QUESTION ANSWERS-STEADY STATE CONDUCTION

QUESTION ANSWERS-STEADY STATE

CONDUCTION

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 Q. List the basic laws which govern heat transfer.

  1.   First law of thermodynamics i.e. Law of conservation of energy

  2.  Second law of thermodynamics: Heat flows along negative temperature gradient.

  3. Law of conservation of mass

  4.  Newton’s Law of motion

  5. The rate equations

Q. What is the significance of heat transfer?

Like transfer of a person from one city to another city, heat transfer is heat energy in motion.

   Q. Definition of thermal conductivity

From Fourier equation

k=q. with dT=1 K, dx=1 m and A=1 m2

 Thus thermal conductivity is the rate of heat transfer in a solid of unit area, unit thickness with unit temperature difference. It is property of a solid for conducting heat.  Its symbol is k. Its units are W/m K.

 Q.   What is basic equation of conduction?

Fourier equation is the fundamental equation of conduction.

It is used in following three forms.

a. Difference form of equation

Q=-k A (Th -Tl)/(x2—x1)

It is used when temperatures at the two ends are fixed and distance between the two ends is also fixed.

b. Differential form of equation

Q=-k A dT/dx

It is used when temperature is a function of x.

c. Second order differential equation

d2T/dx 2 + d2T/dy 2+ d2T/dz 2 + qg/k =(1/α) dT/dt

It is three dimensional non steady state conduction equation.

T is the temperature

t is the time.

K is thermal conductivity

α  is thermal diffusivity

qg is heat generated per unit volume within the system

Q.  What is thermal resistance in conduction and convection respectively?

Conductive rate of heat transfer q.= –dT/x/kA

thermal resistance in conduction Rcond= x /(kA), measured in K W−1  

Convective heat transfer: q = ΔT/(1/hA)

Thermal resistance to convective heat transfer= R th conv = 1/hA

Q. What is difference between heat and temperature?

Heat is the energy in motion or transition. It flows spontaneously from high temperature to low temperature. It varies with temperature. Rises with the increase of temperature and decreases with fall of temperature. The common symbol for heat is Q. Units of heat are kJ.

Temperature is the measurement of heat energy in a body. It is the degree of hotness or coldness of a body. It decides the direction of heat transfer which is always from high temperature to low temperature. The common symbol for temperature is t or T. Its units are oC or K.

Q. Where does internal heat generation found?

When electric current flow in wires/cables.

During chemical reactions

Nuclear reactions

Heat treatment processes.

Q. What are a temperature gradient, velocity gradient and pressure gradient?

Temperature gradient

dt/dx, dt/dy and dt/dz are temperature gradients i.e. temperature variation w.r.t. x, y, z.

Velocity gradient          dv/dx, dv/dy and dv/dz are velocity gradients i.e. velocity variation w.r.t. ‘x’, y, z.

Pressure gradient    dp/dx, dp/dy and dp/dz are pressure gradients i.e. pressure variation w.r.t. ‘x’, y, and z.

Q. Write the temperature distributions for a plane wall, cylinder and a sphere.

Firstly, for a plane wall (TX—Th)/ (Tl—Th) = x/δ                                        Linear variation

Secondly, for a cylinder    (TR—Th)/ (Tl—Th) = ln(r/ri) / ln (r0/ri)                Logarithmic variation

Thirdly, for a sphere       (TR—Th)/ (Tl—Th) = (ro/r) (r–ri)/ (ro—ri)             Hyperbolic variation

Q. Discuss factors effecting thermal conductivity of a material.

The main factors are vibration of the lattice and movement of free electrons. Most important out of these two is movement of free electrons. Movement of free electrons is found in pure metals. Therefore, all pure metals are good thermal conductors.

Density, high density means high thermal conductivity

Effect of temperature: On rise of temperature k decreases for metals, increases for non metals, liquids and gases and vice versa.

Pressure effect: unaffected in case of solids and liquids but increases with increase of pressure in case of gases

Chemical composition, for copper, 400, for aluminum 250, for steel, 66, for water 0.66 and for air 0.027 W/mK

Q. On what factors thermal conductivity of gases depend?

k of gases depends on temperature and pressure.

With the increase of temperature, volume will increase, density will decrease. K is linked with density. Therefore k will decrease will the rise of temperature and vice versa.

When pressure increases, volume will decrease, density will increase and hence k will increase with the increase of pressure and vice versa