Cooling rate for relatively thin plates Calculator

✖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 [k]			+10% -10%
✖The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object.ⓘ Density [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 the metal is the thickness of the base metal and is denoted by h symbol.ⓘ Thickness of the Metal [t]			+10% -10%
✖Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.ⓘ Net Heat Supplied per Unit Length [H_Net]			+10% -10%
✖Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated.ⓘ Temperature to Calculate Cooling Rate [T_c]			+10% -10%
✖Ambient Temperature is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+10% -10%

✖Cooling Rate of Thinplate is the time rate of decrease of temperature of a particular material.ⓘ Cooling rate for relatively thin plates [R_c]

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Formula

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Cooling rate for relatively thin plates

Formula

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

Example

`"0.66206°C/s"=2*pi*"10.18W/(m*K)"*"997kg/m³"*"4.184kJ/kg*K"*(("5mm"/"1000J/mm")^2)*(("500°C"-"37°C")^3)`

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Cooling rate for relatively thin plates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)
R_c = 2*pi*k*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

Cooling Rate of Thinplate - (Measured in Kelvin per Second) - Cooling Rate of Thinplate is the time rate of decrease of temperature of a particular material.
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.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object.
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 the Metal - (Measured in Meter) - Thickness of the metal is the thickness of the base metal and is denoted by h symbol.
Net Heat Supplied per Unit Length - (Measured in Joule per Meter) - Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.
Temperature to Calculate Cooling Rate - (Measured in Kelvin) - Temperature to calculate 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

Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Density: 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 the 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 to Calculate 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

R_c = 2*pi*k*ρ*Q_c*((t/H_Net)^2)*((T_c-t_a)^3) --> 2*pi*10.18*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3)

Evaluating ... ...

R_c = 0.662060171595046

STEP 3: Convert Result to Output's Unit

0.662060171595046 Kelvin per Second -->0.662060171595046 Celsius per Second (Check conversion here)

FINAL ANSWER

0.662060171595046 ≈ 0.66206 Celsius per Second <-- Cooling Rate of Thinplate

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Welding » Heat Flow in Welded Joints » Cooling rate for relatively thin plates

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University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< 13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material

Go Peak Temperature Reached at a Distance of y = 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 the 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 a Distance of y)*Net Heat Supplied per Unit Length)/((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the 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 a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at a Distance of y)

Net heat supplied to achieve given cooling rates for thin plates

Go Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))

Thickness of base metal for desired cooling rate

Go Thickness = Net Heat Supplied per Unit Length*sqrt(Cooling Rate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))

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

Go Thermal Conductivity = Cooling Rate of Thinplate/(2*pi*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))

Cooling rate for relatively thin plates

Go Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)

Relative plate thickness factor

Go Relative Plate Thickness Factor = Thickness of the Metal*sqrt(((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied per Unit Length)

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 to Calculate Cooling Rate-Ambient Temperature)*Density*Specific Heat Capacity))

Net Heat supplied using Relative Thickness Factor

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

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

Go Thermal Conductivity = (Cooling Rate*Net Heat Supplied per Unit Length)/(2*pi*((Temperature to Calculate 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 to Calculate Cooling Rate-Ambient Temperature)^2))/Cooling Rate

Cooling Rate for Relatively Thick Plates

Go Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length

Cooling rate for relatively 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 Cooling rate for relatively thin plates?

Cooling rate for relatively thin plates calculator uses Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3) to calculate the Cooling Rate of Thinplate, The Cooling rate for relatively thin plates formula is defined as the rate at which heat is lost to the surrounding from the weldment. Cooling Rate of Thinplate is denoted by R_c symbol.

How to calculate Cooling rate for relatively thin plates using this online calculator? To use this online calculator for Cooling rate for relatively thin plates, enter Thermal Conductivity (k), Density (ρ), Specific Heat Capacity (Q_c), Thickness of the Metal (t), Net Heat Supplied per Unit Length (H_Net), Temperature to Calculate Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button. Here is how the Cooling rate for relatively thin plates calculation can be explained with given input values -> 0.66206 = 2*pi*10.18*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3).

FAQ

What is Cooling rate for relatively thin plates?

The Cooling rate for relatively thin plates formula is defined as the rate at which heat is lost to the surrounding from the weldment and is represented as R_c = 2*pi*k*ρ*Q_c*((t/H_Net)^2)*((T_c-t_a)^3) or Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3). 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, The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object, 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 the metal is the thickness of the base metal and is denoted by h symbol, Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter, Temperature to calculate 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 Cooling rate for relatively thin plates?

The Cooling rate for relatively thin plates formula is defined as the rate at which heat is lost to the surrounding from the weldment is calculated using Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3). To calculate Cooling rate for relatively thin plates, you need Thermal Conductivity (k), Density (ρ), Specific Heat Capacity (Q_c), Thickness of the Metal (t), Net Heat Supplied per Unit Length (H_Net), Temperature to Calculate Cooling Rate (T_c) & Ambient Temperature (t_a). With our tool, you need to enter the respective value for Thermal Conductivity, Density, Specific Heat Capacity, Thickness of the Metal, Net Heat Supplied per Unit Length, Temperature to Calculate 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.

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