MySQL Entity Framework Error when updating Database

I have a simple console application with which I want to connect to a MySQL database. I've downloaded the EntityFramework, Mysql.Data and Mysql.Data.Entity packages and I've managed to establish the migrations through the PM console. However, whenever I try to update the database, I get the following error:

System.Data.SqlClient.SqlException (0x80131904): A network-related or 
instance-specific error occurred while establishing a connection to SQL 
Server. The server was not found or was not accessible. Verify that the 

instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server) ---> System.ComponentModel.Win32Exception (0x80004005): The system cannot find the file specified
   at System.Data.SqlClient.SqlInternalConnectionTds..ctor(DbConnectionPoolIdentity identity, SqlConnectionString connectionOptions, SqlCredential credential, Object providerInfo, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance, SqlConnectionString userConnectionOptions, SessionData reconnectSessionData, DbConnectionPool pool, String accessToken, Boolean applyTransientFaultHandling, SqlAuthenticationProviderManager sqlAuthProviderManager)
   at System.Data.SqlClient.SqlConnectionFactory.CreateConnection(DbConnectionOptions options, DbConnectionPoolKey poolKey, Object poolGroupProviderInfo, DbConnectionPool pool, DbConnection owningConnection, DbConnectionOptions userOptions)
   at System.Data.ProviderBase.DbConnectionFactory.CreatePooledConnection(DbConnectionPool pool, DbConnection owningObject, DbConnectionOptions options, DbConnectionPoolKey poolKey, DbConnectionOptions userOptions)
   at System.Data.ProviderBase.DbConnectionPool.CreateObject(DbConnection owningObject, DbConnectionOptions userOptions, DbConnectionInternal oldConnection)
   at System.Data.ProviderBase.DbConnectionPool.UserCreateRequest(DbConnection owningObject, DbConnectionOptions userOptions, DbConnectionInternal oldConnection)
   at System.Data.ProviderBase.DbConnectionPool.TryGetConnection(DbConnection owningObject, UInt32 waitForMultipleObjectsTimeout, Boolean allowCreate, Boolean onlyOneCheckConnection, DbConnectionOptions userOptions, DbConnectionInternal& connection)
   at System.Data.ProviderBase.DbConnectionPool.TryGetConnection(DbConnection owningObject, TaskCompletionSource`1 retry, DbConnectionOptions userOptions, DbConnectionInternal& connection)
   at System.Data.ProviderBase.DbConnectionFactory.TryGetConnection(DbConnection owningConnection, TaskCompletionSource`1 retry, DbConnectionOptions userOptions, DbConnectionInternal oldConnection, DbConnectionInternal& connection)
   at System.Data.ProviderBase.DbConnectionInternal.TryOpenConnectionInternal(DbConnection outerConnection, DbConnectionFactory connectionFactory, TaskCompletionSource`1 retry, DbConnectionOptions userOptions)
   at System.Data.ProviderBase.DbConnectionClosed.TryOpenConnection(DbConnection outerConnection, DbConnectionFactory connectionFactory, TaskCompletionSource`1 retry, DbConnectionOptions userOptions)
   at System.Data.SqlClient.SqlConnection.TryOpenInner(TaskCompletionSource`1 retry)
   at System.Data.SqlClient.SqlConnection.TryOpen(TaskCompletionSource`1 retry)
   at System.Data.SqlClient.SqlConnection.Open()
   at System.Data.Entity.Infrastructure.Interception.DbConnectionDispatcher.<Open>b__36(DbConnection t, DbConnectionInterceptionContext c)
   at System.Data.Entity.Infrastructure.Interception.InternalDispatcher`1.Dispatch[TTarget,TInterceptionContext](TTarget target, Action`2 operation, TInterceptionContext interceptionContext, Action`3 executing, Action`3 executed)
   at System.Data.Entity.Infrastructure.Interception.DbConnectionDispatcher.Open(DbConnection connection, DbInterceptionContext interceptionContext)
   at System.Data.Entity.SqlServer.SqlProviderServices.<>c__DisplayClass33.<UsingConnection>b__32()
   at System.Data.Entity.SqlServer.DefaultSqlExecutionStrategy.<>c__DisplayClass1.<Execute>b__0()
   at System.Data.Entity.SqlServer.DefaultSqlExecutionStrategy.Execute[TResult](Func`1 operation)
   at System.Data.Entity.SqlServer.DefaultSqlExecutionStrategy.Execute(Action operation)
   at System.Data.Entity.SqlServer.SqlProviderServices.UsingConnection(DbConnection sqlConnection, Action`1 act)
   at System.Data.Entity.SqlServer.SqlProviderServices.UsingMasterConnection(DbConnection sqlConnection, Action`1 act)
   at System.Data.Entity.SqlServer.SqlProviderServices.CreateDatabaseFromScript(Nullable`1 commandTimeout, DbConnection sqlConnection, String createDatabaseScript)
   at System.Data.Entity.SqlServer.SqlProviderServices.DbCreateDatabase(DbConnection connection, Nullable`1 commandTimeout, StoreItemCollection storeItemCollection)
   at System.Data.Entity.Core.Common.DbProviderServices.CreateDatabase(DbConnection connection, Nullable`1 commandTimeout, StoreItemCollection storeItemCollection)
   at System.Data.Entity.Core.Objects.ObjectContext.CreateDatabase()
   at System.Data.Entity.Migrations.Utilities.DatabaseCreator.Create(DbConnection connection)
   at System.Data.Entity.Migrations.DbMigrator.EnsureDatabaseExists(Action mustSucceedToKeepDatabase)
   at System.Data.Entity.Migrations.Infrastructure.MigratorBase.EnsureDatabaseExists(Action mustSucceedToKeepDatabase)
   at System.Data.Entity.Migrations.DbMigrator.Update(String targetMigration)
   at System.Data.Entity.Migrations.Infrastructure.MigratorBase.Update(String targetMigration)
   at System.Data.Entity.Migrations.Design.ToolingFacade.UpdateRunner.RunCore()
   at System.Data.Entity.Migrations.Design.ToolingFacade.BaseRunner.Run()
ClientConnectionId:00000000-0000-0000-0000-000000000000
Error Number:2,State:0,Class:20
A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server)

EDIT: My connection string is this:

  <connectionStrings>
    <add name="BlogDbContext" connectionString="server=localhost;database=consoledb;uid=root; password=MyPassword" providerName="System.Data.SqlClient" />
  </connectionStrings>

EDIT #2: As many of you have pointed out to me, I wasn't using the correct provider in my App.config file. I've changed my connection string to this:

  <connectionStrings>
    <add name="BlogDbContext" connectionString="server=127.0.0.1;port=3306;database=consoledb;uid=root; password=MyPassword" providerName="MySql.Data.MySqlClient" />
  </connectionStrings>
<providers>
  <provider invariantName="MySql.Data.MySqlClient" type="MySql.Data.MySqlClient.MySqlProviderServices, MySql.Data.Entity.EF6, Version=6.10.8.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d">
  </provider>
</providers>

But I'm now receiving the following error:

System.Data.Entity.Core.ProviderIncompatibleException: An error occurred accessing the database. This usually means that the connection to the database failed. Check that the connection string is correct and that the appropriate DbContext constructor is being used to specify it or find it in the application's config file. See http://go.microsoft.com/fwlink/?LinkId=386386 for information on DbContext and connections. See the inner exception for details of the failure. ---> System.Data.Entity.Core.ProviderIncompatibleException: The provider did not return a ProviderManifestToken string. ---> System.MethodAccessException: Attempt by method 'MySql.Data.MySqlClient.MySqlProviderServices.GetDbProviderManifestToken(System.Data.Common.DbConnection)' to access method 'MySql.Data.MySqlClient.MySqlConnection.get_Settings()' failed.
   at MySql.Data.MySqlClient.MySqlProviderServices.GetDbProviderManifestToken(DbConnection connection)
   at System.Data.Entity.Core.Common.DbProviderServices.GetProviderManifestToken(DbConnection connection)
   --- End of inner exception stack trace ---
   at System.Data.Entity.Core.Common.DbProviderServices.GetProviderManifestToken(DbConnection connection)
   at System.Data.Entity.Utilities.DbProviderServicesExtensions.GetProviderManifestTokenChecked(DbProviderServices providerServices, DbConnection connection)
   --- End of inner exception stack trace ---
   at System.Data.Entity.Utilities.DbProviderServicesExtensions.GetProviderManifestTokenChecked(DbProviderServices providerServices, DbConnection connection)
   at System.Data.Entity.Infrastructure.DefaultManifestTokenResolver.<>c__DisplayClass1.<ResolveManifestToken>b__0(Tuple`3 k)
   at System.Collections.Concurrent.ConcurrentDictionary`2.GetOrAdd(TKey key, Func`2 valueFactory)
   at System.Data.Entity.Infrastructure.DefaultManifestTokenResolver.ResolveManifestToken(DbConnection connection)
   at System.Data.Entity.Utilities.DbConnectionExtensions.GetProviderInfo(DbConnection connection, DbProviderManifest& providerManifest)
   at System.Data.Entity.DbModelBuilder.Build(DbConnection providerConnection)
   at System.Data.Entity.Internal.LazyInternalContext.CreateModel(LazyInternalContext internalContext)
   at System.Data.Entity.Internal.RetryLazy`2.GetValue(TInput input)
   at System.Data.Entity.Internal.LazyInternalContext.InitializeContext()
   at System.Data.Entity.Internal.LazyInternalContext.get_ModelBeingInitialized()
   at System.Data.Entity.Infrastructure.EdmxWriter.WriteEdmx(DbContext context, XmlWriter writer)
   at System.Data.Entity.Utilities.DbContextExtensions.<>c__DisplayClass1.<GetModel>b__0(XmlWriter w)
   at System.Data.Entity.Utilities.DbContextExtensions.GetModel(Action`1 writeXml)
   at System.Data.Entity.Utilities.DbContextExtensions.GetModel(DbContext context)
   at System.Data.Entity.Migrations.DbMigrator..ctor(DbMigrationsConfiguration configuration, DbContext usersContext, DatabaseExistenceState existenceState, Boolean calledByCreateDatabase)
   at System.Data.Entity.Migrations.DbMigrator..ctor(DbMigrationsConfiguration configuration)
   at System.Data.Entity.Migrations.Design.MigrationScaffolder..ctor(DbMigrationsConfiguration migrationsConfiguration)
   at System.Data.Entity.Migrations.Design.ToolingFacade.ScaffoldRunner.RunCore()
   at System.Data.Entity.Migrations.Design.ToolingFacade.BaseRunner.Run()

I've checked my connection string and everything seems fine. The name of the connection is the same as my DbContext class so it should be using its default constructor.

public class BlogDbContext : DbContext
{
    public DbSet<Post> Posts { get; set; }

    public BlogDbContext() : base()
    {

    }
}

The error is occurring because your program is trying to use the SqlClient library (for MS SQL Server) to connect to MySQL, which isn't supported.

As per the documentation, specify the MySQL provider in your connection string:

<connectionStrings>
  <add name="BlogDbContext" connectionString="..." providerName="MySql.Data.MySqlClient" />
</connectionStrings>

That is, change providerName="System.Data.SqlClient" to providerName="MySql.Data.MySqlClient".