 5 x 10⁵, the thickness of boundary layer will go on increasing in the downstream direction.  
• 3. At that point, the fluid motion within the laminar boundary layer becomes unstable and uneven, which causes it to change from a laminar to a turbulent boundary layer.
• 4. The transition zone, or mixed zone, over which the boundary layer flow transitions from laminar to turbulent is shown by distance BC.
• 5. The boundary layer is turbulent and keeps thickening further downstream of the transition zone.
• 6. The part FG demonstrates how the thickness of this boundary layer, which is known as turbulent, is continuously increasing. 

Q4. What do you understand by buoyant force and centre of buoyancy ?

Ans. A. Buoyant Force: Every time a body is submerged in a fluid, the fluid pulls the body upward. The buoyant force, or simply buoyancy, is the upward force that is equivalent to the weight of the fluid that the body has displaced.

B. Centre of Buoyancy: 

• 1. It is described as a point about which the buoyancy force is intended to act.
• 2. Because the weight of the fluid that the body displaces is equivalent to the vertical force of buoyancy. The centre of gravity of the fluid displaced will serve as the centre of buoyancy.3. In Fig. F_B is the force of buoyancy and point B is the centre of buoyancy.

Q5. Castor oil at 25 °C flows at a velocity of 0.1 m/s past a flat plate in a certain process. If the plate is 4.5 m long and is maintained at a uniform temperature of 95 °C. Calculate the following using exact solution:

i. The hydrodynamic and thermal boundary layer thickness on one side of the plate, 

ii. The total drag force per unit width on one side of the plate, 

iii. The local heat transfer coefficient at the trailing edge, and the heat transfer rate.

Ans. Given: t_𝛼 = 25 °C, t_s = 95 °C, L = 4.5 m, U= 0.1 m/s. 

To Find: i. The hydrodynamic and thermal boundary layer thickness on one side of the plate. 

ii. The total drag force per unit width on one side of the plate. 

iii. Thelocal heat transfer coefficient at the trailing edge.

1. Reynolds number at the end of the plate, 

2. The hydrodynamic boundary layer thickness.

3. The thermal boundary layer thickness, 

4. The average skin friction coefficient is given by, 

5. The total drag force, 

7. Local heat transfer coefficient at the trailing edge, 

Q6. Give the empirical correlations for forced convection. 

Ans. 1. The following dimensionless numbers are used in forced convection :  

2. In order to determine the value of convection coefficient h, the following equations are used:

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