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IIT- Hyderabad ME5320 Advanced Heat Transfer Mid-Semester Examination 29th September 2015 1. This is a closed book examination. Use of calculator is permitted. 2. The paper contains 3 questions in 2 printed pages. Please answer all the questions. 3. Maximum marks – 35; Time allowed – 2 hours 4. All the necessary data is provided in the exam paper. 1. A coin of radius ?0 and thickness ? rests on an inclined plane. Initially it is at an ambient temperature ?∞ . The coin is released and begins to
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1 IIT- Hyderabad ME5320 Advanced Heat Transfer Mid-Semester Examination 29 th  September 2015 1.   This is a closed book examination. Use of calculator is permitted. 2.   The paper contains 3 questions in 2 printed pages. Please answer all the questions. 3.   Maximum marks  –   35; Time allowed  –   2 hours 4.   All the necessary data is provided in the exam paper. 1.   A coin of radius    and thickness   rests on an inclined plane. Initially it is at an ambient temperature  ∞  . The coin is released and begins to slide down a plane. The frictional force    is assumed constant and the velocity changes with time according to  =  , where   is a constant. Due to changes in velocity, the heat transfer coefficient ℎ  varies according to ℎ =   where   is a constant. Assuming that the Biot number is small compared to unity and neglect heat loss to the plane, determine the transient temperature of the coin. Assume constant material properties ,   etc. (8 M) 2.   The surface of a semi-infinite plate which is initially at uniform temperature    , is suddenly heated at one end with a time-dependent flux given by  ′′ = √   Where   is constant. Use similarity method to determine the one-dimensional transient temperature. (Hint: Use the transformation  =  √ 4  ) (11 M) 3.   A rectangular plate (shown in Figure)  ×  is maintained at uniform temperature    along three sides. Half the fourth side is insulated while the other half is heated at uniform flux  ′′ . Determine the steady state heat transfer rate through the surface (0,) . The srcin and the axes are marked in the Figure. (16 M)  2 Additional information a.   General form of the SL-differential equation        + 1 ()   +[  ()+    ()]   = 0  From this () =  ∫     ,  (  )  =  2  (  )       (  )  =  3 ()    b.   Error function values are given in the table below ---------------------- END OF PAPER --------------------------
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