Indian Institute of Technology Kharagpur (IIT-K) 2007 M.Tech Chemical engineering Advanced Heat Transfer - Question Paper
Mid Semester Examination (Spring 2007)
Chemical Engineering Department Indian Institute of Technology, Kharagpur Subject: CH61014 Advanced Heat Transfer
Answer all the questions. Assume any missing data
1. Consider a slab of thickness 2L, initially at a constant temperature Tm. At time t =
0 the slab is uniformly heated by a constant volumetric heat source (qs Kcal/hr m3). The two surfaces of the slab are exposed to periodically varying external fluid temperature Tf = Tm+ssin kt (t is the time). The slab starts cooling/heating via convection at the surfaces through the heat transfer coefficient h. The Biot number for the system is greater than 1.
(i) Write down the governing equation that describes the transient heat transfer in the slab. Write down the Boundary Conditions. Mention the type of equation (PDE/ODE, homogeneous/nonhomogeneous) and the boundary conditions.
(ii) Analytically solve the equation to obtain the temperature profile
(iii) To obtain a numerical solution for the above equation in part (i), using Crank Nicholson method
(a) Write down the discretised form of the equation.
(b) Write the matrix from and the algorithm (/steps) required to solve the problem
(5+5+5)
2. A long cylinder of radius 200 mm of a material having a thermal conductivity of 170 W/mC is initially at a uniform temperature of 650C. For heat treatment purposes the cylinder is quenched in a medium at 75C with a heat transfer coefficient of 1700 W/m2oC.
Write down the governing equation and boundary conditions that describe the heat transfer in the cylinder. Derive the functional from of the solution for temperature profile (DO NOT solve for the constants/coefficients).
(5)
3. (a) Determine in K.cal /hr radiative heat loss from each meter of 20 cm diameter heating pipe when it is placed centrally in the brick duct of square cross section 30 cm side.
Temperature of pipe surface =600C, Temperature of brickwork = 200C. Emissivity of pipe surface and brick work equal to 0.8 and 0.9 respectively.
(b) The temperature of an air stream in a duct is being measured by means of a thermocouple. The thermocouple wires and junction are cylindrical, 0.125 cm in diameter and extend across the duct perpendicular to the flow with the junction in the centre of the duct. The thermocouple is shielded by a wall, which is 8 times the diameter of the thermocouple junction. Under steady state condition of operation the following data were measured:
(i) Thermocouple junction temperature = 260C, (ii) Duct wall temperature =150C
(ii) - Emissivity of thermocouple wires and shield are 0.8 and 0.3 respectively. It may be assumed that the convective heat transfer co-efficient from wire to air is 300 W/m2k. Find out the gas and shield temperature. What is the error involved in the measurement of the gas temperature by the thermocouple?
(3+7=10)
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