1. If Q X is heat generated in at distance ‘x’, then heat conducted out at a distance (x + d x) will be
a) Q X + 3d (Q X) d x /d x
b) 2Q X + d (Q X) d x /d x
c) d (Q X) d x /d x
d) Q X + d (Q X) d x /d x
Explanation: Q X + Q g = Q X + d X.
2. Notable example of uniform generation of heat within the conducting medium are
(i) Energy of a nuclear reactor
(ii) Liberation of energy due to some exothermic chemical reactions
(iii) Resistance heating in electrical appliances
Which of the statements made above are correct?
a) i, ii and iii
b) i and ii
c) i and iii
d) Only ii
Explanation: All the statements are correct with respect to plane wall heat conduction.
3. For a plane wall of thickness l with uniformly distributed heat generation q g per unit volume, the temperature t 0 at mid plane is given by
a) t 0 = q g l 2/2k +t w
b) t 0 = q g l 2/4k +t w
c) t 0 = q g l 2/8k +t w
d) t 0 = q g l 2/16k +t w
Explanation: t = q g /2k (l – x) x + t w. At mid plane i.e. x = l/2 we get t 0 = q g l 2/8k +t w.
4. The temperature drop in a plane wall with uniformly distributed heat generation can be decreased by reducing
a) Wall thickness
b) Heat generation rate
c) Thermal conductivity
d) Surface area
Explanation: On decreasing wall thickness, generally temperature drop decreases.
5. Consider a slab of thickness δ with one side (x = 0) insulated and other side (x = δ) maintained at constant temperature. The rate of uniform heat generation within the slab is q g W/m3. Presuming that the heat conduction is in steady state and one dimensional along x direction, the maximum temperature in the slab would occur at x equal
a) δ/2
b) Zero
c) δ/4
d) δ
Explanation: Maximum temperature occurs at the insulated face of the wall where x = 0.
6. There occurs heat conduction and internal heat generation at uniform rate within the conduction medium itself in the following cases
(i) Drying of concrete
(ii) Chemical processes
(iii) Fuel elements in a nuclear reaction
Choose the correct option
a) i only
b) ii only
c) i and iii
d) i, ii and iii
Explanation: All are correct as there is heat conduction in all above cases. The rate of heat generation has to be controlled one, otherwise the resulting temperature growth might result in the failure of the medium.
7. Suppose heat is conducted due to electrons
Where, i = I/A and p is the resistivity, then
a) q g = 2i2 p
b) q g = 3i2 p
c) q g = i2 p
d) q g = 4i2 p
Explanation: It should be i2 p. Here i is current density.
8. In case when both the surfaces of plane wall are at different temperature, we get an expression i.e.
T MAX – T W2 /T W1 – TW2 = (B + 1)2/4B
What is the value of B?
a) (q g) (δ)2/2k (T W1 – TW2)
b) (q g) (δ)3/3k (T W1 – TW2)
c) (q g) (δ)4/4k (T W1 – TW2)
d) (q g) (δ)5/5k (T W1 – TW2)
Explanation: T – T W2 /T W1 – TW2 = [1 – x/ δ] [B x/ δ +1].
9. A 25 mm diameter egg roll (k = 1 W/m degree) is roasted with the help of microwave heating. For good quality roasting, it is desired that temperature at the center of roll is maintained at 100 degree Celsius when the surrounding temperature is 25 degree Celsius. What should be the heating capacity in W/m 3 of the microwave if the heat transfer coefficient on the surface of egg roll is 20 W/m2 degree?
a) 113.31 k W/m3
b) 213.31 k W/m3
c) 313.31 k W/m3
d) 413.31 k W/m3
Explanation: t max = t a + q g R/2h + q g R2/4k.
10. The constants of integration are to be determined from the relevant boundary conditions which are
(i) t = t w at r = R
(ii) q g (π L R2) = -k (2 π R L) (d t/d r)
(iii) Increasing temperature gradient
Choose the correct option?
a) Only i
b) Only ii
c) i and iii
d) i and ii
Explanation: Temperature gradient must be constant.