Thermal Science & Engineering - short answer questions from AMIE exams (Winter 2019)

Write a short note on any four.  

Natural Convection Vs Forced convection
  • Free or natural convection. Free or natural convection occurs where the fluid circulates by virtue of the natural differences in densities of hot and cold fluids; the denser portions of the fluid move downward because of the greater force of gravity, as compared with the force on the less dense.
  • Forced convection. When the work is done to blow or pump the fluid, it is said to be forced convection.
Clapeyran equation      
Clausius-Claperyon equation is a relationship between the saturation pressure, temperature, the enthalpy of evaporation, and the specific volume of the two phases involved. This equation provides a basis for calculations of properties hi a two-phase region. 

\frac{{dp}}{{dT}} = \frac{{{s_g} - {s_f}}}{{{v_g} - {v_f}}} = \frac{{{s_{fg}}}}{{{v_{fg}}}} = \frac{{{h_{fg}}}}{{T.{v_{fg}}}}

This is known as Clausius-Claperyon or Claperyon equation for evaporation of liquids. The derivative
dp/dT is the slope of vapour pressure versus temperature curve.

where, sg = Specific entropy of saturated vapour,
sf = Specific entropy of saturated liquid,
vg = Specific volume of saturated vapour, and
vf = Specific volume of saturated liquid
sfg = Increase in specific entropy,
vfg = Increase in specific volume, and
hfg = Latent heat added during evaporation at saturation temperature T.

  • The art of measuring the moisture content of air is termed “psychrometry”. 
  • Psychrometry is a branch of engineering science, which deals with the study of moist air i.e. dry air mixed with water vapour or humidity. It also includes the study of the behaviour of dry air and water vapour mixture under various sets of conditions.
  • Though the earth’s atmosphere is a mixture of gases including nitrogen (N₂), oxygen (O₂), argon (Ar) and carbon dioxide (CO₂), yet for the purpose of psychrometry, it is considered to be a mixture of dry air and water vapour only.

LMTD and e-NTU method  
Logarithmic Mean Temperature Difference for “Parallel-flow”
Refer to the following figure, which shows the flow arrangement and distribution of temperature in a
single-pass parallel-flow heat exchanger.

{\theta _m} = \frac{{{\theta _1} - {\theta _2}}}{{\ln ({\theta _1}/{\theta _2})}}

Logarithmic Mean Temperature Difference for “Counter-flow”
Refer to the following figure, which shows the flow arrangement and temperature distribution in a single pass counter-flow heat exchanger.

{\theta _m} = \frac{{{\theta _1} - {\theta _2}}}{{\ln ({\theta _1}/{\theta _2})}}

Effectiveness-NTU Method  
LMTD method is useful for determining the overall heat transfer coefficient U based on experimental values of the inlet and outlet temperatures and the fluid flow rates. However, this method is not very convenient for the prediction of outlet temperatures if the inlet temperatures and   U are known. In this case, one has to solve a nonlinear system of two equations and the overall energy balance.

NTU = Number\,of\,transfer\,units = \frac{{{U_0}{A_0}}}{{{c_m}}}

For a parallel-flow heat exchanger
{\varepsilon _p} = \frac{{1 - \exp [ - NTU(1 + R)]}}{{1 + R}}

for a counterflow heat exchanger
{\varepsilon _c} = \frac{{1 - \exp [ - NTU(1 - R)]}}{{1 - {{\rm Re}\nolimits} xp[ - NTU(1 - R)]}}

Kirchoff Law  
Kirchhoff's Law:  The law states that at any temperature the ratio of total emissive power E to the total absorptivity a is a constant foi~ all substances that are in thermal equilibrium, with their environment.

Eb = E/ε
where E is emissive power and ε is emissivity. Eb is energy fall on the surface.  

Thus, Kirchhoff's law also states that the emissivity of a body is equal to its absorptivity when the body remains in thermal equilibrium with its surroundings.

Condensation and boiling
Boiling, evaporation and condensation are terms that refer to the changes in state between liquids and gases:
  • Boiling occurs when a liquid is heated and turns into a gas. Boiling is associated with the transformation of liquid to vapour at a   solid/liquid interface due to convection heat transfer from the solid.
  • Evaporation occurs when a liquid changes to a gas at a temperature below its normal boiling point.
  • Condensation occurs when a gas is cooled and turns into a liquid. It occurs when the temperature of a vapour is   reduced below its saturation temperature
The boiling curve is shown below.

Condensation is shown below.

Heat transfer rates in dropwise condensation may be as much as 10 times higher than in film condensation. 

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