‫به نام آنکه نامش آرامش دلهاست‬
Heat Transfer, Prof. M. Morad, Spring 2020
Sharif University of Technology
3rd Assignment
Due date: Ordibehesht 12
1. Derive an expression for the temperature distribution in the following
plate.
Fig. 1: Schematic of P. 1
2. The two-dimensional solid shown in Figure 2 generates heat internally at
𝑀𝑊
the rate of 90 3 . Using the numerical method calculate the steady-state
𝑚
nodal temperatures for 𝑘 = 20
𝑊
𝑚𝐾
1
.
‫به نام آنکه نامش آرامش دلهاست‬
Heat Transfer, Prof. M. Morad, Spring 2020
Sharif University of Technology
3rd Assignment
Due date: Ordibehesht 12
Fig. 2: Schematic of P. 2
3. A Steady-state temperatures at selected nodal points of the symmetrical
section of a flow channel are known to be T2 = 95˚C, T3 = 117˚C, T5 = 79˚C,
T6 = 77˚C, T8 = 87˚C, and T10 = 77˚C. The wall experiences uniform volumetric
𝑊
heat generation of 𝑞̇ = 106 3 and has a thermal conductivity of 𝑘 =
𝑚
𝑊
10
. The inner and outer surfaces of the channel experience convection
𝑚𝐾
with fluid temperatures of 𝑇∞,𝑖 = 50℃ and 𝑇∞,𝑜 = 25℃ and convection
𝑊
𝑊
coefficients of hi = 500 2 and ho = 250 2 .
𝑚 𝐾
𝑚 𝐾
Fig. 3: Schematic of P. 3
a) Determine the temperatures at nodes 1, 4, 7, and 9.
b) Calculate the heat rate per unit length (W/m) from the outer surface A to
the adjacent fluid.
c) Calculate the heat rate per unit length from the inner fluid to surface B.
d) Verify that your results are consistent with an overall energy balance on
the channel section.
2
‫به نام آنکه نامش آرامش دلهاست‬
Heat Transfer, Prof. M. Morad, Spring 2020
Sharif University of Technology
3rd Assignment
Due date: Ordibehesht 12
4. Consider the square channel shown in the sketch operating under steadystate conditions. The inner surface of the channel is at a uniform
temperature of 600 K, while the outer surface is exposed to convection
𝑊
with a fluid at 300K and a convection coefficient of h = 50 2 . From a
𝑚 𝐾
symmetrical element of the channel, a two dimensional grid has been
constructed and the nodes labeled. The temperatures for nodes 1, 3, 6, 8,
and 9 are identified.
Fig. 4: Schematic of P. 4
a) Beginning with properly defined control volumes, derive the finitedifference equations for nodes 2, 4, and 7 and determine the
temperatures T2, T4, and T7 (K).
b) Calculate the heat loss per unit length from the channel.
Good luck, H. Ahmadian
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