ME 353 Heat Transfer 1

M.M. Yovanovich

P1MT93.MWS

Problem 1 of Midterm Exam, October 1993.

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Two plane walls of thickness: L1 and L2;

thermal conductivity: k1 and k2 are in perfect contact.

Distributed volumetric heat sources within first plane wall

of strength P.

Left boundary of first plane wall is insulated, and right

boundary of second plane wall is cooled by a fluid of

temperature Tf through heat transfer coefficient h.

Steady-state, constant properties.

Resistance concept is used to get temperature drops.

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> restart:

1. The temperature distribution within the first plane wall is

parabolic because it has distributed volumetric heat sources,

and the temperature distribution in the second plane wall is linear

because it is source free.

The maximum temperature Tmax occurs at the insulated boundary

in the first plane wall.

2. Obtain the expression which relates the temperature drop

across the thermal boundary layer (Ts - Tf) in terms of the

parameters P, L1and h.

> `Ts - Tf`:= Q*Rf;

> Q:= P*L1*A; Rf:= 1/(h*A);

> DeltaTs_Tf:= Q*Rf;

3. Obtain the expression which relates the temperature drop

across the second plane wall (Ti - Ts) in terms of the

parameters P, L1, L2 and k2.

> restart:

> `Ti - Ts`:= Q*Rs2;

> Q:= P*A*L1; Rs2:= L2/(k2*A);

> DeltaTi_Ts:= Q*Rs2;

4. Obtain the expression which relates the temperature drop

across the first plane wall (Tmax - Ti) in terms of the

parameters P, L1 and k1.

> `Tmax - Ti`:= Q*Rs1/2;

> Q:= P*A*L1; Rs1:= L1/(k1*A);

> DeltaTmax_Ti:= Q*Rs1/2;