100
Analytical Heat Transfer
(Note: The diameter of the nozzle is much larger than its thickness. No need to perform integration of orthogonal functions
if you run out of time.)
b. Sketch several nozzle wall temperature profiles during transient heating.
c. To increase the firing time, changing the wall thickness L is
considered. Should L be increased or decreased? Why? The
value of the firing time could also be increased by selecting a wall material with different thermophysical properties.
Should materials of larger or smaller values of ρ, c, and k be
chosen?
4.2. A one-side-insulated metal plane wall with a thickness of L is
initially at temperature T i and suddenly the other side is heated
by forced convection water at temperature T ∞ with a convection
heat transfer coefficient h.
a. Outline, step by step, the procedures and the associated initial
and BCs that may be used to solve the temperature distributions in the plane wall. You do not need to solve the transient
temperature distribution.
b. Sketch the temperature profiles in the plane wall during the
heating process. Also, estimate the surface temperature at the
final steady-state condition.
4.3. A long metal plane wall with a thickness of 2L is initially at temperature T i and suddenly both sides are heated by convection
fluid flow at temperature T ∞ with a convection heat transfer coefficient h. Outline the procedures that may be used to solve the
temperature distributions in the plane wall and sketch the temperature profiles in the plane wall during the heating process for
two different cases.
a. Fluid flow is natural convection air.
b. Fluid flow is forced convection water.
c. Also, estimate the surface temperature at the final steady-state
condition. Which fluid flow will reach the steady temperature
faster? Why? Make appropriate assumptions in order to justify
your answers.
4.4. A large flat plate (with a thickness of 2L) initially at T i is suddenly
plunged into a liquid bath at T ∞ . Derive an expression for the
instantaneous temperature distribution in the plate, if,
a. The heat transfer coefficient between the two surfaces of the
plate and the liquid, h, is given as constant and finite.
b. The heat transfer coefficient h between the two surfaces of the
plate and the liquid is very large so that the temperatures on the
two surfaces of the plate may be assumed to change abruptly
to the temperature of the liquid (i.e., T(L,t) = T ∞ , for t > 0).
c. Sketch the instantaneous temperature distribution in the plate
for both (a) and (b) if T ∞ > T i .
4.5. A semiinfinite solid initially at a uniform temperature T i and
suddenly exposed at its surface to a constant heat flux q”.
a. Determine the temperature history in the solid.
Analytical Heat Transfer
(Note: The diameter of the nozzle is much larger than its thickness. No need to perform integration of orthogonal functions
if you run out of time.)
b. Sketch several nozzle wall temperature profiles during transient heating.
c. To increase the firing time, changing the wall thickness L is
considered. Should L be increased or decreased? Why? The
value of the firing time could also be increased by selecting a wall material with different thermophysical properties.
Should materials of larger or smaller values of ρ, c, and k be
chosen?
4.2. A one-side-insulated metal plane wall with a thickness of L is
initially at temperature T i and suddenly the other side is heated
by forced convection water at temperature T ∞ with a convection
heat transfer coefficient h.
a. Outline, step by step, the procedures and the associated initial
and BCs that may be used to solve the temperature distributions in the plane wall. You do not need to solve the transient
temperature distribution.
b. Sketch the temperature profiles in the plane wall during the
heating process. Also, estimate the surface temperature at the
final steady-state condition.
4.3. A long metal plane wall with a thickness of 2L is initially at temperature T i and suddenly both sides are heated by convection
fluid flow at temperature T ∞ with a convection heat transfer coefficient h. Outline the procedures that may be used to solve the
temperature distributions in the plane wall and sketch the temperature profiles in the plane wall during the heating process for
two different cases.
a. Fluid flow is natural convection air.
b. Fluid flow is forced convection water.
c. Also, estimate the surface temperature at the final steady-state
condition. Which fluid flow will reach the steady temperature
faster? Why? Make appropriate assumptions in order to justify
your answers.
4.4. A large flat plate (with a thickness of 2L) initially at T i is suddenly
plunged into a liquid bath at T ∞ . Derive an expression for the
instantaneous temperature distribution in the plate, if,
a. The heat transfer coefficient between the two surfaces of the
plate and the liquid, h, is given as constant and finite.
b. The heat transfer coefficient h between the two surfaces of the
plate and the liquid is very large so that the temperatures on the
two surfaces of the plate may be assumed to change abruptly
to the temperature of the liquid (i.e., T(L,t) = T ∞ , for t > 0).
c. Sketch the instantaneous temperature distribution in the plate
for both (a) and (b) if T ∞ > T i .
4.5. A semiinfinite solid initially at a uniform temperature T i and
suddenly exposed at its surface to a constant heat flux q”.
a. Determine the temperature history in the solid.