Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)
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1 Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re, Pr) Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k) 2. Explain in detail the mechanism of free convection. Show by dimensional analysis (Rayleigh method) that for problems in heat transfer involving free convection only, the Nusselt number Nu= (hl/k) can be expressed as a function of the Prandtl number Pr =(µcp/k) and the Grashof number Gr= [l 3 ρ 2 (βg t)/µ 2 ]. 3. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Buckingham π-theorem method) that data for forced convection may be correlated by an equation of the form St = φ (Re, Pr) Where Stanton number St=(h/ ρvcp); Reynolds number Re=(Vlδ/µ) and Prandtl number Pr=(µCp/k) 4. Neglecting viscous dissipation, the coefficient of convective heat transfer is anticipated to depend upon the following parameters: fluid viscosity µ, fluid density ρ, fluid thermal conductivity k, fluid specific heat cp, flow velocity V and significant length l. Considering mass, length, time and temperature as the significant dimensions, set up a suitable correlation in terms of non-dimensional numbers for the heat flow. Use Buckingham π-theorem method of dimensional analysis.
2 Tutorial 2 1. A steam pipe 50 mm diameter and 4 m long has been placed horizontally and exposed to still air at 25 0 C. If the pipe wall temperature is C, determine the rate of heat loss.at the mean temp. of C, the thermo-physical properties of air are: k = 3.13 x 10-2 kcal/m-hr-deg; γ = x 10-6 m 2 /s Pr = and β = 1/ = 2.31 x 10-3 per K. 2. A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 wide has been designed on free convection heating of liquid bismuth. Metallurgical consideration limits the maximum surfaces temperature of the plate to C and the lowest allowable temperature of bismuth is C. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient is Nu = 0.13(Gr Pr) 1/3 Where the different parameters are evaluated at the mean film temp. 3. A vertical plate is under free convection with ambient still air at 20 0 C. If the plate is heated from one side and maintained at 80 0 C workout the local heat transfer coefficient at 20 cm from the lower edge. What would be the average value of convective coefficient over the 20 cm length? Following correlation for the local Nusselt Number pr Nu x = 0.52 ( Gr Pr) 0.95 pr
3 Tutorial - 3 1) What factors affect the value of convection coefficient for water flowing inside a circular tube? Within a condenser shell, water flows through one hundred thin walled circular tubes (diameter = 22.5 mm and length 5m) which have been arranged in parallel. The mass flow rate of water is 65 kg/s and its inlet and outlet temperatures are known to be 22 0 C and 28 0 C respectively. Predict the average convection coefficient associated with water flow. 2) Air at atmospheric pressure and C flows over a plate at 27 0 C at 3 m/s. Estimate the heat transfer coefficient at 10 cm from the leading edge. The properties of air at 77 0 C are given as : γ = 2.06 x 10-5 m 2 /s; Pr = 0.706; k = W / m K 3) A tube 4 m long is held at C by steam jacketing. A fluid flow through the tube at the rate 175 kg/hr. The tube diameter is 20 mm. The mean temperature (or bulk temp) of the fluid is 30 0 C. The property values of the fluid are given below: Temp 30 0 C 65 0 C C CP (kj/kg K) k (kj/hr m K) ρ (kg/m 3 ) γ (m 2 /sec) 12x x x10-6 4) Flat plate heated to 80 0 C is cooled by air stream at 20 0 C 10 m/s. Calculate the value of local heat transfer coefficient at x=30 cm. The property values of the fluid are given below at T = 50 0 C k= 2.83 x10-2 W/m K γ = x10-6 m 2 /s Pr= 0.698
4 5) Water flows with a velocity of 3 m/s through an annulus between a 3.81 cm ID outer tube and 2.54 cm OD inner tube. The water is at 80 0 C and the inner wall is at 40 0 C. The outer wall of the annulus is insulated. Determine the value of the heat transfer coefficient by using Sieder Tate equation (Also use other empirical correlation and compare h). The following properties of water may be used; T ( 0 C) K (W/m K) µ (kg/m hr) ρ (kg/m 3 ) CP (kj/kg K) ) Water flows in a 50 mm diameter tube at a velocity of 80 cm/sec. The length of tube is 3 m. Determine the heat transfer coefficient if tw = 70 0 C and the bulk temperature of water is 30 0 C. Temperature 30 0 C 70 0 C ρ (kg/m 3 ) Cp (kj/kg K) κ (W/m K) ν (m 2 /sec) 9.2* *10-7 Pr ) Air at 10 0 C and at a pressure of 100 kpa is flowing over a plate at a velocity of 3 m/s. If the plate is 30 cm wide and 65 0 C, calculate the following quantities at X = 30 cm. (i) Boundary layer thickness (ii) Local drag or shearing stress (iii)thermal boundary layer thickness (iv) Local connective heat transfer co-efficient The properties of air at C Density = kg/m 3 ; μ, = 19 x 10-6 kg/m s; Cp = kj/kg K; Pr = 0.7
5 Tutorial 4 1. What happens to the radiant energy when it is incident upon a surface? Give the general equation that relates absorptivity, reflectivity and transmissivity. Of the radiant energy 350 W/m 2 incident upon a surface 250 W/m 2 is absorbed, 60 W/m 2 is reflected and the remainder is transmitted through the surface. Workout the values for absorptivity, reflectivity and transmissivity for the surface material. 2. A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temp. is 290 K. The plate attains a temperature of 295 K when one of its faces receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m 2 deg, workout the reflectivity of the plates. 3. A black body of total area m 2 is completely enclosed in a space bounded by 5 cm thick walls. The walls have a surface area 0.5 m 2 and thermal conductivity 0.92 kcal/m-hr-deg. If the inner surface of the enveloping wall is to be maintained at C and the outer wall surface is at 30 0 C, calculate the temp. of the black body. Neglect the difference between inner and outer surface areas of enveloping material.
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