Thermal conductivity of base metal using given cooling rate (thin plates) Calculator

✖Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness.ⓘ Cooling Rate of Thin Plate [R_c]			+10% -10%
✖The density of electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.ⓘ Density of Electrode [ρ]			+10% -10%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [Q_c]			+10% -10%
✖Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set.ⓘ Thickness of Filler Metal [t]			+10% -10%
✖Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.ⓘ Net Heat Supplied Per Unit Length [H_net]			+10% -10%
✖Temperature for Cooling Rate is calculated is the temperature at which the cooling rate is calculated.ⓘ Temperature for Cooling Rate [T_c]			+10% -10%
✖Ambient Temperature is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+10% -10%

✖Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal conductivity of base metal using given cooling rate (thin plates) [k]

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Formula

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Thermal conductivity of base metal using given cooling rate (thin plates)

Formula

`"k" = "R"_{"c"}/(2*pi*"ρ"*"Q"_{"c"}*(("t"/"H"_{"net"})^2)*(("T"_{"c"}-"t"_{"a"})^3))`

Example

`"10.14832W/(m*K)"="0.66°C/s"/(2*pi*"997kg/m³"*"4.184kJ/kg*K"*(("5mm"/"1000J/mm")^2)*(("500°C"-"37°C")^3))`

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Thermal conductivity of base metal using given cooling rate (thin plates) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3))
k = R_c/(2*pi*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3))
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Cooling Rate of Thin Plate - (Measured in Kelvin per Second) - Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness.
Density of Electrode - (Measured in Kilogram per Cubic Meter) - The density of electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Thickness of Filler Metal - (Measured in Meter) - Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set.
Net Heat Supplied Per Unit Length - (Measured in Joule per Meter) - Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.
Temperature for Cooling Rate - (Measured in Kelvin) - Temperature for Cooling Rate is calculated is the temperature at which the cooling rate is calculated.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature is the temperature of the surrounding.

STEP 1: Convert Input(s) to Base Unit

Cooling Rate of Thin Plate: 0.66 Celsius per Second --> 0.66 Kelvin per Second (Check conversion here)
Density of Electrode: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Thickness of Filler Metal: 5 Millimeter --> 0.005 Meter (Check conversion here)
Net Heat Supplied Per Unit Length: 1000 Joule per Millimeter --> 1000000 Joule per Meter (Check conversion here)
Temperature for Cooling Rate: 500 Celsius --> 773.15 Kelvin (Check conversion here)
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = R_c/(2*pi*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3)) --> 0.66/(2*pi*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3))

Evaluating ... ...

k = 10.1483222949554

STEP 3: Convert Result to Output's Unit

10.1483222949554 Watt per Meter per K --> No Conversion Required

FINAL ANSWER

10.1483222949554 ≈ 10.14832 Watt per Meter per K <-- Thermal Conductivity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Welding » Heat Flow in Welded Joints » Thermal conductivity of base metal using given cooling rate (thin plates)

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< 13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material

Go Peak Temperature Reached at Some Distance = Ambient Temperature+(Net Heat Supplied Per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of Filler Metal*Specific Heat Capacity*Distance From The Fusion Boundary+Net Heat Supplied Per Unit Length)

Position of peak temperature from fusion boundary

Go Distance From The Fusion Boundary = ((Melting Temperature of Base Metal-Temperature Reached at Some Distance)*Net Heat Supplied Per Unit Length)/((Temperature Reached at Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler Metal)

Net heat supplied to weld area to raise it to given temperature from fusion boundary

Go Net Heat Supplied Per Unit Length = ((Temperature Reached at Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler Metal*Distance From The Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at Some Distance)

Net heat supplied to achieve given cooling rates for thin plates

Go Net Heat Supplied Per Unit Length = Thickness of Filler Metal/sqrt(Cooling Rate of Thin Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3)))

Thickness of base metal for desired cooling rate

Go Thickness = Net Heat Supplied Per Unit Length*sqrt(Cooling Rate of Thick Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3)))

Thermal conductivity of base metal using given cooling rate (thin plates)

Go Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3))

Cooling rate for relatively thin plates

Go Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)

Thickness of Base Metal using Relative Thickness Factor

Go Thickness of The Base Metal = Relative Plate Thickness Factor*sqrt(Net Heat Supplied Per Unit Length/((Temperature for Cooling Rate-Ambient Temperature)*Density of Electrode*Specific Heat Capacity))

Relative plate thickness factor

Go Relative Plate Thickness Factor = Thickness of Filler Metal*sqrt(((Temperature for Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied Per Unit Length)

Net Heat supplied using Relative Thickness Factor

Go Net Heat Supplied = ((Thickness of Filler Metal/Relative Plate Thickness Factor)^2)*Density of Electrode*Specific Heat Capacity*(Temperature for Cooling Rate-Ambient Temperature)

Thermal conductivity of base metal using given cooling rate (thick plates)

Go Thermal Conductivity = (Cooling Rate of Thick Plate*Net Heat Supplied Per Unit Length)/(2*pi*((Temperature for Cooling Rate-Ambient Temperature)^2))

Net heat supplied to achieve given cooling rates for thick plates

Go Net Heat Supplied Per Unit Length = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Cooling Rate of Thick Plate

Cooling Rate for Relatively Thick Plates

Go Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length

Thermal conductivity of base metal using given cooling rate (thin plates) Formula

How heat transfer takes place near heat affected zone ?

Heat transfer in a welded joint is a complex phenomenon involving three dimensional movement of a heat source. Heat from the weld zone is transferred more to the other parts of the base metal by means of conduction. Similarly heat is also lost to surroundings by convection from the surface, with radiation component being relatively small except near the weld pool. Thus the analytical treatment of the weld zone is extremely difficult.

How to Calculate Thermal conductivity of base metal using given cooling rate (thin plates)?

Thermal conductivity of base metal using given cooling rate (thin plates) calculator uses Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)) to calculate the Thermal Conductivity, The Thermal conductivity of base metal using given cooling rate (thin plates) formula is the sensitivity of metal towards heat conduction under given conditions. Thermal Conductivity is denoted by k symbol.

How to calculate Thermal conductivity of base metal using given cooling rate (thin plates) using this online calculator? To use this online calculator for Thermal conductivity of base metal using given cooling rate (thin plates), enter Cooling Rate of Thin Plate (R_c), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button. Here is how the Thermal conductivity of base metal using given cooling rate (thin plates) calculation can be explained with given input values -> 10.18001 = 0.66/(2*pi*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3)).

FAQ

What is Thermal conductivity of base metal using given cooling rate (thin plates)?

The Thermal conductivity of base metal using given cooling rate (thin plates) formula is the sensitivity of metal towards heat conduction under given conditions and is represented as k = R_c/(2*pi*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3)) or Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)). Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness, The density of electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set, Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium, Temperature for Cooling Rate is calculated is the temperature at which the cooling rate is calculated & Ambient Temperature is the temperature of the surrounding.

How to calculate Thermal conductivity of base metal using given cooling rate (thin plates)?

The Thermal conductivity of base metal using given cooling rate (thin plates) formula is the sensitivity of metal towards heat conduction under given conditions is calculated using Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)). To calculate Thermal conductivity of base metal using given cooling rate (thin plates), you need Cooling Rate of Thin Plate (R_c), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a). With our tool, you need to enter the respective value for Cooling Rate of Thin Plate, Density of Electrode, Specific Heat Capacity, Thickness of Filler Metal, Net Heat Supplied Per Unit Length, Temperature for Cooling Rate & Ambient Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Thermal Conductivity?

In this formula, Thermal Conductivity uses Cooling Rate of Thin Plate, Density of Electrode, Specific Heat Capacity, Thickness of Filler Metal, Net Heat Supplied Per Unit Length, Temperature for Cooling Rate & Ambient Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

Thermal Conductivity = (Cooling Rate of Thick Plate*Net Heat Supplied Per Unit Length)/(2*pi*((Temperature for Cooling Rate-Ambient Temperature)^2))

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