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Derive the general heat conduction equation for three dimensions in Cartesian coordinates?

Explain multiple effect evaporators with different feed arrangements

 

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Assignment 1

1.What is Thermal Conductivity? Write in brief on its variation with temperature.

 

2.What is lumped capacity? Give the assumptions for lumped capacity analysis.

 

3.Derive the general heat conduction equation for three dimensions in Cartesian coordinates? State equations in cylindrical and spherical coordinates?

 

4.Derive the expression for temperature distribution along the fin with insulated end.

 

5.The wall of a furnace comprises three layers, the first layer is refractory (whose maximum allowable temperature is 1400oC) while the second layer is insulation (whose maximum allowable temperature is 1093oC). The third layer is a plate of 6.35 mm thickness of steel [thermal conductivity = 45 W/(m K)]. Assume the layers to be in very good thermal contact. The temperature T0 on the inside of the refractory is 1370oC, while the temperature T3 on the outside of the steel plate is 37.8o The heat loss through the furnace wall is expected to be 15800 W/m2. Determine the thickness of refractory and insulation that results in the minimum total thickness of the wall.

 

Given thermal conductivities in W/(m K):

Layer k at 37.8oC k at 1093oC
Refractory 3.12 6.23
Insulation 1.56 3.12

 

6.Calculate heat loss per meter of length of a pipe from an insulated pipe carrying hot fluid

Inner diameter =100 mm                   Outer diameter = 120 mm

Temp. of fluid = 358 K                         Temp. of surrounding = 298 K

Thickness of insulation = 30 mm

K for pipe material = 58 W/m K                                K for insulating material = 0.2 W/m K

Inside heat transfer coefficient = 720 W/m2 K      Outside heat transfer coefficient = 9 W/m2 K

 

Assignment 2

1.Explain in detail different types of heat exchangers with diagram

 

2.Explain multiple effect evaporators with different feed arrangements.

 

3.Derive the expression for effectiveness of heat exchanger for parallel flow arrangement.

 

4.What is boiling? Draw pool boiling curve and explain different boiling zones.

 

5.Air at 30ºC is flowing across a tube with a velocity of 25 m/s. The tube could be either a square with 5 cm or a circular cylinder of diameter 5 cm. The tube surface temperature is 124ºC. Compare the rates of heat flow in each case.

Use, NuD = 0.027 (ReD)0.805 (Pr)0.33 for circular tube

NuD = 0.102 (ReD)0.675 (Pr)0.33     for square tube

At 77 ºC, the properties of air are :

ν=20.92 x 10-6  m2 / sec, K = 3×10–2 W/m-K, Pr = 0.7.

 

 

Tutorial No-1

1.Give the physical significance of the following numbers

(i) Prandtl number

(ii) Nusselt number

(iii) Grashoff number

(iv) Stanton number

(v) Reynolds’ number

 

2.Derive the necessary expression for the Critical thickness of insulation for cylinder with neat diagram.

 

3.Air at 300°C and atmospheric pressure is heated as it flows through a tube with a diameter of 25 mm at a velocity of 12 m/sec. Calculate the heat transfer rate per unit length of tube if a constant heat flux condition is maintained at the wall which is at 32°C above the air temperature, over entire length of the tube. Calculate the rise in bulk temperature over a 3.3 m length of the tube. Properties of air are:

i) Dynamic viscosity = 29.7 × 10–6 kg/m.sec

(ii) Thermal conductivity = 0.0461 W/m°K

(iii) Prandtl number = 0.674

(iv) Cp = 1.047 kJ/kg°K

(v) Density = 0.615 kg/m3.

 

4.Consider a plane wall 100mm thick and of thermal conductivity 100 W/m.K. Steady state conditions are known to exist with T1= 400 K and T2= 600 K . Determine the heat flux and the temperature gradient dT/dx for the coordinate systems shown.

t1

 

Tutorial No-2

1.What is LMTD? Derive the equation for ΔTlm for counter flow heat exchanger.

 

2.What is Wien’s law of displacement? Derive the expression.

 

3.Explain vacuum evaporation and boiling point elevation.

 

4.It is observed that the value of the radiation emitted by the sun is maximum at a wavelength of 0.58 microns. Estimate the temperature of surface of sun and emissive power. Consider sun to be a black body.

 

5.1000 kg/hr. of a dilute solution of sodium hydroxide containing 10% NaOH is to be concentrated to 40% NaOH by weight in a single effect evaporator. The feed is available at 25°C. Boiling point of the solution may be considered as 100°C. Specific heat of dilute solution is 4180 J/kgK. Latent heat of vaporization of water is 2239 kJ/kg. Saturated steam corresponding to 1.8 bar pressure and 117°C is available for heating purpose. Latent heat of condensation of steam is 2212 kJ/kg. If the overall heat transfer coefficient for the system is 850 W/m2 K, calculate :

(i) The quantity of water evaporated;

(ii) Steam consumed and steam economy;

(iii) Surface area of the evaporator.

 

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