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Formula Sheet Heat Transfer - Formula Sheets of Mechanical Engineering
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Page 1
Short notes for Heat transfer
Fo u r ie r ’s Law of Heat Conduction
• Q = Heat transfer in given direction.
• A = Cross-sectional area perpendicular to heat flow direction.
• dT = Temperature difference between two ends of a block of thickness dx
• dx = Thickness of solid body
• = Temperature gradient in direction of heat flow.
General Heat Conduction Equation
• Carterisan Coordinates (side parallel to x, y and z-directions)
q g = Internal heat generation per unit volume per unit time
t = Temperature at left face of differential control volume
k x, k y, k z = Thermal conductivities of the material in x, y and z-directions respectively
c = Specific heat of the material
? = Density of the material
a = Thermal diffusivity
dt = Instantaneous time.
o For homogeneous and isotropic material
o For steady state condition (P oi ss on ’s equation)
o For steady state and absence of internal heat generation (Laplace equation)
o For unsteady heat flow with no internal heat generation
Page 2
Short notes for Heat transfer
Fo u r ie r ’s Law of Heat Conduction
• Q = Heat transfer in given direction.
• A = Cross-sectional area perpendicular to heat flow direction.
• dT = Temperature difference between two ends of a block of thickness dx
• dx = Thickness of solid body
• = Temperature gradient in direction of heat flow.
General Heat Conduction Equation
• Carterisan Coordinates (side parallel to x, y and z-directions)
q g = Internal heat generation per unit volume per unit time
t = Temperature at left face of differential control volume
k x, k y, k z = Thermal conductivities of the material in x, y and z-directions respectively
c = Specific heat of the material
? = Density of the material
a = Thermal diffusivity
dt = Instantaneous time.
o For homogeneous and isotropic material
o For steady state condition (P oi ss on ’s equation)
o For steady state and absence of internal heat generation (Laplace equation)
o For unsteady heat flow with no internal heat generation
• Cylindrical Coordinates
o For homogeneous and isotropic material,
o For steady state unidirectional heat flow in radial direction with no internal heat
generation,
• Spherical Coordinates
o For homogeneous and isotropic material
o For steady state uni-direction heat flow in radial direction with no internal heat
generation,
• Thermal resistance of hollow cylinders
• Thermal Resistance of a Hollow Sphere
• Heat Transfer through a Composite Cylinder
Page 3
Short notes for Heat transfer
Fo u r ie r ’s Law of Heat Conduction
• Q = Heat transfer in given direction.
• A = Cross-sectional area perpendicular to heat flow direction.
• dT = Temperature difference between two ends of a block of thickness dx
• dx = Thickness of solid body
• = Temperature gradient in direction of heat flow.
General Heat Conduction Equation
• Carterisan Coordinates (side parallel to x, y and z-directions)
q g = Internal heat generation per unit volume per unit time
t = Temperature at left face of differential control volume
k x, k y, k z = Thermal conductivities of the material in x, y and z-directions respectively
c = Specific heat of the material
? = Density of the material
a = Thermal diffusivity
dt = Instantaneous time.
o For homogeneous and isotropic material
o For steady state condition (P oi ss on ’s equation)
o For steady state and absence of internal heat generation (Laplace equation)
o For unsteady heat flow with no internal heat generation
• Cylindrical Coordinates
o For homogeneous and isotropic material,
o For steady state unidirectional heat flow in radial direction with no internal heat
generation,
• Spherical Coordinates
o For homogeneous and isotropic material
o For steady state uni-direction heat flow in radial direction with no internal heat
generation,
• Thermal resistance of hollow cylinders
• Thermal Resistance of a Hollow Sphere
• Heat Transfer through a Composite Cylinder
• Heat Transfer through a Composite Sphere
• Critical Thickness of Insulation:
o In case of cylinder,
where, k 0 = Thermal conductivity, and h = Heat transfer coefficient
o The drop in temperature across the wall and the air film will be proportional to their
resistances, = hL/k.
• Steady Flow of Heat along a Rod Circular fin
?=pd
Page 4
Short notes for Heat transfer
Fo u r ie r ’s Law of Heat Conduction
• Q = Heat transfer in given direction.
• A = Cross-sectional area perpendicular to heat flow direction.
• dT = Temperature difference between two ends of a block of thickness dx
• dx = Thickness of solid body
• = Temperature gradient in direction of heat flow.
General Heat Conduction Equation
• Carterisan Coordinates (side parallel to x, y and z-directions)
q g = Internal heat generation per unit volume per unit time
t = Temperature at left face of differential control volume
k x, k y, k z = Thermal conductivities of the material in x, y and z-directions respectively
c = Specific heat of the material
? = Density of the material
a = Thermal diffusivity
dt = Instantaneous time.
o For homogeneous and isotropic material
o For steady state condition (P oi ss on ’s equation)
o For steady state and absence of internal heat generation (Laplace equation)
o For unsteady heat flow with no internal heat generation
• Cylindrical Coordinates
o For homogeneous and isotropic material,
o For steady state unidirectional heat flow in radial direction with no internal heat
generation,
• Spherical Coordinates
o For homogeneous and isotropic material
o For steady state uni-direction heat flow in radial direction with no internal heat
generation,
• Thermal resistance of hollow cylinders
• Thermal Resistance of a Hollow Sphere
• Heat Transfer through a Composite Cylinder
• Heat Transfer through a Composite Sphere
• Critical Thickness of Insulation:
o In case of cylinder,
where, k 0 = Thermal conductivity, and h = Heat transfer coefficient
o The drop in temperature across the wall and the air film will be proportional to their
resistances, = hL/k.
• Steady Flow of Heat along a Rod Circular fin
?=pd
• Generalized Equation for Fin Rectangular fin
• Heat balance equation if A c constant and A s 8 P(x) linear
• General equation of 2
nd
order
? = c1e
mx
+ c2e
-mx
o Heat Dissipation from an Infinitely Long Fin (l ? 8)
? Heat transfer by conduction at base
o Heat Dissipation from a Fin Insulated at the End Tip
o Heat Dissipation from a Fin loosing Heat at the End Tip
Page 5
Short notes for Heat transfer
Fo u r ie r ’s Law of Heat Conduction
• Q = Heat transfer in given direction.
• A = Cross-sectional area perpendicular to heat flow direction.
• dT = Temperature difference between two ends of a block of thickness dx
• dx = Thickness of solid body
• = Temperature gradient in direction of heat flow.
General Heat Conduction Equation
• Carterisan Coordinates (side parallel to x, y and z-directions)
q g = Internal heat generation per unit volume per unit time
t = Temperature at left face of differential control volume
k x, k y, k z = Thermal conductivities of the material in x, y and z-directions respectively
c = Specific heat of the material
? = Density of the material
a = Thermal diffusivity
dt = Instantaneous time.
o For homogeneous and isotropic material
o For steady state condition (P oi ss on ’s equation)
o For steady state and absence of internal heat generation (Laplace equation)
o For unsteady heat flow with no internal heat generation
• Cylindrical Coordinates
o For homogeneous and isotropic material,
o For steady state unidirectional heat flow in radial direction with no internal heat
generation,
• Spherical Coordinates
o For homogeneous and isotropic material
o For steady state uni-direction heat flow in radial direction with no internal heat
generation,
• Thermal resistance of hollow cylinders
• Thermal Resistance of a Hollow Sphere
• Heat Transfer through a Composite Cylinder
• Heat Transfer through a Composite Sphere
• Critical Thickness of Insulation:
o In case of cylinder,
where, k 0 = Thermal conductivity, and h = Heat transfer coefficient
o The drop in temperature across the wall and the air film will be proportional to their
resistances, = hL/k.
• Steady Flow of Heat along a Rod Circular fin
?=pd
• Generalized Equation for Fin Rectangular fin
• Heat balance equation if A c constant and A s 8 P(x) linear
• General equation of 2
nd
order
? = c1e
mx
+ c2e
-mx
o Heat Dissipation from an Infinitely Long Fin (l ? 8)
? Heat transfer by conduction at base
o Heat Dissipation from a Fin Insulated at the End Tip
o Heat Dissipation from a Fin loosing Heat at the End Tip
• Fin Efficiency
• Fin efficiency is given by
• If l ? 8 (infinite length of fin),
• If finite length of fin,
• Fin Effectiveness
• Lumped Parameter System
Q = - ? ? Ta T hA
dt
dT
VCp ? ? ?
? ?
? ?
?
dt
VCp
hA
Ta T
dT
? ) (
Read MoreFAQs on Formula Sheet: Heat Transfer - Formula Sheets of Mechanical Engineering
| 1. What is heat transfer? |  |
Ans. Heat transfer refers to the process of the exchange of thermal energy between two or more objects or systems. It can occur through conduction, convection, or radiation.
| 2. How does conduction work in heat transfer? | |
Ans. Conduction is the transfer of heat between two objects that are in direct contact with each other. It occurs when the molecules in a solid material vibrate and transfer their thermal energy to adjacent molecules.
| 3. What is convection and how does it contribute to heat transfer? | |
Ans. Convection is the transfer of heat through the movement of fluids, such as liquids or gases. It occurs when the heated particles in the fluid rise and the cooler particles sink, creating a circular motion that transfers heat.
| 4. How does radiation play a role in heat transfer? | |
Ans. Radiation is the transfer of heat through electromagnetic waves. Unlike conduction and convection, radiation does not require a medium to transfer heat. It can occur through empty space and is responsible for the heat we receive from the sun.
| 5. Can you provide an example of each type of heat transfer? | |
Ans. Sure! An example of conduction is when you touch a hot stove and feel the heat transferred from the stove to your hand. An example of convection is when you boil water in a pot, and the heated water rises to the top while cooler water sinks. An example of radiation is when you feel the warmth of the sun on your skin on a sunny day.
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