This page calculates the temperature (T_c ) of an isothermal (constant temperature) cylinder embedded in a semi-infinite medium at a specified depth (d) from an isothermal surface.

Define the cylinder's radius, length, depth, and the heat load, as well as the conductivity and the isothermal temperature applied to the medium surrounding the cylinder. This page will calculate the cylinder temperature.

Embedded Cylinder and Flow Conditions

Description	Symbol	Value	Units
Radius	R		Meters
Length	L		Meters
Depth	d		Meters
Heat Load	Q		W

Conducting Medium's Properties (Default is for Epoxy [high fill], Units in SI)

Description	Symbol	Value	Units
Conductivity	k		W/(m-^oC)
Isothermal Temperature	T_i		^oC

Results for Isothermal Embedded Cylinder

This page calculates the temperature (T₁) of one isothermal (constant temperature) cylinder based on conduction in an infinite medium to a second embedded cylinder at known temperature (T₂). Heat (Q) is conducted from cylinder 1 to 2.

Define the radii of the cylinders, the length (both cylinders are assumed to have the same length), the temperature of one cylinder, the distance between the cylinders and the heat flow. This page will calculate their corresponding shape factor and the temperature of the embedded cylinder.

Do you want to know more ?

Embedded Cylinders and Flow Conditions

Description	Symbol	Value	Units
Cylinder 1 Radius	R₁		Meters
Cylinder 2 Radius	R₂		Meters
Cylinder Length	L		Meters
Cylinder 2 Temperature	T₂		^oC
Distance	d		Meters
Heat Flow from Cylinder 1 to 2	Q		W

Conducting Medium's Properties (Default is for Epoxy [high fill], Units in SI)

Description	Symbol	Value	Units
Conductivity	k		W/(m-^oC)

Results for two Isothermal Embedded Cylinders

This page calculates the isothermal (constant temperature) embedded rectangular volume temperature (T_b) and the shape factor (sf) of a rectangular volume embedded in a semi-infinite medium having isothermal surface.

Define the rectangular volume's width, length, height, depth, and the heat flow, as well as the conductivity and the isothermal temperature applied to the medium surrounding the rectangular box. This page will calculate the rectangular box temperature and the corresponding shape factor.

Do you want to know more ?

Embedded rectangular box and Flow Conditions

Description	Symbol	Value	Units
Width	W		Meters
Length	L		Meters
Height	H		Meters
Depth	d		Meters
Heat Flow	q		W

Conducting Medium's Properties (Default is for Epoxy [high fill], Units in SI)

Description	Symbol	Value	Units
Conductivity	k		W/(m-^oC)
Isothermal Temperature	T_i		^oC

Results for Isothermal Embedded rectangular box

Material Properties

Metals

Material	Conductivity (W/m-C)	Density (kg/m)³	Specific Heat (J/kg-C)

Non-metals

Material	Conductivity W/m-C	Density kg/m³	Specific Heat J/kg-C

Air

Properties at Atmospheric Pressure

Temperature C	Conductivity W/m-C	Density kg/m³	Specific Heat J/kg-C	Dynamic Viscosity kg/m-s	Kinematic Viscosity m²/s	Thermal Diffusivity m²/s

Gases

Properties at Atmospheric Pressure

Gas	Temperature C	Conductivity W/m-C	Density kg/m³	Specific Heat J/kg-C	Dynamic Viscosity kg/m-s	Kinematic Viscosity m²/s	Thermal Diffusivity m²/s

Water

Water (Saturated) - Thermal Properties

Temperature C	Conductivity W/m-C	Density kg/m³	Specific Heat J/kg-C	Dynamic Viscosity kg/m-s

Liquids

Liquid	Temperature C	Conductivity W/m-C	Density kg/m³	Specific Heat J/kg-C	Kinematic Viscosity m²/s	Thermal Diffusivity m²/s	C.T.E. 1/C

Other libraries

Material Property Libraries on the Web

Below is a list of links to other material property databases on the Web.

MatWeb - Free Material Database

IDES Plastic Materials Database - Prospector Products

WebElements Periodic Table

Metal Suppliers On-Line

This page calculates the plate temperature (T_p) for an isothermal (constant temperature) thin flat plate embedded in a semi-infinite medium with an applied isothermal temperature.

Define the width, length, depth, and the heat load of the plate, as well as the conductivity and the isothermal temperature applied to the medium surrounding the plate. This page will calculate the plate temperature.

Do you want to know more ?

Embedded Plate and Flow Conditions

Description	Symbol	Value	Units
Width	W		Meters
Length	L		Meters
Depth	d		Meters
Heat Load	Q		W

Conducting Medium's Properties (Default is for Epoxy [high fill], Units in SI)

Description	Symbol	Value	Units
Conductivity	k		W/(m-^oC)
Isothermal Temperature	T_i		^oC

Results for Isothermal Embedded Plate

This page calculates the temperature difference and the thermal contact conductance (thermal resistance) for an interface formed by two conforming, rectangular, rough surfaces as a function of contact pressure in the low pressure range.

Define the surface properties and the interface material , as well as the conductivity and the isothermal temperature applied to the medium surrounding the plate. the interstitial material can be either a gas or a liquid (gas parameter is zero). This page will calculate the temperature difference and the thermal resistance between the two surfaces.

Do you want to know more ?

Material and State Conditions (Choose a defined materials or enter your own data)

Description	Symbol	Value	Units
Contact Pressure of Surfaces	P		MPa
Width of Common Surface	W		m
Length of Common Surface	L		m
Heat Load on Surface 1	q		W
Surface 1
Microhardness of Surface 1	H_C1		MPa
Effective RMS Surface Roughness 1	sig₁		micrometer
Thermal Conductivity of Surface 1	k₁		W/(m ^oC)
Absolute Asperity Slope = 0.125 (sig₁)^0.402	m₁		None
Surface 2
Microhardness of Surface 2	H_C2		MPa
Effective RMS Surface Roughness 2	sig₂		micrometer
Thermal Conductivity of Surface 2	k₂		W/(m ^oC)
Absolute Asperity Slope = 0.125 (sig₂)^0.402	m₂		None
Interstitial Material
Thermal Conductivity of Gap Substance	k		W/(m ^oC)
Gas Parameter (@ T₀ = 50^oC and P₀ = 1 atm) (M₀ 0 for liquid)	M₀		m
Average Interface Thickness	t		m
Gas Temperature (needed if substance is a gas)	T_g		^oC
Gas pressure (needed if substance is a gas)	P_g		kPa

Results for Thermal Grease Interface Resistance

Description	Symbol	Value	Units
Microhardness used in Calculation	H_C		MPa
Effective RMS Surface Roughness = (sig₁²+sig₂²)^1/2	sig		micrometer
Effective Mean Absolute Asperity Slope = 0.125 (sig)^0.402	m		None
Harmonic Mean Thermal Conductivity = 2k₁k₂/(k₁+k₂)	k_s		W/(m ^oC)
Contact Conductive HTC₁ = 1.25k₁(m₁/sig₁)(P/H₁)^0.95	h_c1		W/(m² ^oC)
Contact Conductive HTC₂ = 1.25k₂(m₂/sig₂)(P/H₂)^0.95	h_c2		W/(m² ^oC)
Contact Conductive HTC = 1.25k_s(m/sig)(P/H_C)^0.95	h_c		W/(m² ^oC)
Gas Parameter = M₀(T/T₀)(P_g,0/P_g)	M_g		m
Effective Gap Thickness₁ = 1.53sig₁(P/H₁)^-0.097	Y₁		m
Effective Gap Thickness₂ = 1.53sig₂(P/H₂)^-0.097	Y₂		m
Effective Gap Thickness = 1.53sig(P/H_C)^-0.097	Y		m
Gap Conductive HTC₁ = k_g/ (Y₁+ M)	h_g1		W/(m² ^oC)
Gap Conductive HTC₂ = k_g/ (Y₂+ M)	h_g2		W/(m² ^oC)
Gap Conductive HTC = k_g/ (Y+ M)	h_g		W/(m² ^oC)
Joint Conductive HTC₁ = h_c1 + h_g1	h_j1		W/(m² ^oC)
Joint Conductive HTC₂ = h_c2 + h_g2	h_j2		W/(m² ^oC)
Joint Conductive HTC =	h_j		W/(m² ^oC)
Interface Thermal Resistance = 1/ (WLh_j)	r_j		^oC/W
Temperature Difference = q/ (WLh_j)	T_1-2	>	^oC
NOTE: HTC stands for Heat Transfer Coefficient

This page calculates the temperature T_n at one side of an isothermal (constant temperature) multilayer wall.

Define the height, depth, the low temperature on one side of the wall and a constant heat flow (from T_n to T₁) through the wall. This page will calculate the higher temperature on the other side of the wall. The layers up to a zero value for Thickness or Conductivity will be included in the calculation.

Do you want to know more ?

Multilayer Wall and Flow Conditions

Description	Symbol	Value	Units
Height	H		Meters
Depth	D		Meters
Temperature 1	T₁		^oC
Heat Flow	q		W

Layer	Sym	Thickness (m)	Sym	Conductivity (W/m-^oC)
Layer 1	t1		k1
Layer 2	t2		k2
Layer 3	t3		k3
Layer 4	t4		k4
Layer 5	t5		k5
Layer 6	t6		k6
Layer 7	t7		k7
Layer 8	t8		k8
Layer 9	t9		k9
Layer 10	t10		k10

Results for Isothermal Multilayer Wall

This page calculates the temperature rise across a multilayer cylinder for a heat load (Q) applied to its inner surface at r0 and flowing to the outer surface.

Define the cylinder's inside radius, length and the heat load conducted through the layers. This page will calculate the temperature rise between the inner and outer surfaces of this cylinder stack. For a positive heat load T0 > Tn and for a negative heat load Tn > T0.

Do you want to know more ?

Verification Test Case

Multilayer Cylinder and Flow Conditions

Description	Symbol	Value	Units
Inner Radius	R₀		Meters
Length	L		Meters
Heat Flow from Inner to Outer Surface	Q		W

Layer Thickness and Conductivity (First zero value ends the list)	Sym	Thickness (m)	Sym	Conductivity (W/m-^oC)
Layer 1 Thickness and Conductivity	t₁		k₁
Layer 2 Thickness and Conductivity	t₂		k₂
Layer 3 Thickness and Conductivity	t₃		k₃
Layer 4 Thickness and Conductivity	t₄		k₄
Layer 5 Thickness and Conductivity	t₅		k₅
Layer 6 Thickness and Conductivity	t₆		k₆
Layer 7 Thickness and Conductivity	t₇		k₇
Layer 8 Thickness and Conductivity	t₈		k₈
Layer 9 Thickness and Conductivity	t₉		k₉
Layer 10 Thickness and Conductivity	t₁₀		k₁₀

Results for Isothermal Multilayer Cylinder

This page calculates the net radiant heat exchange for two isothermal (constant temperature) parallel flat black plates of equal size.

Define the plate size, spacing, and the plate temperatures. This page will calculate the view factor between plates 1 and 2 and calculate the net radiant heat exchange between the two plates using this view factor.

Do you want to know more ?

Radiation Conditions

Description	Symbol	Value	Units
Plate Length	L		Meters
Plate Width	W		Meters
Spacing (between plates)	D		Meters
Plate 1 Temperature	T₁		K
Plate 2 Temperature	T₂		K

Results for Isothermal Plates

Description	Symbol	Value	Units
x = L/D	x		None
y = W/D	y		None
A = ln((1+x²)*(1+y²)/(1+x²+y²))^0.5	A		None
B = y(1+x²)^0.5tan^-1(y/(1+x²)^0.5)	B		None
C = x(1+y²)^0.5tan^-1(x/(1+y²)^0.5)	C		None
D = ytan^-1(y)+xtan^-1(x)	D		None
E = 2/(pixy)	E		None
View Factor_(1-2) = (A+B+C-D)*E	VF_(1-2)		None
Heat Radiated = 56.69E-9VF_(1-2)LW(T₁⁴-T₂⁴)	q		W

This page calculates the net radiant heat exchange for two isothermal (constant temperature) perpendicular flat black plates of different lengths but equal widths.

Do you want to know more ?

Radiation Conditions

Description	Symbol	Value	Units
Plate 1 Length	L₁		Meters
Plate 2 Length	L₂		Meters
Width	W		Meters
Plate 1 Temperature	T₁		K
Plate 2 Temperature	T₂		K

Results for Isothermal Plates

Description	Symbol	Value	Units
x = L₂/W	x		None
y = L₁/W	y		None
z = x²+y²	z		None
A = ln((1+x²)*(1+y²)/(1+z))	A		None
B = y²(ln(y²(1+z)/(z*(1+ y²))))	B		None
C = x²(ln(x²(1+z)/(z*(1+ x²))))	C		None
D = ytan^-1(1/y)+xtan^-1(1/x)-(z)^0.5*tan^-1(1/z^0.5)	D		None
View Factor_(1-2) = (1/4(A+B+C)+D)/(piy)	VF_(1-2)		None
Heat Radiated = 56.69e-9VF_(1-2)L₁W(T₁⁴-T₂⁴)	q		W

This page calculates the net radiant heat exchange for two isothermal (constant temperature) parallel square flat black plates of different edge lengths.

Define the edge length of the plates, spacing, and the plate temperatures. This page will calculate the view factor between plates 1 and 2 and calculate the net radiant heat exchange between the two plates using this view factor.

Do you want to know more ?

Radiation Conditions

Description	Symbol	Value	Units
Plate 1 Edge Length	L₁		Meters
Plate 2 Edge Length	L₂		Meters
Spacing (between plates)	D		Meters
Plate 1 Temperature	T₁		K
Plate 2 Temperature	T₂		K

Results for Isothermal Plates

Description	Symbol	Value	Units
x = L₁/D*(1+L₂/L₁)	x		None
y = L₁/D*(1-L₂/L₁)	y		None
	A		None
	B		None
	C		None
View Factor_(1-2) =	VF_(1-2)		None
Heat Radiated = 56.69e-9VF_(1-2)L₁²*(T₁⁴-T₂⁴)	q		W

This page calculates the net radiant heat exchange for two isothermal (constant temperature) parallel flat black disks.

Define the disk radii, spacing, and the disk temperatures. This page will calculate the view factor between disks 1 and 2 and calculate the net radiant heat exchange between the two disks using this view factor.

Do you want to know more ?

Radiation Conditions

Description	Symbol	Value	Units
Disk 1 Radius	rad₁		Meters
Disk 2 Radius	rad₂		Meters
Spacing (between disks)	D		Meters
Disk 1 Temperature	T₁		K
Disk 2 Temperature	T₂		K

Results for Isothermal Disks

Description	Symbol	Value	Units
r₁ = rad₁/D	r₁		None
r₂ = rad₂/D	r₂		None
x = 1+(1+r₂²)/r₁²	x		None
View Factor_(1-2) = 0.5(x-(x²-4(r₂/r₁)²)^0.5)	VF_(1-2)		None
Heat Radiated = 56.69E-9VF_(1-2)pirad₁²(T₁⁴-T₂⁴)	q		W

This page calculates the head loss coefficient and head loss of a fluid across thin-walled parallel louvers inside a tube of square cross section.

Define the number of louvers, angle and flow conditions in the tube. The head loss across the louvers will be calculated.

Do you want to know more ?

Tube and Flow Properties

Description	Symbol	Value	Units
Number of Louvers in Tube	N		None
Angle of Louvers in Tube	A		Degrees
Flow Velocity in the Tube	u_m		m/s
Width of the Tube	a		Meters
Kinematic Viscosity	v		kg/m-s

Results for Head Loss of Louvers

Equations Used	Symbol	Value	Units
k_qu = Function of Angle and Number of Louvers	k_qu		None
Hydraulic Diameter of the Tube = a	D_h		Meters
Reynolds Number = u_m * D_h / v	Re		None
X =	X		None
Head Loss Coefficient = X +	k_loss		None
Head Loss = k_loss * (u_m² / (2 * g) )	hl		Meters

This page calculates the convective and radiative heat transfer from an isothermal vertical plate. The average convective heat transfer coefficient is calculated assuming natural convection conditions. The convection calculation automatically switches between laminar and turbulent convection correlations based on Rayleigh number. The plate transfers heat from only one of its sides. It is assumed to be insulated on the other.

Define the plate size, surface temperature and ambient temperature. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the heat transfer by convection and radiation from the isothermal plate.

To account for convection only, make the emissivity equal to 0. Similarly, to account for radiation only, make the tehrmal conductivity = 0.

Do you want to know more ?

Plate and Flow Conditions

Fluid Properties at Film Temperature, Except for Density. (Defaults are for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_p+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density at reference temperature of 20 C	rho_ref		kg/m³
Density calculated at film temperature T_f	rho		kg/m³
Emissivity	e		None

Plate Dimensions

Description	Symbol	Value	Units
Plate Width (across flow)	W		Meters
Plate Height (with flow)	H		Meters
Plate Temperature	T_p		^oC
Ambient Temperature	T_a		^oC

Results for Plate

Description	Symbol	Value	Units
Prandlt Number = v/a	Pr		None
Grashof Number = gcte(T_p-T_a)*H³/v²	Gr		None
Rayleigh Number = Gr*Pr	Ra		None
Nusselt=	Nu		None
Average Heat Transfer Coefficient = Nu*k/H	h		W/m²-C
Convective HeatTransfer = hWH*(T_p-T_a)	q_conv		W
Radiative Heat Transfer= SigmaWHe(Tp⁴-Ta⁴)	q_rad		W
Total Heat Transfer = q_conv + q_rad	q_tot		W

This page calculates the average heat transfer coefficient and surface temperature for an isoflux (constant and uniform flux) parallel plate vertical channel open to ambient from both ends in a natural convection environment. The convection calculation are based on Rayleigh number.

Define the channel size, uniform heat load and ambient air fluid temperature. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the temperature of the plates.

Do you want to know more ?

Channel and Flow Conditions

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_p+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density	rho		kg/m³

Channel Dimensions

Description	Symbol	Value	Units
Channel Width (across flow)	W		Meters
Channel Height (with flow)	H		Meters
Channel Gap	S		Meters
Total uniform heat load on plates	q		Watts
Ambient Temperature	T_a		^oC

Results for Plate

Description	Symbol	Value	Units
Flux = q / (2WH)	q^"		W/m²
Prandlt Number = Cp*µ / k	Pr		None
Rayleigh Number = gBq^"S⁴rho²C_p/ (µk²)	Ra^*		None
Ra*S/H	Ra*S/H		None
Nusselt Number = ( 48H /( RaS) + 2.51 / (Ra*S / H)^(2/5) )^-0.5	Nu		None
Average Heat Transfer Coefficient = Nu*k/S	h		W/m²-C
Plates temperature	T_p		^oC

This page calculates the average heat transfer coefficient and heat convected from an isothermal (constant temperature) heated horizontal flat plate's upper surface at a specified temperature in a natural convection environment. The convection calculation automatically switches between calculation methods based on Rayleigh number.

Define the plate size, surface temperature, ambient air fluid temperature. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the heat transfer by convection from the isothermal plate.

Do you want to know more ?

Plate and Flow Conditions

Fluid Properties at Film Temperature, Except for Density. (Defaults are for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_p+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		m²/s
Density at reference temperature of 20 C	rho_ref		kg/m³
Density calculated at film temperature T_f	rho		kg/m³
Emissivity	e		^None

Plate Dimensions

Description	Symbol	Value	Units
Plate Width	W		Meters
Plate Length	L		Meters
Plate Temperature	T_p		^oC
Ambient Temperature	T_a		^oC

Results for Plate

Description	Symbol	Value	Units
Prandtl Number = v/a	Pr		None
Grashof Number = gcte(T_p-T_a)((WL)/(2W+2L)³)/v²	Gr		None
Rayleigh Number = Gr*Pr	Ra		None
Nusselt Number =	Nu		None
Average Heat Transfer Coefficient = Nuk/((WL)/(2W+2L))	h		W/m²-C
Convective Heat Transfer = hWL*(T_p-T_a)	q_conv		W
Radiative Heat Transfer = SigmaWLe(Tp⁴-Ta⁴)	q_rad		W
Total Heat Transfer = q_conv + q_rad	q_tot		W

This page calculates the heat transfer coefficient, heat convected and heat radiated from an isothermal horizontal cylinder assuming natural convection. The convection calculation is based on Rayleigh number and is valid for Rayleigh numbers between 10^-5 and 10¹². The ends of the cylinder are assumed to be adiabatic.

Define the channel size, cylinder temperature and ambient air fluid temperature. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the heat convected from the cylinder.

To account for convection only, make the emissivity equal to 0. Similarly, to account for radiation only, make the tehrmal conductivity = 0.

Do you want to know more ?

Cylinder and Flow Conditions

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_c+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Dynamic Viscosity	µ		kg/m-s
Density at reference temperature of 20 C	rho_ref		kg/m³
Density calculated at film temperature T_f	rho		kg/m³
Thermal Conductivity	k		W/m-^oC
Emissivity	e		^None

Cylinder Dimensions

Description	Symbol	Value	Units
Length	L		Meters
Diameter	D		Meters
Cylinder Temperature	T_c		^oC
Ambient Temperature	T_a		^oC

Results for Cylinder

Description	Symbol	Value	Units
Prandlt Number = Cp*µ / k	Pr		None
Area = PI * D	A		m²
Rayleigh Number = gB rho²C_p(T_c-T_a)D³ / kµ	Ra		None
Nusselt = {0.60+(0.387Ra_D^1/6) / [1+(0.559/Pr)^9/16]^(8/27)}²	Nu		None
Average Heat Transfer Coefficient = Nu*k/HD	h		W/m²-C
Convective Heat Transfer = hA(Tc-Ta)	q_conv		W
Radiative Heat Transfer	q_rad		W
Total Heat Transfer	q		W

This page calculates the average heat transfer coefficient and heat convected from an isothermal (constant temperature) heated horizontal flat plate's lower surface at a specified temperature in a natural convection environment.

Do you want to know more ?

Plate and Flow Conditions

Fluid Properties at Film Temperature, Except for Density. (Defaults are for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_p+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density at reference temperature of 20 C	rho_ref		kg/m³
Density calculated at film temperature T_f	rho		kg/m³
Emissivity	e		^None

Plate Dimensions

Description	Symbol	Value	Units
Plate Width (across flow)	W		Meters
Plate Length (along flow)	L		Meters
Plate Temperature	T_p		^oC
Ambient Temperature	T_a		^oC

Results for Plate

Description	Symbol	Value	Units
Prandtl Number = v/a	Pr		None
Grashof Number = gcte(T_p-T_a)((WL)/(2W+2L))³/v²	Gr		None
Rayleigh Number = Gr*Pr	Ra		None
Nusselt Number = 0.27(Gr*Pr)^0.25	Nu		None
Average Heat Transfer Coefficient = Nuk/((WL)/(2W+2L))	h		W/m²-C
Convective Heat Transfer = hWL*(T_p-T_a)	q_conv		W
Radiative Heat Transfer = SigmaWLe(Tp⁴-Ta⁴)	q_rad		W
Total Heat Transfer = q_conv + q_rad	q_tot		W

This page calculates the natural convection heat transfer between two concentric cylinders maintained at constant temperatures. The calculation is based on Rayleigh number and is valid for Rayleigh numbers below 10⁷.

Define the dimensions of the cylinders and their temperatures. You also need to define the fluid properties. This page will calculate the heat convected between the cylinders based on the flow conditions.

Do you want to know more ?

Cylinders and Flow Conditions

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_i+T_o)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Coefficient of Thermal Expansion	B		1/K
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density at reference temperature of 20 C	rho_ref		kg/m³
Density calculated at film temperature T_f	rho		kg/m³

Cylinders Dimensions

Description	Symbol	Value	Units
Length	L		Meters
Inner Cylinder Diameter	D_i		Meters
Outer Cylinder Diameter	D_o		Meters
Inner Cylinder Temperature	T_i		^oC
Outer Cylinder Temperature	T_o		^oC

Results for Concentric Cylinders

Description	Symbol	Value	Units
Gap between cylinders	d		m
Effective conductivity	k_eff		W/m-^oC
Prandlt Number = Cp*µ / k	Pr		None
Rayleigh_d = gB rho²C_p(T_i-T_o)d³ / kµ	Ra_d		None
Rayleigh_c^* = Ra_d(ln(D_o/D_i))⁴) / d³(D_i^-3/5+D_o^-3/5)⁵	Ra_c^*		None
Heat transfer = 2Pi k_effL (T_i-T_o) / ln(D_o/D_i)	q		W

This page calculates the average heat transfer coefficient and heat convected from an isothermal (constant temperature) square rod at a specified temperature in free stream flow.

Define the rod size, surface temperature, ambient air fluid temperature and approach flow speed. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the heat transfer by convection from the isothermal square rod.

Do you want to know more ?

Rod and Flow Conditions

Description	Symbol	Value	Units
Rod Width	W		Meters
Rod Length (perpendicular to flow)	L		Meters
Rod Temperature	T_r		^oC
Ambient Temperature	T_a		^oC
Flow Velocity	u_m		m/s

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_r+T_a)/2	T_f		^oC
Conductivity	k		W/m-^oC
Kinematic Viscosity	v		m²/s
Thermal Diffusivity	a		m²/s

Results for Isothermal Rod

Description	Symbol	Value	Units
Prandtl Number = v/a	Pr		None
Reynolds Number = u_m*W/v	Re		None
Nusselt Number = 0.102Re^0.675 * Pr^1/3	Nu		None
Heat Transfer Coefficient = Nu*k/W	h		W/m²-C
Heat Dissipated from Rod = hWL4(T_r-T_a)	q		W

This page calculates the heat transfer coefficient and temperature of a PCB board with components. Components are assume to be isothermal blocks. Temperatures at each row of components is calculated for the specified conditions.

Define the PC board properties, component properties, and air flow properties. This page will calculate a heat transfer coefficient based on the flow conditions, calculate the resistance between the components and the air, as well as the component temperature.

Do you want to know more ?

PC Board Properties

Description	Symbol	Value	Units
Width of PCB (Lateral to Flow)	W_b		Meters
Height of flow channel above PCB	H_F		Meters
Are their card guides at leading edges of PCB ?	G		None
Conductivity of the board (no copper)	k_b		W/m-^oC
Thickness of the board	t		Meters
Volume of copper per area of PCB (Lateral to Flow)	phi₁		m³/m²
Volume of copper per area of PCB (Parallel to Flow)	phi₂		m³/m²
Conductivity of the PCB copper	k_c		W/m-^oC

Component Properties

Description	Symbol	Value	Units
Number of components (Parallel to Flow)	N		None
Length (Parallel to Flow)	b		Meters
Pitch (Parallel to Flow)	d		Meters
Number of components (Lateral to Flow)	M		None
Width (Lateral to Flow)	S		Meters
Pitch (Lateral to Flow)	w		Meters
Height (Protruding into Flow)	e		Meters
Heat Load per Component	q		W
Air gap between PCB and component	del		Meters
Number of leads per component	n		None
Length of leads	L		Meters
Cross-sectional area of one lead	A_l		m²
Thermal conductivity of leads	k_l		W/m-^oC

Air Flow Properties

Description	Symbol	Value	Units
Ambient temperature (at entrance)	T_a		^oC
Average flow velocity in free flow area between boards	u_m		m/s
Thermal conductivity of air	k_a		W/m-^oC
Specific heat of air	C_p		J/kg-^oC
Air density	rho		kg/m³

Results for PC Board

Equations Used	Symbol	Value	Units
Value of G for heat transfer coefficient calculation	G		None
Flow area per PCB = W_b * H_F - (M * S * e)	a		m²
Flow rate = u_m * a	F		m³/s
Lateral conductance of the board = (k_b * t) + (k_c * phi₁)	C₁		W/^oC
Streamwise conductance of the board = (k_b * t) + (k_c * phi₂)	C₂		W/^oC
Resistance across air gap = del / (k_a * S * b)	r_c		^oC/W
Resistance across the leads = L / (k_l * n * A_l)	r_l		^oC/W
Interface resistance = 1 / ( (1/r_c) + (1/r_l) )	R_i		^oC/W
Exposed surface area = S * b + 2e (S + b)	A₁		m²

Equations Used	Symbol	Units
Heat transfer coefficient =	h	W/m²-^oC
Effective area =	A₂	m²
Overall thermal resistance= 1 / (h x A₁ + 1 / ( R_i + 1/ (A₂ x h) ) )	R	^oC/W
Local air temperature = (qM(N-1)) / (FrhoC_p)	T_l	^oC
Component temperature = T_l + q * R	T_c	^oC

N	h	Units	A₂	Units	R	Units	T_c	Units
1		W/m²-^oC		m²		^oC/W		^oC
2		W/m²-^oC		m²		^oC/W		^oC
3		W/m²-^oC		m²		^oC/W		^oC
4		W/m²-^oC		m²		^oC/W		^oC
5		W/m²-^oC		m²		^oC/W		^oC
6		W/m²-^oC		m²		^oC/W		^oC
7		W/m²-^oC		m²		^oC/W		^oC
8		W/m²-^oC		m²		^oC/W		^oC
9		W/m²-^oC		m²		^oC/W		^oC
10		W/m²-^oC		m²		^oC/W		^oC

This page calculates the average heat transfer coefficient and heat convected from an isothermal (constant temperature) flat plate at a specified temperature in free stream flow. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

Define the plate size, surface temperature, ambient air fluid temperature and approach flow speed. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the heat transfer by convection from the isothermal plate.

Do you want to know more ?

Plate and Flow Conditions

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_p+T_a)/2	T_f		^oC
Specific Heat	C_p		J/kg-^oC
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density	rho		kg/m³

Plate Dimensions

Description	Symbol	Value	Units
Plate Width (across flow)	W		Meters
Plate Length (along flow)	L		Meters
Plate Temperature	T_p		^oC
Ambient Temperature	T_a		^oC
Flow Velocity	u_m		m/s

Results for Isothermal Plate

Description	Symbol	Value	Units
Prandtl Number = v/a	Pr		None
Reynolds Number = u_m*L/v	Re		None
Nusselt Number =	Nu		None
Heat Transfer Coefficient = Nu*k/L	h		W/m²-C
Heat Dissipated from Plate = hWL*(T_p-T_a)	q		W

This page calculates the heat transfer coefficient for fully developed flow in a smooth circular tube. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

Define the tube size, heat load on the wall, fluid bulk temperature and flow speed. You also need to define the fluid properties. This page will calculate a heat transfer coefficient based on the flow conditions as well as the average tube wall temperature.

Do you want to know more ?

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Specific Heat	C_p		J/kg-^oC
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density	Rho		kg/m³

Tube Dimensions

Description	Symbol	Value	Units
Tube Diameter	D		Meters
Tube Length	L		Meters
Heat Load	q		watts
Bulk Fluid Temperature	T_b		^oC
Flow Velocity	u_m		m/s

Results for Circular Tube

Description	Symbol	Value	Units
Prandtl Number = Cp*µ / k	Pr		None
Reynolds Number = Rhou_mD / µ	Re		None
Friction =	f		None
Nusselt =	Nu		None
Heat Transfer Coefficient = Nu*k / D	h		W/m²-C
Area = Pi * D * L	A		m²
Average Wall Temperature = T_b+ q / (h*A)	T_w		^oC

This page calculates the mean heat transfer coefficient for simultaneously developing velocity and temperature fields in a circular smooth tube. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

Do you want to know more ?

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Specific Heat	C_p		J/kg-^oC
Thermal Conductivity	k		W/m-^oC
Dynamic Viscosity	µ		kg/m-s
Density	Rho		kg/m³

Tube Dimensions

Description	Symbol	Value	Units
Tube Diameter	D		Meters
Tube Length	L		Meters
Heat Load	q		watts
Bulk Fluid Temperature	T_b		^oC
Flow Velocity	u_m		m/s

Results for Circular Tube

Description	Symbol	Value	Units
Prandtl Number = Cp*µ / k	Pr		None
Reynolds Number = Rhou_mD / µ	Re		None
Friction_f-dev =	f		None
Nusselt_f-dev =	Nu_f-dev		None
Nusselt_m =	Nu_m		None
Heat Transfer Coefficient Multiplier = Nu_m / Nu_f-dev	h_mult		None
Mean Heat Transfer Coefficient = Nu_m*k / D	h_m		W/m²-C
Area = Pi * D * L	A		m²
Average Wall Temperature = T_b+ q / (h_m*A)	T_w		^oC

This page calculates the average heat transfer coefficient and heat convected from an isothermal (constant temperature) circular rod at a specified temperature in free stream flow.

Do you want to know more ?

Rod and Flow Conditions

Description	Symbol	Value	Units
Rod Diameter	D		Meters
Rod Length (perpendicular to flow)	L		Meters
Rod Temperature	T_r		^oC
Ambient Temperature	T_a		^oC
Flow Velocity	u_m		m/s

Fluid Properties at Film Temperature (Default is for Air at 20C)

Description	Symbol	Value	Units
Film Temperature = (T_r+T_a)/2	T_f		^oC
Conductivity	k		W/m-^oC
Kinematic Viscosity	v		m²/s
Thermal Diffusivity	a		m²/s

Results for Isothermal Rod

Description	Symbol	Value	Units
Prandtl Number = v/a	Pr		None
Reynolds Number = u_m*D/v	Re		None
Nusselt Number =	Nu		None
Heat Transfer Coefficient = Nu*k/D	h		W/m²-C
Heat Dissipated from Rod = hpiDL(T_r-T_a)	q		W

About the Thermal Wizard

The Thermal Wizard is developed and maintained by Maya HTT. We hope you find it is a useful tool to help you understand common heat transfer problems and thermal phenomena. If you do find any problems, then please report them via our Feedback Form and we will investigate. Maya HTT will make changes, additions and deletions to the web site from time to time without any notification to users of The Thermal Wizard.

Disclaimer

This Disclaimer applies to any application, software code, algorithm, form, documentation and any other component of the THERMAL WIZARD (collectively the “Thermal Wizard”) that is made available to you from time to time by Maya Heat Transfer Technologies Ltd. (“MAYA HTT”). The Thermal Wizard is provided for your personal use and any commercial, industrial or other type of use is strictly prohibited. MAYA HTT is providing you with the Thermal Wizard free of charge, but to the maximum extent permitted by applicable laws, MAYA HTT FULLY DISCLAIMS AND ASSUMES NO LIABILITY WHATSOEVER, UNDER ANY THEORY OF LAW, FOR ANY TYPE OF DAMAGE OF ANY KIND THAT YOU MAY SUFFER ARISING OF THE USE (OR INABILITY TO USE) THE THERMAL WIZARD, WHETHER DIRECT OR INDIRECT. YOU ARE USING THE THERMAL WIZARD AT YOUR OWN RISKS AND IT IS PROVIDED TO YOU "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT. Without limiting the generality of the foregoing, you are hereby advised that the Thermal Wizard may be unavailable from time to time, may include technical inaccuracies, be incomplete or contain bugs, errors, viruses or similar codes with detrimental effects. You agree that this Disclaimer and your use of the Thermal Wizard are governed by the laws in force in the Province of Quebec, Canada, and you agree to the exclusive jurisdiction of the courts located in the judicial district of Montreal to adjudicate any dispute arising out of this Disclaimer or your use (or inability to use) the Thermal Wizard.

Should any user of the Thermal Wizard provide MAYA HTT with information including feedback data, questions, comments, suggestions or the like regarding the Thermal Wizard, such information shall be deemed to be non-confidential and MAYA HTT shall have no obligation of any kind with respect to such information and shall be free to reproduce, use, disclose and distribute the information to others without limitation. Further, MAYA HTT shall be free to use such information (and any ideas, concepts, know-how or techniques contained in such information) for any purpose whatsoever including, but not limited to developing, manufacturing and marketing products incorporating such information.

Welcome to the Thermal Wizard

Our calculators:

Conduction Calculators

Convection Calculators

Radiation Calculators

Head Loss Coefficients

Others

Metals

Non-metals

Air

Gases

Water

Liquids

Other libraries

Material Property Libraries on the Web

About the Thermal Wizard

Disclaimer