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Heat Transfer Formulas for GATE ME Exam
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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 Heat Transfer Formulas for GATE ME Exam
| 1. What are the main heat transfer formulas I need to memorise for GATE ME? |  |
Ans. The essential formulas cover three modes: conduction (Fourier's law: Q = -kA dT/dx), convection (Newton's law of cooling: Q = hA(Ts - T∞)), and radiation (Stefan-Boltzmann law: Q = εσA(T⁴ - Tsurr⁴)). Additionally, thermal resistance concepts, LMTD (Log Mean Temperature Difference) for heat exchangers, and fin efficiency equations are critical. Students should refer to flashcards or mind maps on EduRev to visualise these relationships and ensure quick recall during the exam.
| 2. How do I calculate heat transfer rate using thermal resistance in composite walls? | |
Ans. Heat transfer rate through composite walls uses the analogy: Q = ΔT_total / R_total, where total thermal resistance equals the sum of individual layer resistances (R = L/kA for each layer). This series resistance concept applies to walls with multiple materials in contact. Understanding thermal resistance networks helps solve complex multi-layer problems efficiently and is frequently tested in GATE mechanical engineering examinations.
| 3. What's the difference between LMTD and effectiveness-NTU method for heat exchangers? | |
Ans. LMTD (Log Mean Temperature Difference) method works best when inlet and outlet temperatures are known, using Q = U × A × LMTD. The effectiveness-NTU method is preferred when outlet temperatures are unknown, defining effectiveness as actual heat transfer divided by maximum possible transfer. NTU (Number of Transfer Units) depends on heat capacity rates and heat exchanger configuration, making it more flexible for design calculations in heat transfer problems.
| 4. Which heat transfer formula should I use for fins, and how does fin efficiency affect calculations? | |
Ans. Fin efficiency (η) modifies the basic convection formula: Q_fin = η × h × A_fin × (T_base - T∞). Fin efficiency decreases with longer fins due to temperature gradients along the fin length. The effectiveness of finned surfaces depends on fin material thermal conductivity, geometry, and convection coefficient. Proper fin calculations are essential for designing heat exchangers and cooling systems tested in GATE mechanical engineering.
| 5. How do I know when to apply radiation heat transfer formulas versus conduction and convection? | |
Ans. Radiation dominates when surfaces operate at high temperatures (typically above 300-400 K) or when other modes are negligible. Use Stefan-Boltzmann radiation formula (Q = εσA(T₁⁴ - T₂⁴)) for direct radiation, or the linearised form Q = h_r × A × ΔT when temperature differences are small. Combined heat transfer problems require all three modes; identify dominant mechanisms to simplify calculations effectively for GATE exam questions.
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