Reference no: EM132329980

Advanced Heat Transfer Assignment - Answer all Questions.

Question 1 -

a) What are Heisler charts? Explain its significance.

b) A short cylindrical aluminium bar, having thermal conductivity, 200W/m.K and thermal diffusivity, 8.4 X 10-5 m2 /s of diameter 6 cm and height 3 cm is initially at a uniform temperature of 175^oC. Suddenly the surfaces are subjected to convective cooling with a heat transfer coefficient of 250 W/m2 .K into an ambient at 25^oC. Calculate the center temperature of the cylinder one minute after the start of cooling.

Question 2 -

a) Explain Dirichlet and Newmann Boundary conditions as applied to conduction with examples.

b) Write the finite difference form of the two dimensional steady state heat conduction equation with internal heat generation at a constant rate 'g' for a region 0.03m X 0.03m by using a mesh size Δx=Δy= 0.01 m for a material having thermal conductivity 25 W/m.K and heat generation rate, 107 W/m3 . All the boundary surfaces are maintained at 100C. Express the finite difference equations in matrix form for the unknown node temperatures.

Question 3 -

a) Discuss the assumptions made in the Nusselts theory of film condensation on a vertical plate.

b) Prove that by using dimensional analysis Nusselt number is a function of Reynolds number and Prandtl number in forced convection.

Question 4 -

a) Explain in detail, the differences between implicit and explicit methods.

b) By using approximate integral boundary layer analysis, derive the equation for the local heat transfer coefficient for the flow over flat plate in terms of the Reynolds number.

Question 5 -

a) Explain and discuss the significance of (i) Rayleigh number and (ii) Nusselt number in natural convection.

b) Air at 200C flowing at 25 m/s passes over a flat plate, the surface of which is maintained at 270^oC. Calculate the rate at which heat is transferred from both the sides of the plate per unit width over a distance of 0.25 m from the leading edge. Properties of air at 145^oC are Prandtl number = 0.687; Viscosity = 2.8 X 10-5 m2/s and thermal conductivity = 3.49 X 10-5 kW/m.K.

Question 6 -

a) Write short notes on Gas radiation.

b) A 15 cm outer diameter steel pipe lies 2m vertically and 8 m horizontally in a large room with an ambient temperature of 300C. If the pipe surface is at 2500C, calculate the total rate of heat loss from the pipe to the atmosphere. Properties of air at 1400C are density = 0.854 kg/m3; specific heat, cp= 1.01 kJ/kg.K; thermal conductivity = 0.035 W/m.K; Prandtl number = 0.684 and viscosity = 27.8 X 10-6 m2 /s.

Question 7 -

Draw the radiation network for a specular diffuse surface losing heat to a large enclosure. Obtain an expression for the heat transfer under these circumstances. How does this heat transfer compared with that which would be lost by a completely diffuse surface with the same emissivity.

Question 8 -

a) Define Schmidt and Lewis numbers. Discuss the significances of each.

b) Assuming laminar film condensation, calculate the ratio of condensing heat transfer coefficient on a vertical tube to that of a horizontal tube of same diameter and length.