Convection
Newtons Law of Cooling
Learning Objectives:

State Newton’s law of cooling.

Calculate rate of heat flow by convection using Newton’s law of cooling.

Understand the governing equation relevant to natural convection.
Convection is expressed by Newton’s law of cooling as:
\[\dot{Q} = h A_{s}(T_{s}  T_{\infty}) = \rho V C_P \dfrac{dT}{dt}\]
Where h is the convection heat transfer coefficient
\( A_{s}\) is the surface area through which convection heat transfer takes place
\( T_{s}\) is the surface temperature
\( T_{\infty}\) is the temperature of the fluid sufficiently far from the surface
Solved Example: 81101
When heat is transferred from one particle of hot body to another by actual motion of the heated particles, it is referred to as heat transfer by: (SSC JE ME paper 6 March 2017 Morning)
A. Conduction
B. Convection
C. Radiation
D. Conduction and convection
Correct Answer: B
Solved Example: 81102
When heat is transferred by molecular collision, it is referred to as heat transfer by:
A. Conduction
B. Convection
C. Radiation
D. Scattering
Correct Answer: B
Solved Example: 81103
Heat transfer in liquid and gases takes place by: (UPPCL JE March 2021Shift I)
A. Conduction
B. Convection
C. Radiation
D. Conduction and convection
Correct Answer: B
Solved Example: 81104
In convection heat transfer from hot flue gases to water tube, even though flow may be turbulent, a laminar flow region (boundary layer of film) exists close to the tube. The heat transfer through this film takes place by:
A. Convection
B. Radiation
C. Conduction
D. Both convection and conduction
Correct Answer: C
Solved Example: 81105
Consider a hot boiled potato kept on a plate and cooled by natural convection in air. During the first minute, the temperature drops by 10$^{\circ}\mathrm{C}$. During the second minute, will the temperature drop be more than, less than or same as that during the first minute?
A. More than 10$^{\circ}\mathrm{C}$
B. Less than 10$^{\circ}\mathrm{C}$
C. Equal to 10$^{\circ}\mathrm{C}$
D. Can't say
Correct Answer: B
Solved Example: 81106
Air at 300$^\circ$C flows over a plate of dimensions 0.50 m, by 0.25 m. if the convection heat transfer coefficient is 250 $W/m^2.K$; determine the heat transfer rate from the air to one side of the plate when the plate is maintained at 400$^\circ$C.
A. 8125 W
B. 512.8 W
C. 6635 W
D. 5400 W
\begin{align*} q &=h A\left( T_{\infty }T_{s}\right)\\ &= 250\left( 0.25 \times 0.50\right) \left(30040\right)\\ &=8125\ W \end{align*}
Correct Answer: A
Solved Example: 81107
Film coefficient is defined as Inside diameter of tube
A. Equivalent thickness of film
B. Thermal conductivity Equivalent thickness of film Specific heat $\times$ Viscosity
C. Thermal conductivity Molecular diffusivity of momentum Thermal diffusivity
D. Film coefficient $\times$ Inside diameter Thermal conductivity
Correct Answer: B
Types of Convection
Learning Objectives:

Differentiate between free and forced convection heat transfer.

Understand the important physical aspects of free convection.

Understand the relevant dimensionless numbers for natural convection.

Able to use Nusselt number empirical correlations to solve natural convection problems.

Able to use convection correlations to solve forced convection problems for external and internal flows.
There are two types of Convection:

Free Convection: the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid.
A free convection flow field is a selfsustained flow driven by the presence of a temperature gradient. (As opposed to a forced convection flow where external means are used to provide the flow.) As a result of the temperature difference, the density field is not uniform also. Buoyancy will induce a flow current due to the gravitational field and the variation in the density field. In general, a free convection heat transfer is usually much smaller compared to a forced convection heat transfer. It is therefore important only when there is no external flow exists. 
Forced convection: The fluid is forced to flow over the surface by external means such as a fan, pump, or the wind.
Solved Example: 81201
The process of heat transfer from one particle of the fluid to another by the actual movement of the fluid particles due to difference of density caused by temperature of the particle is known as:
A. Conduction
B. Free convection
C. Forced convection
D. Radiation
Correct Answer: B
Critical Radius of Insulation
Learning Objectives:

Calculate ideal insulation thickness of pipes and wires considering the concepts of critical thickness of insulation.
Adding insulation to a cylindrical piece or a spherical shell, insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates. For a cylinder, \[r_{cr} = \dfrac{k_{\mathrm{insulation}}}{h_\infty}\] For a sphere, \[r_{cr} = \dfrac{2k_{\mathrm{insulation}}}{h_\infty}\] where,
\(r_{cr}\) = Critical radius of insulation
\(h_\infty\) = Convection coefficient outside the pipe sufficiently away from the surface
Note that for most applications, the critical radius is so small. Thus, we can insulate hot water or steam pipes without worrying about the possibility of increasing the heat transfer by insulating the pipe.
Solved Example: 81301
A steam pipe 10 cm ID, and 11 cm OD, is covered with an insulating substance (k= 1W/mK). The steam temperature and ambient temperature are 200$^{\circ}\mathrm{C}$ and 20$^{\circ}\mathrm{C}$. If the convective heat transfer coefficient between the insulation surface and air is 8 W/sq mK, find the critical radius of insulation.
A. 12.5 cm
B. 9.5 cm
C. 11.9 cm
D. 13.3 cm
$\quad r_{cr} = \dfrac{k}{h}= \dfrac{1}{8}= 0.125\ m = 12.5\ cm$
Correct Answer: A
Solved Example: 81302
For pipes, the radius of the pipe is taken higher than the critical radius, so that any insulation added will ______. (UPRVUNL AE ME July 2021)
A. Keep loss unaltered
B. Decrease heat loss
C. Enable heat gain
D. Increase heat loss
Correct Answer: B
Solved Example: 81303
The critical radius is the insulation radius at which the resistance to heat flow is: (RPSC Lecturer Tech Edu 2020 Mech Paper II)
A. Maximum
B. Minimum
C. Zero
D. Remain Same Throughout
Correct Answer: B
Heat Generation in Solids
Learning Objectives:

Solve problem involving some form of energy generation.
Conversion of some form of energy into heat energy in a medium is called heat generation. Heat generation leads to a temperature rise throughout the medium.
Some examples of heat generation are resistance heating in wires, exothermic chemical reactions in solids, and nuclear reaction. Heat generation is usually expressed per unit volume (\(W/m^3\)).
In most applications, we are interested in maximum temperature \(T_{max}\) and surface temperature \(T_s\) of solids which are involved with heat generation. The maximum temperature \(T_{max}\) in a solid that involves uniform heat generation will occur at a location furthest away from the outer surface when the outer surface is maintained at a constant temperature, \(T_s\).
Solved Example: 81401
The back side of a metallic plate is perfectly insulated while the front side absorbs a solar radiant flux of 800 $W/m^2$. The convection coefficient between the plate and the ambient air is 12 $W /m^2. K$. Neglecting radiation exchange with the surroundings, calculate the temperature of the plate under steadystate conditions if the ambient air temperature is 20$^{\circ}\mathrm{C}$.
A. 52.5 $^{\circ}\mathrm{C}$
B. 66.5 $^{\circ}\mathrm{C}$
C. 87 $^{\circ}\mathrm{C}$
D. 98.2 $^{\circ}\mathrm{C}$
\[q_{s}''A_{s}hA\left( T_{s}T_{\infty }\right) =0\] \[T_{s} =T_{\infty }+\dfrac {q_{s}''}{h} = 20+\dfrac {800}{12}=87\ ^{\circ }C\]
Correct Answer: C
Dimensionless Numbers
Learning Objectives:

To identify the pertinent dimensionless numbers governing phenonmenon of convective heat transfer and understand their physical significance.
Solved Example: 81502
Reynolds number is practically the ratio of: (UPRVUNL AE ME July 2021)
A. Viscous forces to inertial force
B. Frictional forces to viscous forces
C. Inertial forces to frictional forces
D. Inertial forces to viscous forces
Correct Answer: D
Solved Example: 81503
Which of the following is NOT a dimensionless parameter? (ISRO IPRC Tech Asst Mechanical 2016)
A. Froude number
B. DarcyWeishbach friction factor
C. Mach number
D. None of the above
Correct Answer: D
Solved Example: 81504
Which of the following is dimensionless? (NPCIL SA/ST ME GJ Nov 2019 ShiftI)
A. Specific speed
B. Specific volume
C. Specific gravity
D. Specific weight
Correct Answer: C